text:
User:EGM6341.s10.Team1.toddmock/HW7

= Problem 1: Linearization about xmax =

Given
We are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle f(x)=rx(1-\dfrac{x}{x_{max}})
 * }.
 * }.

and

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x=\hat{x}+y
 * }.
 * }.

where

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \hat{x}=x_{max}
 * }.
 * }.

Find
Need to find the growth equation $$\dfrac{dy}{dt}$$

Solution
Using the above relations we have that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle f(x)=r(x_{max}+y)(1-\dfrac{x_{max}+y}{x_{max}})
 * }.
 * }.

canceling out some terms leads to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle r(x_{max}+y)(1-1-\dfrac{y}{x_{max}})
 * }.
 * }.

If we continue on algebraic manipulation we have

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -r(x_{max}+y)(\dfrac{y}{x_{max}})
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -r(y+\dfrac{y^2}{x_{max}})
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -ry(1+\dfrac{y}{x_{max}})
 * }.
 * }.

Thus we then can approximate

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dfrac{dy}{dt}=-ry
 * }.
 * }.

which can then lead to the exponential relation

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:38, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y=y_0e^{-rt}
 * }.
 * }.

= Problem 2: Verification of differential equation =

Given
We know that the rate of change is given as:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dot{x}=rx(1-\frac{x}{x_{max}})
 * }.
 * }.

Find
Need to solve the differential equation to come up with a relation for x(t)

Solution
From separation of variables we can go from the original equation

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dot{x}=\frac{dx}{dt}=rx(1-\frac{x}{x_{max}})
 * }.
 * }.

to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \int_{x_0}^{x}\frac{x_{max}}{x(x_{max}-x)}dx=\int_{t_0}^{t}rdt
 * }.
 * }.

we can separate this into fractions to solve it and we obtain

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \frac{1}{x(1-\frac{1}{x_{max}}x)}=\frac{a}{x}+\frac{b}{1-\frac{1}{x_{max}}x}
 * }.
 * }.

from here we must determine the coefficients a and b. To do this we rearrange to get

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \frac{a-\frac{a}{x_{max}}x+bx}{x(1-\frac{1}{x_{max}}x)}
 * }.
 * }.

combining like terms and setting this equation equal to 1 we get

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x(b-\frac{a}{x_{max}})+a=1
 * }.
 * }.

right away we can see that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle a=1
 * }.
 * }.

and

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle b-\frac{1}{x_{max}}=0, b=\frac{1}{x_{max}}
 * }.
 * }.

Thus giving the integral

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \int_{x_0}^{x}\frac{1}{x}dx+\int_{x_0}^{x}\frac{1}{(x_{max}-x)}dx=\int_{t_0}^{t}rdt
 * }.
 * }.

evaluation of the integral leads to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle ln(\frac{x}{x_0})-ln(\frac{x_{max}-x}{x_{max}-x_0})= rt
 * }.
 * }.

which then gives upon rearranging

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x(t)=\frac{x_{max}x_0e^{rt}}{x_{max}+x_0(e^{rt}-1)}
 * }.
 * }.

= Problem 10: Verification of elliptical equation =

Given
From [[media:Egm6341.s10.mtg42.djvu|42-1]] we are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x=aCos(t)
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y=bSin(t)
 * }.
 * }.

Find
We are tasked with showing that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \qquad\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1
 * }.
 * }.

Solution
if we square both the x and y terms from above we obtain

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x^2=a^2Cos^2(t)
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y^2=b^2Sin^2(t)
 * }.
 * }.

Using the trigonometric relation

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle Cos^2(t)+Sin^2(t)=1
 * }.
 * }.

we can see that by cancelation of the a and b terms in

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dfrac{a^2Cos^2(t)}{a^2}+\dfrac{b^2Sin^2(t)}{b^2}
 * }.
 * }.

will indeed yield the result that we are looking for

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \qquad\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1
 * }.
 * }.

= Problem 11: Eccentricity and differential arc length =

Given
From [[media:Egm6341.s10.mtg42.djvu|42-2]] we are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl= \sqrt{dx^2+dy^2}
 * }.
 * }.

and the Eccentricity is

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=[1-\dfrac{b^2}{a^2}]^{1/2}
 * }.
 * }.

Find
We are to show both of these relations are true

Solution
For the differential arc length shown below

 * {| style="width:100%" border="0" align="left"

 * [[Image:elly.png]]
 * }.
 * }.
 * }.

we can use simple geometric relations specifically the Pythagorean

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl^2= {dx^2+dy^2}
 * }.
 * }.

which then gives

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl= \sqrt{dx^2+dy^2}
 * }.
 * }.

For the eccentricity consider the next figure

 * {| style="width:100%" border="0" align="left"

 * [[Image:elly2.png]]
 * }.
 * }.
 * }.

The eccentricity is defined as the fraction of the distance c (the center to the focus) to the major axis a:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=\dfrac{c}{a}
 * }.
 * }.

It is known that the sum of the distance from one focus to the edge of the ellipse and from that same edge to the other focus is equal to 2a:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle |(f1) b| + |(f2) b| = 2a
 * }.
 * }.

Since the two lines were chosen to intersect at the y axis at point (b,0) then we know for sure that the line segments are equal to each other i.e. both are equal to major axis a. Therefore the determination of c becomes a simple geometry problem in which:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle c^2=a^2-b^2
 * }.
 * }.

of

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle c=\sqrt{a^2-b^2}
 * }.
 * }.

Therefore using the above definition of eccentricity

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=\dfrac{\sqrt{a^2-b^2}}{a}
 * }.
 * }.

which is the same as

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=[1-\dfrac{b^2}{a^2}]^{1/2}
 * }.
 * }.

title: User:EGM6341.s10.Team1.toddmock/HW7


text: File:Elly.png

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: File:Elly.png


title: File:Elly2.png


text:
User:Egm6341.s2010.Team1/HW7

= Problem 1: Linearization about xmax =

Given
We are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle f(x)=rx(1-\dfrac{x}{x_{max}})
 * }.
 * }.

and

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x=\hat{x}+y
 * }.
 * }.

where

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \hat{x}=x_{max}
 * }.
 * }.

Find
Need to find the growth equation $$\dfrac{dy}{dt}$$

Solution
Using the above relations we have that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle f(x)=r(x_{max}+y)(1-\dfrac{x_{max}+y}{x_{max}})
 * }.
 * }.

canceling out some terms leads to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle r(x_{max}+y)(1-1-\dfrac{y}{x_{max}})
 * }.
 * }.

If we continue on algebraic manipulation we have

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -r(x_{max}+y)(\dfrac{y}{x_{max}})
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -r(y+\dfrac{y^2}{x_{max}})
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle -ry(1+\dfrac{y}{x_{max}})
 * }.
 * }.

Thus we then can approximate

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dfrac{dy}{dt}=-ry
 * }.
 * }.

which can then lead to the exponential relation

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:38, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y=y_0e^{-rt}
 * }.
 * }.

= Problem 2: Verification of differential equation =

Given
We know that the rate of change is given as:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dot{x}=rx(1-\frac{x}{x_{max}})
 * }.
 * }.

Find
Need to solve the differential equation to come up with a relation for x(t)

Solution
From separation of variables we can go from the original equation

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dot{x}=\frac{dx}{dt}=rx(1-\frac{x}{x_{max}})
 * }.
 * }.

to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \int_{x_0}^{x}\frac{x_{max}}{x(x_{max}-x)}dx=\int_{t_0}^{t}rdt
 * }.
 * }.

we can separate this into fractions to solve it and we obtain

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \frac{1}{x(1-\frac{1}{x_{max}}x)}=\frac{a}{x}+\frac{b}{1-\frac{1}{x_{max}}x}
 * }.
 * }.

from here we must determine the coefficients a and b. To do this we rearrange to get

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \frac{a-\frac{a}{x_{max}}x+bx}{x(1-\frac{1}{x_{max}}x)}
 * }.
 * }.

combining like terms and setting this equation equal to 1 we get

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x(b-\frac{a}{x_{max}})+a=1
 * }.
 * }.

right away we can see that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle a=1
 * }.
 * }.

and

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle b-\frac{1}{x_{max}}=0, b=\frac{1}{x_{max}}
 * }.
 * }.

Thus giving the integral

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \int_{x_0}^{x}\frac{1}{x}dx+\int_{x_0}^{x}\frac{1}{(x_{max}-x)}dx=\int_{t_0}^{t}rdt
 * }.
 * }.

evaluation of the integral leads to

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle ln(\frac{x}{x_0})-ln(\frac{x_{max}-x}{x_{max}-x_0})= rt
 * }.
 * }.

which then gives upon rearranging

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x(t)=\frac{x_{max}x_0e^{rt}}{x_{max}+x_0(e^{rt}-1)}
 * }.
 * }.

= Problem 3: Hermite-Simpson Algorithm to integrate Verhulst equation =

Find
Use Hermite-Simpson rule to integrate the above given Verhulst equation

Given
Refer Lecture slide (1) [[media:Egm6341.s10.mtg38.djvu|p.38-3]]

$$ f(x)=rx (1-\frac {x}{x_{max}}) $$

$$ x_{max}=10\,$$

$$ r=1.2 \,$$

2cases:

$$ x_{0}=2 <\frac {1}{2}x_{max} $$

$$ x_{0}=7 >\frac {1}{2}x_{max} $$

Such that $$ AbsTol= O(10^{-6})\, $$ for $$ t \isin [0,10]$$

Solution
For the first case:

$$ x_{0}=2 \, $$

Matlab Code:

---

For the second case:

$$ x_{0}=7 \, $$

Matlab Code:

Solved by :Egm6341.s10.team1.lei03:52, 23 April 2010 (UTC)

= Problem 4: Reproduce the Chaotic System of Population Dynamics =

Problem Statement
Reproduce Figure 15.6 and 15.7 in "Differential equations : linear, nonlinear, ordinary, partial " on page 455-456

Ref: Lecture Notes [[media:Egm6341.s10.mtg40.djvu|p.40-1]]

Solution
(1) Figure 15.6 Copy the code directly from the book (2) Figure 15.7 Change initial conditions from random to 0.1 and 0.1+10e-16 at r=4

- EGM6341.s10.Team1.Ya-Chiao Chang 18:08, 21 April 2010 (UTC)

=Problem 5: Determine the limit on the step size in the Hermite-Simpson method, Forward Euler, Backward Euler=

Statement
Hermite-Simpson algorithm was used to find $$\hat{h}=0.125$$ to give an error of order $$10^{-6}$$ from the true value where $$\hat{h}$$ is the step size between nodes in the numerical solution. The function to be integrated was the population logistic equation,

 * $$\dot{x}=rx\left ( 1-\frac{x}{x_{max}} \right )$$

The numerical integration using the Hermite-Simpson algorithm was compared to the true value for x,

 * $$x\left ( t \right )=\frac{x_0x_{max}e^{rt}}{x_{max}+x_0\left ( e^{rt}-1 \right )}$$

For this problem, the step size is increased at a rate of $$h_{new}=2^k\hat{h}$$ where $$k=1,2,3,...$$

Solution
The differential equation is first integrated using ODE45 (at MATLAB command).

Next the Hermite-Simpson algorithm is run using increasing values of step size. The max step size is limited by the size of the interval $$t\in [0,10]$$. The step size maxes out at 8. A step size of 16 is not allowed. Therefore this algorithm is stable at integrating this function.

Next the Forward Euler integration is used. The step size maxes at 2 at which point it wildly oscillates about $$x_{max}=10$$

Finally, backward Euler integration is used. The step size is allowed to go to 8 so it is stable like the Hermite-Simpson algorithm. Notice, though, that the answer is less accurate for the same number of steps compared to the Hermite-Simpson method

EGM6341.s10.Team1.Kumanchik 20:15, 23 April 2010 (UTC)

=Problem 6: Interceptor Simulation using Hermite-Simpson algorithm=

Statement
Use the Hermite-Simpson algorithm to determine the trajectory of an interceptor given the following inputs.

 * $$T(t)=\left\{\begin{matrix}

6000 N, & 0\leq t< 27, & 33\leq t\leq 40\\ 1000 N, & 27\leq t< 33 & \end{matrix}\right.$$

 * $$\alpha(t)=\left\{\begin{matrix}

0.03 rad & 0\leq t< 21\\ \frac{0.13-0.09}{27-21}(t-21)+0.09 rad & 21\leq t< 27\\ \frac{-0.2+0.13}{33-27}(t-27)-0.13 rad & 27\leq t< 33\\ \frac{-0.13+0.2}{40-33}(t-33)-0.2 rad & 33\leq t\leq 40 \end{matrix}\right.$$

 * $$\mathbf{f}=

\begin{bmatrix} \dot{\gamma}\\ \dot{v}\\ \dot{x}\\ \dot{y} \end{bmatrix}=\begin{bmatrix} \frac{T-D}{mv}sin(\alpha)+\frac{L}{mv}cos(\alpha)-\frac{g}{v}cos(\gamma)\\ \frac{T-D}{m}cos(\alpha)+\frac{L}{m}sin(\alpha)-gsin(\gamma)\\ vcos(\gamma)\\ vsin(\gamma) \end{bmatrix}$$

 * $$\mathbf{z}=\begin{bmatrix}

\gamma\\ v\\ x\\ y \end{bmatrix}$$

 * $$DL=\left\{\begin{matrix}

D(\alpha,v,y)=0.5C_d\rho v^2S_{ref}\\ L(\alpha,v,y)=0.5C_c\rho v^2S_{ref} \end{matrix}\right. $$

 * $$\left\{\begin{matrix}

C_d(\alpha)=A_1\alpha^2+A_2\alpha+A_3\\ C_l(\alpha)=B_1\alpha+B_2\\ \rho(y)=C_1y^2+C_2y+C_3 \end{matrix}\right.$$

 * $$\left\{\begin{matrix}

m=1005 kg\\ g=9.81 \frac{m}{s^2}\\ S_{ref}=0.3376 m^2\\ A_1=-1.9431\\ A_2=-0.1499\\ A_3=0.2359\\ B_1=21.9\\ B_2=0\\ C_1=3.312e^{-9} \frac{kg}{m^5}\\ C_2=-1.142e^{-4} \frac{kg}{m^4}\\ C_3=1.224 \frac{kg}{m^3} \end{matrix}\right.$$

 * $$t\in [0,40]$$ seconds
 * $$h=1$$ seconds

Solution
The control inputs are the thrust, T, and the angle of attack, $$\alpha$$. They are plotted below.

The Hermite-Simpson algorithm takes the solution to a differential equation and subdivides it into nodes. Each node is related to the next by,

 * $$z_{i+1}=z_{i}+\frac{h}{6}\left [ f_i+4f_{i+\frac{1}{2}}+f_{i+1} \right ]$$
 * $$z_{i+\frac{1}{2}}=\frac{1}{2}\left [ z_i+z_{i+1} \right ]+\frac{h}{8}\left [ f_i-f_{i+1} \right ]$$

However, this equation is dependent on the $$z_{i+1} \,$$ node which appears in the $$f_{i+1} \,$$ and $$f_{i+\frac{1}{2}}$$ terms. Therefore, the equation is solved for by the Newton Raphson method,

 * $$F=-z_{i+1}+z_{i}+\frac{h}{6}\left [ f_i+4f_{i+\frac{1}{2}}+f_{i+1} \right ]=0$$

Intelligently choosing values for $$z_{i+1} \,$$ allows $$F \,$$ to approach 0. The intelligent algorithm is,

 * $$z^{(k+1)}=z^{(k)}-\frac{dF(z^{(k)})}{dz}^{-1}F(z^{(k)})$$

where $$k $$ is the previous guess and $$k+1$$ is the next guess. This algorithm can search for $$z_{i+1}$$ by starting with $$z^{k}=z_i$$. Using $$F$$ as a metric, the algorithm can stop when $$F\approx0$$ or for this problem we choose $$F$$ of $$O(10^{-9})$$.

This solution can be extended to this interceptor problem which solves a system of differential equations. Placing the differential equations in matrix form, the solution remains identical. Keep in mind that the differential of a matrix is the Jacobian. The result of the interceptor problem is plotted below. The time step is 1 second between 0 and 40 seconds.

The source code of the interceptor algorithm

Thrust and angle functions (control variables)

EGM6341.s10.Team1.Kumanchik 22:55, 23 April 2010 (UTC) =Problem 7: Integrate the logistic equation using an inconsistent trapezoidal-Simpson algorithm=

Statement
Integrate the logistic equation,
 * $$\dot{x}=rx\left ( 1-\frac{x}{x_{max}} \right )$$

Using the Hermite-Simpson algorithm and the inconsistent Trapezoidal-Simpson algorithm, compare their errors for the same step size, $$h=0.125$$. Both methods require the Newton-Raphson method so use a error for each node of $$O(10^{-9})$$. Compare the integrations to the true integral of the logistic equation,
 * $$x\left ( t \right )=\frac{x_0x_{max}e^{rt}}{x_{max}+x_0\left ( e^{rt}-1 \right )}$$

Solution
The Hermite-Simpson algorithm was adjusted to create the inconsistent trapezoidal-Simpson algorithm. Both solutions were subtracted from the true solution. The error in the Hermite-Simpson algorithm was designed from problem 5 as less than $$O(10^{-6})$$. Using the same parameters on the inconsistent trapezoidal-Simpson algorithm yields worse error by about 3 orders of magnitude. The errors from the true value are plotted below. The line on the bottom is the Hermite-Simpson error. It is much smaller than the inconsistent trapezoidal-Simpson error.

EGM6341.s10.Team1.Kumanchik 20:15, 23 April 2010 (UTC)

= Problem 8: Solve Logistic Equation by Using Inconsistent Trap-Simpson Algorithm =

Problem Statement
Compare with Hermite-Simpson results using same value of h Ref: Lecture Notes [[media:Egm6341.s10.mtg41.djvu|p.41-3]] [[media:Egm6341.s10.mtg39.djvu|p.39-1]]

Solution
Inconsistent Trap-Simpson Algorithm Matlab code change from $$ x_{\frac{1}{2}} = \!\,\frac{1}{2}*[x(i)+x(i+1)]+\frac{h}{8}*(f_1-f_2)$$ to $$ x_{\frac{1}{2}} = \!\,\frac{1}{2}*[x(i)+x(i+1)]$$

(1) initial condition is $$x_0 = \!\, 2 $$

- (2) initial condition is $$x_0 = \!\, 7 $$

II Compare with Problem 3-Hermite-Simpson Algorithm to integrate Verhulst equation the reslt is pretty much the same EGM6341.s10.Team1.Ya-Chiao Chang 19:13, 23 April 2010 (UTC)

=Problem 9: Show that CD = AB plus H.O.T. for a small change in gamma=

Find
Verify that $$ \bar{CD} = \bar{AB} + H.O.T. \,$$ for small $$ d\gamma \,$$ and determine what the higher-order terms are.

Solution
$$ tan(d\gamma)=\frac{\bar{AB}}{V} \Rightarrow \bar{AB}=Vtan(d\gamma) \,$$ $$ sin(d\gamma)=\frac{\bar{CD}}{V+dV} \Rightarrow \bar{CD}=(V+dv)sin(d\gamma) \,$$ $$ \bar{CD} = \bar{AB} + (V+dv)sin(d\gamma) - Vtan(d\gamma) \,$$ Both $$ sin(x)\,$$ ≈ $$ x \,$$ and $$ tan(x) \,$$ ≈ $$ x \,$$ when x is small, thus $$ \bar{CD} \,$$ ≈ $$ \bar{AB} + (V+dV)d\gamma - V{d\gamma} \,$$

To determine what the higher-order terms are, use Taylor series expansions. $$ sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ... \,$$ $$ tan(x) = x + \frac{x^3}{3} + \frac{2x^5}{15} + \frac{17x^7}{315} + ... \,$$

Egm6341.s10.team1.andrewdugan 07:42, 23 April 2010 (UTC)

= Problem 10: Verification of elliptical equation =

Given
From [[media:Egm6341.s10.mtg42.djvu|42-1]] we are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x=aCos(t)
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y=bSin(t)
 * }.
 * }.

Find
We are tasked with showing that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \qquad\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1
 * }.
 * }.

Solution
if we square both the x and y terms from above we obtain

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x^2=a^2Cos^2(t)
 * }.
 * }.

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle y^2=b^2Sin^2(t)
 * }.
 * }.

Using the trigonometric relation

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle Cos^2(t)+Sin^2(t)=1
 * }.
 * }.

we can see that by cancelation of the a and b terms in

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \dfrac{a^2Cos^2(t)}{a^2}+\dfrac{b^2Sin^2(t)}{b^2}
 * }.
 * }.

will indeed yield the result that we are looking for

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle \qquad\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1
 * }.
 * }.

= Problem 11: Eccentricity and differential arc length =

Given
From [[media:Egm6341.s10.mtg42.djvu|42-2]] we are given that

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl= \sqrt{dx^2+dy^2}
 * }.
 * }.

and the Eccentricity is

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=[1-\dfrac{b^2}{a^2}]^{1/2}
 * }.
 * }.

Find
We are to show both of these relations are true

Solution
For the differential arc length shown below

 * {| style="width:100%" border="0" align="left"

 * [[Image:elly.png]]
 * }.
 * }.
 * }.

we can use simple geometric relations specifically the Pythagorean

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl^2= {dx^2+dy^2}
 * }.
 * }.

which then gives

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle dl= \sqrt{dx^2+dy^2}
 * }.
 * }.

For the eccentricity consider the next figure

 * {| style="width:100%" border="0" align="left"

 * [[Image:elly2.png]]
 * }.
 * }.
 * }.

The eccentricity is defined as the fraction of the distance c (the center to the focus) to the major axis a:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=\dfrac{c}{a}
 * }.
 * }.

It is known that the sum of the distance from one focus to the edge of the ellipse and from that same edge to the other focus is equal to 2a (Stewart, James. Calculus . Pacific Grove : Brooks/Cole publishing company, 1999. 0534359493):

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle |(f1) b| + |(f2) b| = 2a
 * }.
 * }.

Since the two lines were chosen to intersect at the y axis at point (b,0) then we know for sure that the line segments are equal to each other i.e. both are equal to major axis a. Therefore the determination of c becomes a simple geometry problem in which:

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle c^2=a^2-b^2
 * }.
 * }.

of

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle c=\sqrt{a^2-b^2}
 * }.
 * }.

Therefore using the above definition of eccentricity

 * {| style="width:100%" border="0" align="left"

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=\dfrac{\sqrt{a^2-b^2}}{a}
 * }.
 * }.

which is the same as

 * {| style="width:100%" border="0" align="left"

$$ $$ Egm6341.s10.team1.toddmock 23:39, 20 April 2010 (UTC)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle e=[1-\dfrac{b^2}{a^2}]^{1/2}
 * }.
 * }.

=Problem 12: Verify the expression for the circumference of an ellipse=

Given
The arc length of an ellipse is $$ dl = [dx^2+dy^2]^\frac{1}{2} \,$$. $$ x = acost \,$$ $$ y = bsint \,$$ The eccentricity $$ e \,$$ is defined as $$ e = [1-\frac{b^2}{a^2}]^\frac{1}{2} \,$$.

Find
Verify that $$ C = \int{dl}=a\int_{t=0}^{2\pi}[1-e^2cos^2t]^\frac{1}{2}dt \,$$.

Solution
$$ dx = \frac{d}{dt}[acost]=-asint \,$$ $$ dy = \frac{d}{dt}[bsint]=bcost \,$$ $$ C = \int{dl}=\int_{t=0}^{2\pi}[(-asint)^2+(bcost)^2]^\frac{1}{2}dt=\int_{t=0}^{2\pi}[a^2sin^2t+b^2cos^2t]^\frac{1}{2}dt \,$$ $$ C = a\int_{t=0}^{2\pi}[sin^2+\frac{b^2}{a^2}cos^2t]^\frac{1}{2}dt \,$$, and since $$ sin^2t+cos^2t=1 \,$$, $$ C = a\int_{t=0}^{2\pi}[1-cos^2t+\frac{b^2}{a^2}cos^2t]^\frac{1}{2}dt=a\int_{t=0}^{2\pi}[1-(1-\frac{b^2}{a^2})cos^2t]^\frac{1}{2}dt \,$$

Egm6341.s10.team1.andrewdugan 05:23, 23 April 2010 (UTC)

= Problem 13: Use $$\alpha$$ As A Differential Variable to Calculate the Circumference of Ellipse =

Problem Statement
We already have $$C= \!\,\int dl \!\,= \!\,a\int_{t=0}^{2 \pi}[1-e^2cos^2t]^\frac{1}{2}dt$$ What if we change the differential variable from t to $$\alpha$$ Ref: Lecture Notes [[media:Egm6341.s10.mtg42.djvu|p.42-2]]

Solution

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = 4*\!\,[dx^2+dy^2]^\frac{1}{2} $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

x = \!\,asin(\alpha), y = \!\,bcos(\alpha) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

dx = \!\,acos(\alpha)d\alpha, dy = \!\,-bsin(\alpha)d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

dx^2 = \!\,a^2cos^2(\alpha)(d\alpha)^2, dy^2 = \!\,b^2sin^2(\alpha)(d\alpha)^2 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[a^2cos^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[a^2cos^2(\alpha)+a^2sin^2(\alpha)-a^2sin^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[\underbrace{(a^2cos^2(\alpha)+a^2sin^2(\alpha))}_{a^2}-a^2sin^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = \!\,4*a*[1-\underbrace{(1-(\frac{b}{a})^2)}_{e^2}sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = \!\,4a[1-e^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$ - $$C = \!\,\int_{o}^{\pi/2}dl = \!\,4a[1-e^2sin^2(\alpha)]^\frac{1}{2}d\alpha$$ - EGM6341.s10.Team1.Ya-Chiao Chang 18:09, 21 April 2010 (UTC)
 * $$ \displaystyle
 * $$ \displaystyle
 * }

=Problem 14: Verify the change of variables expression for I in Clenshaw-Curtis quadrature=

Given
Clenshaw-Curtis quadrature utilizes the change of variables of $$ x=cos\theta \,$$. Before the change of variables, $$ I = \int_{-1}^{+1}f(x)dx \,$$.

Find
Verify that $$ I = \int_{0}^{\pi}f(cos\theta)sin{\theta}d\theta \,$$.

Solution
$$ I = \int_{-1}^{+1}f(x)dx \,$$ $$ f(x)=f(cos\theta) \,$$ $$ dx = \frac{d}{dx}(cos\theta) = -sin{\theta}d\theta \,$$ $$ sin^{-1}(-1)=\pi \,$$ thus, lower limit $$ -1 \Rightarrow \pi \,$$ $$ sin^{-1}(1)=0 \,$$ thus, lower limit $$ 1 \Rightarrow 0 \,$$ $$ I = \int_{\pi}^{0}f(cos\theta)(-sin{\theta}d\theta) \,$$

Egm6341.s10.team1.andrewdugan 05:25, 23 April 2010 (UTC)

= Problem 16: Find the Cosine Series coeffient ak =

Find
Find

$$ a_{k}=\frac {2}{\pi}\int_{0}^{\pi}f(\cos \theta) \cos (k \theta)d \theta $$

Given
We know Fourier Cosine Series:

$$ f(\cos\theta)=\frac{a_{0}}{2}+\sum _{k=1}^{\infin} a_{k}\cos (k\theta) $$

Solution
$$ a_{0}=\frac{1}{\pi}\int _{-\pi}^{\pi} f(\cos\theta)d\theta $$

$$ =\frac{2}{\pi}\int _{0}^{\pi} f(\cos\theta)d\theta $$

$$ a_{n}=\frac{1}{\pi}\int _{-\pi}^{\pi} f(\cos\theta)\cos(k\theta) d\theta $$

$$ =\frac{2}{\pi}\int _{0}^{\pi} f(\cos\theta) cos(k\theta)d\theta $$

Solved by :Egm6341.s10.team1.lei03:54, 23 April 2010 (UTC)

=Problem 17: Find int if cosine series is know =

Find
[[media:Egm6341.s10.mtg42.djvu|p.42-3]]

$$ I=a_{0}+\sum_{j=1}^{\infin} \frac{2a_{2j}}{1-(2j)^2} $$

Given
[[media:Egm6341.s10.mtg42.djvu|p.42-2]]

$$ I= \int_{-1}^{+1}f(x)dx= \int_{0}^{\pi} f(\cos\theta) \sin\theta d\theta\, $$

[[media:Egm6341.s10.mtg42.djvu|p.42-3]]

$$ f(\cos\theta)=\frac{a_{0}}{2}+\sum _{k=1}^{\infin} a_{k}\cos (k\theta) $$

Solution
$$ I=\int_{0}^{\pi}(\frac{a_{0}}{2}+\sum _{j=1}^{\infin}a_{2j}\cos(2j\theta))\sin\theta d\theta$$

$$ =\int_{0}^{\pi}\frac {a_{0}}{2}\sin\theta d\theta +\int_{0}^{\pi}\sum _{j=1}^{\infin}a_{2j}\cos(2j\theta)\sin\theta d\theta$$

$$ =-\frac{a_{0}}{2} \cos\theta |_{0}^{\pi}+ \sum _{j=1}^{\infin}\int_{0}^{\pi}a_{2j}\cos(2j\theta)\sin\theta d\theta$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j} \int_{0}^{\pi}\cos(2j\theta)\sin\theta d\theta$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j} \int_{0}^{\pi}-[\sin((2j+1)\theta)-\sin((2j-1)\theta)]d\theta $$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}[\int_{0}^{\pi}-\sin((2j+1)\theta)d\theta +\int_{0}^{\pi}\sin((2j-1)\theta)d\theta] $$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}[\frac{1}{2j+1} \cos(2j+1)\theta|_{0}^{\pi}-\frac{1}{2j-1} \cos(2j-1)\theta|_{0}^{\pi}]$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}\frac{2}{1-(2j)^{2}} $$

 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow I=a_{0}+\sum _{j=1}^{\infin}\frac{2a_{2j}}{1-(2j)^{2}} $$ $$
 * $$\displaystyle
 * }
 * }

Solved by :Egm6341.s10.team1.lei03:54, 23 April 2010 (UTC)

=Contributing Members= Egm6341.s10.team1.toddmock 23:47, 20 April 2010 (UTC) EGM6341.s10.Team1.Ya-Chiao Chang 18:10, 21 April 2010 (UTC) Egm6341.s10.team1.lei 03:55, 23 April 2010 (UTC) Author of Problems 3, 16 and 17 Egm6341.s10.team1.andrewdugan 07:44, 23 April 2010 (UTC) Author of Problems 9, 12 and 14 EGM6341.s10.Team1.Kumanchik 20:15, 23 April 2010 (UTC) Author of problems 5, 6, and 7

title: User:Egm6341.s2010.Team1/HW7


text: File:Student Notes.pdf

title: File:Student Notes.pdf


text:
Survey research and design in psychology/Lectures/ANOVA II

Outline
Explains use of ANOVA, including the design, assumptions, and interpretations for one-way ANOVA, one-way repeated measures ANOVA, factorial ANOVA, mixed-design ANOVA (SPANOVA), ANCOVA, and MANOVA.


text:
User:Anuttra

Hi. My name is Anuttra Settheewongsakun. Everyone calls me Annie. I graduated from TSIS and am currently studying TIM at Mahidol University. I'm doing the hospitality module.

Homework

Ans1) Cloud computing allowas us to share resources and information to different computers and other devices. In cloud computing after making a file of your work you can upload it on the internet due to tyhis software and everyone can get access to your file or information. Whereas in a normal computer your files cannot be downloaded by others and it cannot be shared publicly.

Ans2) Everyone has to has access to a software or a system to get to cloud computing first then only it is possible for class computing to take place in a classroom. Cloud computing also has many advantages if used in a classroom.They are: 1) teachers can keep track of the students work and have access to their work 2) all students has access to this system it makes it easier for students to learn something new from their classmates and they can also share ideas 3) it is also a great way of sharing knowledge with one another and also to know if you are on the right track or not

Social Networking Homework 1) The site i chose is Digg 2) I chose this site because its interesting and there are many news up there which interest you. The site is a social networking site and in this site we, common people can write articles and post it. The ones that has a lot of reader or is interesting will then be posted on the homepage of the site. It's a great way to learn and share knowledge. 3) My favorite site out of the 4 is obviously Digg, but if all over then its facebook because it is another site which makes it possible to communicate with many people.

What is the best smartphone operating system and why? ans) The best smatphone operating system is Symbian. This is because it has excellent browsing ability and the page didplayed looks like the original. The symbian ia also very adept at handling mail links and PDF"s.Taking and sending images is also very fast for Symbian. Moreover,emailing is also very easy.

The best PC available in the market When buying a Pc certain things have to be taken into account. Such as proccessor, harddrive, memory,optical drives,external connectors, monitors,etc. It is a choice between an AMD and an Intel processor. The difference is really between the number of cores and speed.Most desktop computers now use a type of memory called DDR3 and it is best to have atleast 4GB.The larger the drive and the faster, the better the performance and capacity.What good is a desktop PC unless it also has a monitor? Previously users would need to choose between a CRT or LCD monitor, but LCDs are pretty much the standard now because of their reduced size and power consumption.THe best PC is Gateway DX4840-02e. a 23-inch HD monitor a wide selection of ports, and because it's a Costco exclusive, you get a two-year warranty as well as Costco's concierge service. The desktop has a 640GB hard drive, so you'll have plenty of room to store digital photos and other multimedia files.All four memory banks are populated, but there's room for two additional hard drives and another optical drive (this model comes with a DVD burner installed in the upper bay). The 640GB hard drive provides ample storage for large multimedia files and comes with Windows 7 Home Premium (64-bit) and Nero 9 Essentials. The display delivers reasonably good viewing angle performance, good color quality, and reasonably equipped with DVI, HDMI, and VGA ports

title: User:Anuttra


text:
Survey research and design in psychology/Tutorials/ANOVA and qualitative analysis

Contents

 * 1) /Analysis of variance/
 * 2) /Qualitative analysis/


text:
Qualitative analysis/Data analysis tutorial

See Survey research and design in psychology/Tutorials/Qualitative analysis.


text:
User talk:Chaizaa

''Find the specs on the best PC on the face of the earth. ''

Motherboard: Gigabyte - GA-EX58-EXTREME

Processor: Intel® Core™Extreme i7-980X

Memory: OCZ 6GB. DDRIII-1333 3G1333

Case: ASUS - TA-250(Black)

Power Supply: Coolermaster - RS-550-ACLY

Hard drive: WESTERN DIGITAL WDBAAH0020HCH 2.0 TB My Book Studio WDBAAH0020HCH 2.0 TB Desktop USB 2.0 / Firewire

CD/DVD： LG BlueRay BH10LS30

Monitor: XL2370 SAMSUNG XL2370

Video Accelerator Card: ASUS EAH5870 V2 1 GB GDDR5 256 BIT 850/4800

Keyboard+Mouse: Logitech G9x & G35 & G13 & G19

Sound Card: Creative Int Sound Blaster X-FI Elite Pro Stereo Output : 116dB SNR quality- Control Box- 64MB of on-board X-RAM

''What is the best smart phone operating system? Why?''

In my opinion, the best smart phone operating system is Android because it is a open source whose all codes and information are open to the public. This allows anyone to copy, make changes, and modify parts or the whole software without violating the copyright agreement. Moreover, this makes open source software develop faster than any of the non-open source such as iOS, Palm WebOS, BlackBerry OS, because users themselves are the developers. No developers can understand the consumers better than the consumers themselves. Because all the information about the program on how it was built, modified etc. are shown to public. Everyone could re-write the whole or just part of the software as much as they feel like to.

Hello everybody!

My name is Kraipit Lertsiriworaphong. Student ID: 5180772 My nick name is Shine. My major is Social Science.

18. How can you add an item from the Frequently Used Program area to the Pinned Item area in Windows XP?

Right click on the program Frequently Used Program area and click "Pin to start menu" --Chaizaa 08:28, 7 May 2010 (UTC)

14. In Windows XP, what is the keyboard shortcut to copy a file?

Ctrl + C --Chaizaa 08:31, 7 May 2010 (UTC)

Assignment 2 "Social Networking"

What is the site you selected?

Digg

What is the site's purpose and why is it considered a web 2.0 site?

This site purpose is to let the users be able to share their content such as an article, music, picture etc. on the web. Users can give comments and talk to each other. Besides, what is voted by other users the most can be in the main page of the website. The reason this website is considered a web 2.0 site is because this website is a social-networking site where all the users can interact with each other.

What is your favorite website and why?

My favorite website is MOG. Even though it is said that all access is not available in Thailand yet, it looks like such a very useful place to discover a lot of new, unique music.

Assignment 1 "Cloud Computing"

How is cloud computing different than using a normal computer?
 * 1) Cloud computing needs Internet access while a normal computer does not require Internet access
 * 2) Users can access Cloud Computing anytime and anyplace while a normal computer cannot
 * 3) Users can share information and data via cloud computing while users cannot do that via a normal computer
 * 4) Information and data will never be gone in cloud computing while there are possibilities that information and data could be lost in a normal computer

How could you turn a classroom into a cloud computing classroom?
 * 1) Create a server for the classroom
 * 2) Set up a password for students to get access to software
 * 3) Every student sign up to have their own account
 * 4) Now students and teachers can share file together in the server that is created

Welcome
 Hello Chaizaa, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 16:13, 1 May 2010 (UTC)

title: User talk:Chaizaa


text:
User talk:Paphamat

Paphamat is my first name. but the name that everyone uses to call me is 'Birdie'. I'm majoring in Internaitonal Business at Mahidol University, International College. ...interested in travelling, singing, and having a happy life ^^.

, Birdie Paphamat 07:40, 21 April 2010 (UTC)

1st Assignment - 1)How is cloud computing different than using a normal computer? -data and information can be stored on the internet instead of the hardware, which allows users to keep as much data as they want there (on-demand). Apart from that, users can do different tasks in different software on the internet, which have faster processing system. Moreover, cloud computing allows users to access to the data anytime, anywhere with internet connection.

- 2)How could you turn a classroom into a cloud computing classroom? -for example, in wikiversity.org, students can post their homework, files or share ideas on the classroom's website, which is more comfortable that the old turn-in system. Friends can also edit friends' homeworks on the site, which saves a lot of time.

2nd Assignment(L) "What is the best smart phone operating system and why?"

- Different smart phone OS suits different lifestyles, wheather for business or entertainment use. However, personally, the best samrt phone operating system is iPhone OS. Because, iPhone has tons of application asd usage for you to choose, for example, gaming, music, calling, browsing the internet and thousands of application of your interest that easily be downloaded. Moreover, the drawback of iPhone Os that has been critisized; its non-multitasking application, will be soon out of concern since the Apple company is coming up with the new iPhone 4G, which allow users to use 'multitasking'. This new feature will even increase the ability of this operating system to be better than the other OSs.

-3rd Assignment: The best PC in the world = Apple iMac

* Processor = 2.8GHz Intel Core i7 (quad core) (which is the best processor) * Memory = 4GB (two 2GB SO-DIMMs) of 1066MHz DDR3 SDRAM; supports up to 16GB * Hard drive = 2TB Hard Drive * Keyboard = Apple Keyboard * Mouse = Apple Mouse * Monitor = 27-inch (viewable) LED-backlit glossy 16:9 widescreen TFT active-matrix display; 2560 by 1440 pixels; millions of colors; IPS technology * Video card = ATI Video Drivers for OS 9 & OS X or NVIDIA Video Drivers for OS 9 & OS X

Paphamat 15:46, 5 July 2010 (UTC)

Paphamat 09:18, 18 June 2010 (UTC)

title: User talk:Paphamat


text:
User talk:Micky95

Hello!!

I am Pitchaporn Tamkhun. Please call me Chompoo. My student ID is 5180687. I am in IB major.

See you guys in class. ^^

1st Homework

1. How is cloud computing different from using a normal computer? - Using cloud computing allows us to access information from the same resources by any computer and any time, i.e. Youtube and Google Document.

2. How could you turn a class room into a cloud computing classroom? - Put the information you want to share on a website like Wikiversity which allows all students to gain the same data. For example, a file which contains information is uploaded on a website by the teacher for students to download.

Copyright problem with File:12309 381950449599 807034599 3614376 7724981 n.jpg
10. How do you list a file in the My Recent Documents list in Windows XP? - Drag and Drop progarm you want to pinned item area Pitchaporn--Micky95 08:39, 7 May 2010 (UTC)

Image Tagging Image:DSC01784.JPG
Thanks for uploading Image:DSC01784.JPG. I notice the image page currently doesn't specify who created the content, so the copyright status is unclear. If you have not created this media yourself then you need to argue that we have the right to use the media on Wikimedia Commons (see copyright tagging below). If you have not created the media yourself then you should also specify where you found it, i.e., in most cases link to the website where you got it, and the terms of use for content from that page. If the content is a derivative of a copyrighted work, you need to supply the names and a licence of the original authors as well.

If the media also doesn't have a copyright tag, then you must also add one. If you created/took the picture, audio, or video then you can use to release it under the multilicense GFDL plus Creative Commons Attribution-ShareAlike All-version license or PD-self to release it into the public domain. See commons:Commons:Copyright tags for the full list of copyright tags that you can use.

Note that any unsourced and untagged images will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have uploaded other media, please check that you have specified their source and copyright tagged them, too. You can find all your uploads using the Gallery tool. Thank you. TeleComNasSprVen (discuss • contribs) 06:29, 15 March 2014 (UTC)

title: User talk:Micky95


text:
User talk:Jordanlin14

Hello! Mr.Brain! My name is Wei-min Lin. My nickname is Jordan. My Major is IB(International Business). This is my fourth tri-mester here in MUIC. I am looking forward to learn more about computer because i know computer is going to be one of the major effects in the future. Thank you very much and enjoy your day.

, Jordan Jordanlin14 07:51, 21 April 2010 (UTC)

[[File:jordanlin.jpg]

Second assignment: what is the best smart phone operating system and why? BlackBerry is the best smart phone operating system because it contains many convenient functions, which are E- mail, Corporate data, Instant messaging, Phone, internet and internet access, MMS and SMS, and organizer. Moreover, there are some newest models of blackberry smartphones such as camera and video recording, media player, and social networking. personally, one of the main function of a BlackBerry smartphone is the BBM system. The system allows people to be able to chat with each other with out spending a large amount of money, all they have to do is pay around 350 baht per month, then they are able to chat with friends and access to facebook, and e-mail. BBM is a system that can connect people together in this 21 century.

Wei-min Lin    Thank you very much and enjoy your day.

Jordanlin14 09:12, 18 June 2010 (UTC)

Third assignment:

What is the best PC spec? According from what i have researched, i think the best PC Spec is Apple's product call "IMAC"

* Processor = 2.8GHz Intel Core i7 (quad core) (which is the best processor) * Memory = 4GB (two 2GB SO-DIMMs) of 1066MHz DDR3 SDRAM; supports up to 16GB * Hard drive = 2TB Hard Drive * Keyboard = Apple Keyboard * Mouse = Apple Mouse * Monitor = 27-inch (viewable) LED-backlit glossy 16:9 widescreen TFT active-matrix display; 2560 by 1440 pixels; millions of colors; IPS technology * Video card = ATI Video Drivers for OS 9 & OS X or NVIDIA Video Drivers for OS 9 & OS X

This is the link: http://www.apple.com/imac/specs.html Wei-min LIN Thank you very much and enjoy your day~

Jordanlin14 15:53, 5 July 2010 (UTC)

title: User talk:Jordanlin14


text:
Instructional design/Force field analysis/How force field analysis is used?

Back to ID Homepage > ID force field analysis > What is force field analysis? > How force field analysis is presented in a figure? > How force field analysis is used?

Now you have basic concept of force field analysis and its representative figures, and you might start wondering about how force field analysis can be used in your organization. Generally force field analysis provides functions of
 * Reducing insufficient specification of variables,
 * Identifying strengths and weaknesses, and
 * Recognizing relation to larger system.

An Example of Using FFA as Motivation Techniques
This fragment of the interview conducted by Paul Grantham will provide you an example of how force field analysis is used in the field of psychological intervention.

Context: Talia is a 30 years old asylum seeker presenting with employment problems and low mood. Her motivation for addressing her problems is affected by repeated failure to obtain work. Paul Grantham, a consultant and a clinical psychologist, demonstrates how to bypass issues of resistance to help the client. In the clip, after having talked about factors driving Talia to seek more works, Paul Grantham tried to find out those factors decreasing Talia’s motivation of working. Obviously, he was using force field analysis to help create personal change on motivation. Now, try to relate this case to your working situation and think about:
 * Have you ever used any strategy similar to force field analysis before? If you have, what was the situation or problem you were encountering?
 * Is there any change happening in your organization that you think force field analysis might be an effective tool?

Summary
Now you are almost done with the lesson. The last task for you is to watch a summary video below which will help you review what you have learned during the lesson. In next lesson, you will learn a set of procedures of conducting a force field analysis.


title: File:PG2.jpg


text: File:Summary-yh.jpg

title: File:Summary-yh.jpg


text:
Cisco Networking/CCNA Voice

CCNA Voice - Cisco Certified Network Associate Voice

Prerequisite The ../CCNA/ certification is a prerequisite to the CCNA Voice certification.

Exams There are 2 paths to aquiring the CCNA Voice certification.

/640-460 IIUC/ - Implementing Cisco IOS Unified Communications. This exam is geared towards small to medium telephony installations using Cisco Unified Communications Manager Express, Cisco Unity Express, and the UC500 Smart Business Communications System solutions.

or

642-436 CVOICE - Cisco Voice over IP. This exam is geared towards a broader understanding of VOIP telephony and larger or enterprise telephony installations using dial plans, and the implementation of gateways, gatekeepers and IP-IP gateways.

CCNA Voice is a prerequisite to achieving the ../CCVP/ Cisco Certified Voice Professional certification.

title: Cisco Networking/CCNA Voice


text:
Cisco Networking/CCNA Voice/640-460 IIUC

640-460 IIUC - Implementing Cisco IOS Unified Communications. This exam is geared towards small to medium telephony installations using Cisco Unified Communications Manager Express, Cisco Unity Express, and the UC500 Smart Business Communications System solutions.


text:
Cisco Networking/CCNA Voice/642-436 CVoice

642-436 CVOICE - Cisco Voice over IP. This exam is geared towards a broader understanding of VOIP telephony and larger or enterprise telephony installations using dial plans, and the implementation of gateways, gatekeepers and IP-IP gateways.

This exam is one option for aquiring the CCNA Voice certification.

This exam is also a requirement for the CCVP certification.


text:
Cisco Networking/CCVP

CCVP Cisco Certified Voice Professional

title: Cisco Networking/CCVP


text:
User talk:SeanBob

 Hello SeanBob, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 13:41, 21 April 2010 (UTC)

title: User talk:SeanBob


text:
User:Rjorjorjo/HW7

HW 6 Problem Set  =Reprodace the Chaotic System of Population Dynamics=

Problem Statement
Reproduce Figure 15.6 and 15.7 in "Differential equations : linear, nonlinear, ordinary, partial " on page 455-456

Ref: Lecture Notes [[media:Egm6341.s10.mtg40.djvu|p.40-1]]

Solution
(1) Figure 15.6 Copy the code directly from the book (2) Figure 15.7 Change initial conditions from random to 0.1 and 0.1+10e-16 at r=4

=Use $$\alpha$$ As A Differential Variable to Calculate the Circumference of Ellipse=

Problem Statement
We already have $$C= \!\,\int dl \!\,= \!\,a\int_{t=0}^{2 \pi}[1-e^2cos^2t]^\frac{1}{2}dt$$ What if we change the differential variable from t to $$\alpha$$ Ref: Lecture Notes [[media:Egm6341.s10.mtg42.djvu|p.42-2]]

Solution

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = 4*\!\,[dx^2+dy^2]^\frac{1}{2} $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

x = \!\,asin(\alpha), y = \!\,bcos(\alpha) $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

dx = \!\,acos(\alpha)d\alpha, dy = \!\,-bsin(\alpha)d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

dx^2 = \!\,a^2cos^2(\alpha)(d\alpha)^2, dy^2 = \!\,b^2sin^2(\alpha)(d\alpha)^2 $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[a^2cos^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[a^2cos^2(\alpha)+a^2sin^2(\alpha)-a^2sin^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\, \int_{o}^{\pi/2}dl = \!\,4[\underbrace{(a^2cos^2(\alpha)+a^2sin^2(\alpha))}_{a^2}-a^2sin^2(\alpha)+b^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = \!\,4*a*[1-\underbrace{(1-(\frac{b}{a})^2)}_{e^2}sin^2(\alpha)]^\frac{1}{2}d\alpha $$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

 * {| style="width:100%" border="0" align="left"

C = \!\,\int_{o}^{\pi/2}dl = \!\,4a[1-e^2sin^2(\alpha)]^\frac{1}{2}d\alpha $$ - $$C = \!\,\int_{o}^{\pi/2}dl = \!\,4a[1-e^2sin^2(\alpha)]^\frac{1}{2}d\alpha$$
 * $$ \displaystyle
 * $$ \displaystyle
 * }

=Solve Logistic Equation by Using Inconsistent Trap-Simpson Algorithm=

Problem Statement
Compare with Hermite-Simpson results using same value of h Ref: Lecture Notes [[media:Egm6341.s10.mtg41.djvu|p.41-3]] [[media:Egm6341.s10.mtg39.djvu|p.39-1]]

Solution
Inconsistent Trap-Simpson Algorithm Matlab code change from $$ x_{\frac{1}{2}} = \!\,\frac{1}{2}*[x(i)+x(i+1)]+\frac{h}{8}*(f_1-f_2)$$ to $$ x_{\frac{1}{2}} = \!\,\frac{1}{2}*[x(i)+x(i+1)]$$

(1) initial condition is $$x_0 = \!\, 2 $$

- (2) initial condition is $$x_0 = \!\, 7 $$

II Compare with Problem 3-Hermite-Simpson Algorithm to integrate Verhulst equation the result is pretty much the same

title: User:Rjorjorjo/HW7


text:
Cisco Networking/CCNA

CCNA or Cisco Certified Network Associate is an associate level Cisco certification that lays the foundation of networking skills. It establishes a professional’s stature in the world of networking and validates that the professional is capable of working for the upkeep of enterprise level networks. The core CCNA certification is CCNA (Routing & Switching).

There is only one path to achieving CCNA certification; the 200-301 CCNA Exam

A complete list of Cisco Exams click here.

title: Cisco Networking/CCNA


text:
User talk:Thanabodi

My name is Thanabodi Chinwattanaporn and my ID number is 5180827. major:IB

title: User talk:Thanabodi


text: File:HW7 chaos fig15 6.pdf

title: File:HW7 chaos fig15 6.pdf


text: File:HW7 chaos fig15 6.jpg

title: File:HW7 chaos fig15 6.jpg


text: File:HW7 chaos fig15 7.jpg

title: File:HW7 chaos fig15 7.jpg


text:
User talk:Mongkhon

--Mongkhon 15:30, 21 April 2010 (UTC)my name is Mongkhon Chanwengchutichot. I'm 20 years old now. I have two sisters. i love to play all kinds of sports such as football, basketball, badminton. I love to hang around with my friends and we love to watch cinema also.

title: User talk:Mongkhon


text:
User talk:Wanwarang

--Wanwarang 15:31, 21 April 2010 (UTC) My name is Wanwarang Horpatraporn. My nick name is NN. My major is TIM. I learn in Mahidol for 3 terms. In the future, I want to have my own resort. When I have free time, I like to go out and watch movie with my friends.

Welcome
 Hello Wanwarang, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 20:12, 21 April 2010 (UTC)

page,you can look it up and you also can edit it.

title: User talk:Wanwarang


text:
User talk:Poon

Phutich Paisalsak (Poon) was born 28 August 1990, in Bangkok. I study in Mahidol University International College. This is my Fourth semester in Mahidol. Tourism Industry Management (TIM) is my major.

Cloud Computing

1.How is cloud computing different than using a normal computer?

Cloud computing is a technology that uses the internet as central share network. It also allows other users to access the network. Users can save as many works as they want on the network. These help them to have more space for other important applications in storage. You can see if your friends are working. Moreover, using cloud computing helps users get new friends. In addition, it is convenient to do work. A good example of cloud computing is yahoo, g-mail, and Amazon. Cloud computing only needs the internet connection. Normal computing does not have internet access. Presently you can access to internet almost everywhere in the central business district, which makes life become more convenient.

2.How could you turn a classroom into a cloud computing classroom?

First of all, all the students in the classroom need to register network like, Amazon, Yahoo, and G-mail etc. These networks are connecting together. Moreover, students will have to plan their schedule, which uses to set for work as a team. Furthermore, students will use their ID number to access the network which is safe and personal. For example, Wikiversity offers us for more comfortable work. Instructor can post anything on Wikiversity and students can read them. They can share an assignment with others.

Section1 Phutich Paisalsak 5180663 Tassawat Wangsupakitkosol 5180718

title: User talk:Poon


text:
User:Egm6341.s10.team3.ynahn81/HW7-6

= (6) Solution of optimal control of bunt maneuver of aircraft using Hermite-Simpson (HS) algorithm and Newton-Raphson (NR) method for the given control inputs = Ref: Lecture notes [[media:Egm6341.s10.mtg40.djvu|p.40-3]] and [[media:Egm6341.s10.mtg41.djvu|p.41-1]]

Problem Statement
 The given equations of motion of aircraft are

 * {| style="width:100%" border="0" align="left"

\mathbf{\dot{z}} = \begin{Bmatrix} \dot{\gamma} \\ \dot{v} \\ \dot{x} \\ \dot{y} \end{Bmatrix} = \begin{Bmatrix} \frac{T-D}{mv}\sin\alpha + \frac{L}{mv}\cos\alpha - \frac{g}{v}\cos\gamma \\ \frac{T-D}{m}\cos\alpha + \frac{L}{m}\sin\alpha - g\sin\gamma \\ v\cos\gamma \\ v\sin\gamma \end{Bmatrix} = \begin{Bmatrix} f_{1}(\mathbf{z}) \\ f_{2}(\mathbf{z}) \\ f_{3}(\mathbf{z}) \\ f_{4}(\mathbf{z}) \end{Bmatrix} = \mathbf{f}(\mathbf{z}) $$ $$  Here, $$\displaystyle D$$ and $$\displaystyle L$$ are
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\begin{cases} D(y,v,\alpha) = \frac{1}{2}C_{d}\rho v^{2}S_{ref} \\ L(y,v,\alpha) = \frac{1}{2}C_{l}\rho v^{2}S_{ref} \end{cases} $$  where
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\begin{cases} C_{d}(\alpha) = A_{1}\alpha^2 + A_{2}\alpha + A_{3} \\ C_{l}(\alpha) = B_{1}\alpha + B_{2} \\ \rho(y) = C_{1}y^2 + C_{2}y + C_{3} \end{cases} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Solve the above equations of motion of aircraft when the below control inputs $$\displaystyle T(t)$$ and $$\displaystyle \alpha(t)$$ are given.

 * {| style="width:100%" border="0" align="left"

T(t) = \begin{cases} 6000 \; N, & \mbox{for }0 \leq t < 27 \; \mbox{and} \; 33 \leq t \leq 40 \\ 1000 \; N, & \mbox{for }27 \leq t < 33 \end{cases} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

\alpha(t) = \begin{cases} 0.03 \; rad, & \mbox{for }0 \leq t < 21 \\ \frac{0.13-0.09}{27-21}(t-21) + 0.09 \; rad, & \mbox{for }21 \leq t < 27 \\ \frac{-0.2+0.13}{33-21}(t-27) - 0.13 \; rad, & \mbox{for }27 \leq t < 33 \\ \frac{-0.13+0.2}{40-33}(t-33) - 0.2\; rad, & \mbox{for }33 \leq t \leq 40 \end{cases} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

The solution should be obtained using Hermite-Simpson (HS) algorithm and Newton-Raphson (NR) method.  Solve the same equations of motion using "ode45" command in Matlab to verify the solution by HS and NR is correct.

Solution
All required parameters can be obtained from the Subchan and Zbikowski paper. (Subchan and Zbikowski, Optim. Control Appl. Meth. 2007; 28:311-353)
 * {| style="width:100%" border="0" align="left"

\begin{cases} m = 1005 \; kg \\ g = 9.81 \; m/s^2 \\ S_{ref} = 0.3376 \; m^2 \\ A_{1} = -1.9431 \\ A_{2} = -0.1499 \\ A_{3} = 0.2359 \\ B_{1} = 21.9 \\ B_{2} = 0 \\ C_{1} = 3.312 \times 10^{-9} \; kg/m^5 \\ C_{2} = -1.142 \times 10^{-4} \; kg/m^4 \\ C_{3} = 1.224 \; kg/m^3 \end{cases} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

The below Matlab function returns the given control input thrust $$\displaystyle T(t)$$.
 The below Matlab function returns the given control input angle of attack $$\displaystyle \alpha(t)$$.

Let us use the notation $$\displaystyle \mathbf{z}(t_{i}) = \mathbf{z}_{i}$$ for simplification. In class meeting, we already obtained the below HS algorithm. (see [[media:Egm6341.s10.mtg37.djvu|p.37-2]])
 * {| style="width:100%" border="0" align="left"

\mathbf{z}_{i+1} = \mathbf{z}_{i} + \frac{h/2}{3}\left[\mathbf{f}(\mathbf{z}_{i})+4\mathbf{f}(\mathbf{g}(\mathbf{z}_{i},\mathbf{z}_{i+1}))+\mathbf{f}(\mathbf{z}_{i+1})\right] $$ $$
 where
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\mathbf{g}(\mathbf{z}_{i},\mathbf{z}_{i+1}) = \mathbf{z}_{i+1/2} = \frac{1}{2}\left(\mathbf{z}_{i} + \mathbf{z}_{i+1}\right) + \frac{h}{8}\left(\mathbf{f}(\mathbf{z}_{i}) - \mathbf{f}(\mathbf{z}_{i+1})\right) $$ $$

 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

The below Matlab function returns vector $$\displaystyle \mathbf{f}(\mathbf{z})$$ (see (Eq. 1)) for a given vector $$\displaystyle \mathbf{z}(t)$$.

By rearrange terms of (Eq.4), let us define $$\displaystyle \mathbf{F}(\mathbf{z}_{i+1})$$ as below.
 * {| style="width:100%" border="0" align="left"

\mathbf{F}(\mathbf{z}_{i+1}) = \mathbf{z}_{i+1} - \mathbf{z}_{i} - \frac{h/2}{3}\left[\mathbf{f}(\mathbf{z}_{i})+4\mathbf{f}(\mathbf{g}(\mathbf{z}_{i},\mathbf{z}_{i+1}))+\mathbf{f}(\mathbf{z}_{i+1})\right] = 0 $$ $$

 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }

We can find the value of $$\displaystyle \mathbf{z}_{i+1}$$ which satisfies (Eq.6) using NR method. (see [[media:Egm6341.s10.mtg38.djvu|p.38-1]])
 * {| style="width:100%" border="0" align="left"

\mathbf{z}_{i+1}^{(k+1)} = \mathbf{z}_{i+1}^{(k)} - \left[\frac{d\mathbf{F}(\mathbf{z}_{i+1}^{(k)})}{d\mathbf{z}}\right]^{-1}\mathbf{F}(\mathbf{z}_{i+1}^{(k)}) $$ $$
 Since time step is small, $$\displaystyle \mathbf{z}_{i}$$ can be used as the initial value of $$\displaystyle \mathbf{z}_{i+1}^{(k)}$$, i.e. $$\displaystyle \mathbf{z}_{i+1}^{(0)}=\mathbf{z}_{i}$$.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }

Now, note that we need to calculate $$\displaystyle \frac{d\mathbf{F}(\mathbf{z}_{i+1}^{(k)})}{d\mathbf{z}}$$ to use NR method.
 * {| style="width:100%" border="0" align="left"

\left[\frac{d\mathbf{F}(\mathbf{z}_{i+1}^{(k)})}{d\mathbf{z}}\right] = \mathbf{I} - \frac{h/2}{3}\left[4\frac{d\mathbf{f}(\mathbf{g})}{d\mathbf{g}}\frac{\mathbf{g}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}} + \frac{d\mathbf{f}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}}\right] $$ $$
 where $$\displaystyle \mathbf{I}$$ is a identity matrix. From (Eq. 5), we can calculate $$\displaystyle \frac{\mathbf{g}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}}$$ as below.
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\frac{\mathbf{g}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}} = \frac{1}{2}\mathbf{I} - \frac{h}{8}\frac{d\mathbf{f}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}} $$ $$

 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

Based on (Eq. 8) and (Eq. 9), we can calculate $$\displaystyle \frac{d\mathbf{F}(\mathbf{z}_{i+1}^{(k)})}{d\mathbf{z}}$$ once we know $$\displaystyle \frac{d\mathbf{f}(\mathbf{z}_{i+1})}{d\mathbf{z}_{i+1}}$$. Therefore, let us calculate $$\displaystyle \frac{d\mathbf{f}(\mathbf{z})}{d\mathbf{z}}$$ using (Eq. 1).
 * {| style="width:100%" border="0" align="left"

\begin{align} \frac{d\mathbf{f}(\mathbf{z})}{d\mathbf{z}} & =
 * $$\displaystyle
 * $$\displaystyle

\begin{bmatrix} \frac{df_{1}(\mathbf{z})}{d\gamma} & \frac{df_{1}(\mathbf{z})}{dv} & \frac{df_{1}(\mathbf{z})}{dx} & \frac{df_{1}(\mathbf{z})}{dy}    \\ \frac{df_{2}(\mathbf{z})}{d\gamma} & \frac{df_{2}(\mathbf{z})}{dv} & \frac{df_{2}(\mathbf{z})}{dx} & \frac{df_{2}(\mathbf{z})}{dy}    \\ \frac{df_{3}(\mathbf{z})}{d\gamma} & \frac{df_{3}(\mathbf{z})}{dv} & \frac{df_{3}(\mathbf{z})}{dx} & \frac{df_{3}(\mathbf{z})}{dy}    \\ \frac{df_{4}(\mathbf{z})}{d\gamma} & \frac{df_{4}(\mathbf{z})}{dv} & \frac{df_{4}(\mathbf{z})}{dx} & \frac{df_{4}(\mathbf{z})}{dy} \end{bmatrix} \\ & = \begin{bmatrix} \frac{g}{v}\sin\gamma & -\frac{T}{mv^2}\sin\alpha - \frac{C_{d}\rho S_{ref}}{2m}\sin\alpha + \frac{C_{l}\rho S_{ref}}{2m}\cos\alpha + \frac{\rho}{v^2}\cos\gamma & 0 & -\frac{C_{d}(2C_{1}y+C_{2})vS_{ref}}{2m}\sin\alpha + \frac{C_{l}(2C_{1}y+C_{2})vS_{ref}}{2m}\cos\alpha    \\ -g\cos\gamma & -\frac{C_{d}\rho vS_{ref}}{m}\cos\alpha - \frac{C_{d}\rho vS_{ref}}{m}\sin\alpha & 0 & -\frac{C_{d}(2C_{1}y+C_{2})v^2S_{ref}}{2m}\cos\alpha - \frac{C_{l}(2C_{1}y+C_{2})v^2S_{ref}}{2m}\sin\alpha    \\ -v\sin\gamma & \cos\gamma & 0 & 0    \\ v\cos\gamma & \sin\gamma & 0 & 0 \end{bmatrix} \\ \end{align} $$ $$
 The below Matlab function returns vector $$\displaystyle \frac{d\mathbf{f}(\mathbf{z})}{d\mathbf{z}}$$ (see (Eq. 10)) for a given vector $$\displaystyle \mathbf{z}(t)$$.

 *
$$\displaystyle (Eq. 10)
 * }
 * }

Now, we can calculate (Eq. 6), (Eq. 8) and (Eq. 9) using the provided Matlab functions. Since we have all required information in order to perform NR method given in (Eq. 7), the solution of the equations of motion given in (Eq. 1) can be obtained.

The below Matlab function returns vector $$\displaystyle \mathbf{z}(t)$$ for the given time range $$\displaystyle t \in [0, 40]$$.

To verify the obtained solution from our own code, let us solve the same equations of motion using "ode45" command in Matlab.

Now, let us compare our results to the results from "ode45" command.

Plot $$\displaystyle \gamma(t) $$ vs $$\displaystyle t $$

 Plot $$\displaystyle v(t) $$ vs $$\displaystyle t $$

 Plot $$\displaystyle x(t) $$ vs $$\displaystyle t $$

 Plot $$\displaystyle y(t) $$ vs $$\displaystyle t $$

 Plot $$\displaystyle y(x) $$ vs $$\displaystyle x $$

As shown above figures, the solution from our own code is really consistent with the result from Matlab ode45 command.

title: User:Egm6341.s10.team3.ynahn81/HW7-6


text:
User:Learnceasy

Hi there! This is my page! Just trying to learn some things here, at Wikiversity!

title: User:Learnceasy


text:
User talk:Learnceasy

I don't really TALK so much!

Welcome
 Hello Learnceasy, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 20:12, 21 April 2010 (UTC)

title: User talk:Learnceasy


text: File:Thrust.jpg

title: File:Thrust.jpg


text: File:Inputalp.jpg

title: File:Inputalp.jpg


text: File:HW7C 1.png

title: File:HW7C 1.png


text:
User talk:Webdeblee

 Hello Webdeblee, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 18:04, 21 April 2010 (UTC)

title: User talk:Webdeblee


text:
User talk:Ligia

 Hello Ligia, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 18:04, 21 April 2010 (UTC)

title: User talk:Ligia


text:
User talk:Wim2010

 Hello Wim2010, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 18:04, 21 April 2010 (UTC)

title: User talk:Wim2010


text:
User:Webdeblee

Web Developer working in Northern California College level web design instructor

title: User:Webdeblee


text:
User talk:Dantes~enwikiversity

 Hello Dantes, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 18:37, 21 April 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Dantes. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Dantes~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:33, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:05, 19 April 2015 (UTC)

title: User talk:Dantes~enwikiversity


text: User:Achado

title: User:Achado


text:
User talk:Achado

 Hello Achado, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 20:05, 21 April 2010 (UTC)

title: User talk:Achado


text:
User:Egm6341.s2010.Team1.lei/HW7

For HW7,I am responsible for problem 3,16 and 17.

=Problem 3-Hermite-Simpson Algorithm to integrate Verhulst equation =

Find
Use Hermite-Simpson rule to integrate the above given Verhulst equation

Given
Refer Lecture slide (1) [[media:Egm6341.s10.mtg38.djvu|p.38-3]]

$$ f(x)=rx (1-\frac {x}{x_{max}}) $$

$$ x_{max}=10\,$$

$$ r=1.2 \,$$

2cases:

$$ x_{0}=2 <\frac {1}{2}x_{max} $$

$$ x_{0}=7 >\frac {1}{2}x_{max} $$

Such that $$ AbsTol= O(10^{-6})\, $$ for $$ t \isin [0,10]$$

Solution
For the first case:

$$ x_{0}=2 \, $$

Matlab Code:

---

For the second case:

$$ x_{0}=7 \, $$

Matlab Code:

=Problem 16-Find the Cosine Series coeffient ak =

Find
Find

$$ a_{k}=\frac {2}{\pi}\int_{0}^{\pi}f(\cos \theta) \cos (k \theta)d \theta $$

Given
We know Fourier Cosine Series:

$$ f(\cos\theta)=\frac{a_{0}}{2}+\sum _{k=1}^{\infin} a_{k}\cos (k\theta) $$

Solution
$$ a_{0}=\frac{1}{\pi}\int _{-\pi}^{\pi} f(\cos\theta)d\theta $$

$$ =\frac{2}{\pi}\int _{0}^{\pi} f(\cos\theta)d\theta $$

$$ a_{n}=\frac{1}{\pi}\int _{-\pi}^{\pi} f(\cos\theta)\cos(k\theta) d\theta $$

$$ =\frac{2}{\pi}\int _{0}^{\pi} f(\cos\theta) cos(k\theta)d\theta $$

=Problem 17-Find int if cosine series is know =

Find
[[media:Egm6341.s10.mtg42.djvu|p.42-3]]

$$ I=a_{0}+\sum_{j=1}^{\infin} \frac{2a_{2j}}{1-(2j)^2} $$

Given
[[media:Egm6341.s10.mtg42.djvu|p.42-2]]

$$ I= \int_{-1}^{+1}f(x)dx= \int_{0}^{\pi} f(\cos\theta) \sin\theta d\theta\, $$

[[media:Egm6341.s10.mtg42.djvu|p.42-3]]

$$ f(\cos\theta)=\frac{a_{0}}{2}+\sum _{k=1}^{\infin} a_{k}\cos (k\theta) $$

Solution
$$ I=\int_{0}^{\pi}(\frac{a_{0}}{2}+\sum _{j=1}^{\infin}a_{2j}\cos(2j\theta))\sin\theta d\theta$$

$$ =\int_{0}^{\pi}\frac {a_{0}}{2}\sin\theta d\theta +\int_{0}^{\pi}\sum _{j=1}^{\infin}a_{2j}\cos(2j\theta)\sin\theta d\theta$$

$$ =-\frac{a_{0}}{2} \cos\theta |_{0}^{\pi}+ \sum _{j=1}^{\infin}\int_{0}^{\pi}a_{2j}\cos(2j\theta)\sin\theta d\theta$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j} \int_{0}^{\pi}\cos(2j\theta)\sin\theta d\theta$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j} \int_{0}^{\pi}-[\sin((2j+1)\theta)-\sin((2j-1)\theta)]d\theta $$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}[\int_{0}^{\pi}-\sin((2j+1)\theta)d\theta +\int_{0}^{\pi}\sin((2j-1)\theta)d\theta] $$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}[\frac{1}{2j+1} \cos(2j+1)\theta|_{0}^{\pi}-\frac{1}{2j-1} \cos(2j-1)\theta|_{0}^{\pi}]$$

$$ =a_{0}+\sum _{j=1}^{\infin}a_{2j}\frac{2}{1-(2j)^{2}} $$

 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow I=a_{0}+\sum _{j=1}^{\infin}\frac{2a_{2j}}{1-(2j)^{2}} $$ $$
 * $$\displaystyle
 * }
 * }

Egm6341.s10.team1.lei03:57, 23 April 2010 (UTC)

title: User:Egm6341.s2010.Team1.lei/HW7


text: File:Outgamma.jpg

title: File:Outgamma.jpg


text: File:Outv.jpg

title: File:Outv.jpg


text: File:Outx.jpg

title: File:Outx.jpg


text: File:Outy.jpg

title: File:Outy.jpg


text: File:Outxy.jpg

title: File:Outxy.jpg


text:
Response testing/WMF Projects/Newbie treatment at Criteria for speedy deletion

History
the project was begun on 5 October, 2009, there were 249 edits, and the last edit but one to the project page was on January 7, 2010; The final edit on January 22 was to point to a discussion later archived. The talk page history shows, from 31 October, 2009, through January 19, 2010, 522 edits. This was the original proposal:

 * This page is created to take up Wikipedia:Requests for comment/new users#Lets all create an extra account the challenge - create a wikipedia account, write an article and see if it lasts seven days.

 * Info I'd like to collect here:
 * Did your article survive or get deleted?
 * what tags did it get
 * Were you welcomed?
 * Did anyone else edit your article and if soo what did they do?
 * Did you feel welcomed?
 * Did you feel ignored?
 * Did you feel bitten?

The first test result was posted the next day, and it brought immediate discussion: Searching for the Wrong-Eyed Jesus. Individual reports were moved to subpages, this one became Wikipedia:Newbie treatment at CSD/Skomorokh

Links

 * Wikipedia:Newbie treatment at Criteria for speedy deletion
 * Wikipedia talk:Newbie treatment at Criteria for speedy deletion
 * User:Ikip/Newbie treatment at Criteria for speedy deletion/complaints
 * User talk:Ikip/Newbie treatment at Criteria for speedy deletion/complaints
 * Wikipedia:WikiProject Article Rescue Squadron/Newsletter/20091001/Interview2
 * Wikipedia:Wikipedia Signpost/2009-11-09/New pages experiment
 * Wikipedia:Requests for bureaucratship/SoWhy
 * User:WereSpielChequers/Newbie treatment at NPP
 * User talk:WereSpielChequers/Archive 10
 * Wikipedia:Administrators' noticeboard/IncidentArchive577#Concerns_about_NuclearWarfare_and_Wikipedia:Newbie_treatment_at_CSD

Opinions / Thoughts / Talking points
This area is for you to drop any opinions, thoughts or talking points in. In particular, if you have a 'feeling' about something, and would like to discuss it further - this is the spot! Don't feel that your thoughts or arguments have to be fully formed, and don't jump down the throat of editors who might be unsure about how they feel, but wish to express something :-)

Privatemusings' Thoughts
I think this project exposes interesting tensions in the wiki environment - in many ways it was rather blatantly contrary to the 'wp:point' guidelines, on the other hand, I have no doubt it was executed in good faith. In fact, good faith is about the best you can attribute to the project, because again, in rather typical wiki fashion, it wasn't really competently designed or executed - to me it came across as bumbling, the 'drama' it created was predictable, and it hasn't really delivered any insight particularly. I suspect it's more valuable as something to study (here, for example) than in its desired and stated goals.

It touches on 'AGF', 'wp:point', and even the use of 'socks' - fundamentally it illustrates to me how these rules are not actually treated as matters of principle (despite editors genuinely believing they are doing so) - they're actually really just 'by definition' something someone of ill intent contravenes. Using rules which boil down to intent is not a workable solution - it absolutely creates drama and disharmony rather than resolving it - not a great idea, and this is a good example :-) Privatemusings 03:28, 24 July 2010 (UTC)


text:
Talk:Response testing/WMF Projects/Newbie treatment at Criteria for speedy deletion

Procedure for this resource page
I have established a minimal guideline for the conduct of this project, shown on the resource page. If anyone considers the material I established to be harmful, please fix it. If it is acceptable but could be improved, and you think the improvement obvious, go ahead and improve it. If you expect "improvement" to be controversial, I request but cannot demand that changes be discussed first. Thanks for your care with this resource, studies similar to this have created controversy and disruption in the past, and it is my hope to avoid that, or at least to ensure that no legitimate objection remains without having been addressed and resolved by consensus. There is no rush, please be patient with other participants. --Abd 00:04, 22 April 2010 (UTC)

Guidelines for this resource
Please feel free to propose amendments to these guidelines, as threaded discussion below the guideline and acceptance signatures. No guideline is purely binding here, but a guideline established by consensus may prevent disruption in the future, setting a default standard that participants are ordinarily expected to follow. Signing individual guidelines is voluntary, but is intended to reassure those who might possibly object to this process that participants are committed to fairness and accuracy, not blame and misrepresentation. --Abd 00:04, 22 April 2010 (UTC)

Do not out editors
Do not out other editors, i.e., reveal their real-world identity, without an established and agreed-upon necessity for it, and without confidence and probably evidence that the Wikiversity community and agents of the WikiMedia Foundation will approve of it. Because discussing this can involve outing the editor, do not discuss outing, on-wiki, in any way that will reveal real-world identity, or point to a resource (presumably outside the WMF universe) that does. Real-world identity should not generally matter for the purposes of this study, and there might be studies where it would be important, but these guidelines cover only this particular project.
 * Accept. --Abd 00:04, 22 April 2010 (UTC)

Describe, do not judge
Avoid judging the actions of editors in the evidence-gathering phase of this project, and this project should not move beyond that phase without consensus to do so, and ample time for objection. In the evidence-gathering phase, diffs and permanent version links will be collected and arranged to facilitate study of the subject testing project and response to it, and neutral summaries created to make learning about the incident easier.
 * Accept. --Abd 00:04, 22 April 2010 (UTC)

Edit summaries are always neutral evidence
An edit summary from an original edit is always allowed as part of a "neutral summary." Caution should be used in adding summarization beyond that, such original research or synthesis should enjoy maximum consensus. If an editor has retracted a statement made in an edit or in a summary, that should be cited as well.
 * Accept. --Abd 00:04, 22 April 2010 (UTC)

Avoid cherry-picking
Collect evidence using stated criteria or categories such as "All edits by Editor X linking to the testing project or referring to it." Then be complete within the criteria provided (but participants will naturally take time to complete collection).
 * Accept. --Abd 00:04, 22 April 2010 (UTC)

Pick the rest of the cherries
If you believe that evidence has been cherry-picked, pick the rest of the cherries, i.e., complete the evidence, broadening categories as needed, but without making categories overbroad; i.e., add a new category if broadening the original evidence category would expand it so much that the picture is muddied. As an example of over-broadening, if the category mentioned above were expanded to "All edits by Editor X during the project period," it could muddy the picture, unless there were very few other edits. Please do not accuse editors of cherry-picking; people will naturally bring up evidence they think important, but our task as a working group will be to balance and complete this.
 * Accept. --Abd 00:04, 22 April 2010 (UTC)

Keep the resource page clean
The resource page itself should enjoy continued consensus, with ample time for objection before material is placed on it. Even after discussion, material may be removed from the page if new objection is raised, to allow discussion. Exceptions to this should be explicitly confirmed by consensus, probably by consensus in a broader forum should consensus here not be complete.
 * Accept. --Abd 00:04, 22 April 2010 (UTC)
 * I just "violated" this, because I'd collected links here to pages on Wikipedia, then decided to go ahead and place it on the resource page. However, if anyone thinks that what I did was controversial and should be discussed first, please revert. Thanks. --Abd 02:54, 23 April 2010 (UTC)

present and correct
Just a quick note to say that I do intend to begin work here before too long :-) - I'm a wee bit busy at the mo, so my pace will be glacial, as usual - my only feedback on the above in terms of guidelines, is that I'm a big advocate of what I view as the 'wiki way' which is to be bold, follow your nose, listen to concerns, de-escalate at all times, assume good faith, and you'll be alright. Perhaps I should give greater profile to my longstanding committment to stop anything that I'm up to for a chat if anyone wants one (you bring the biscuits, I'll make tea :-) cheers, Privatemusings 06:12, 27 April 2010 (UTC)
 * The biscuits are in the oven. As to the wiki way, yes. --Abd 14:37, 27 April 2010 (UTC)


text:
User talk:Topspeak~enwikiversity

 Hello Topspeak, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:33, 22 April 2010 (UTC)

Note
So you know, we are not an encyclopedia and merely copying and pasting information from Wikipedia is not what we are here for. Please make sure to make any of your pages educational based and class oriented. Ottava Rima (talk) 00:33, 22 April 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Topspeak. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Topspeak~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:08, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:24, 19 April 2015 (UTC)

title: User talk:Topspeak~enwikiversity


text:
Survey research and design in psychology/Tutorials/ANOVA/Descriptive statistics

Descriptive statistics

 * 1) For ANOVA results, report descriptive statistics (M, SD, Skewness, Kurtosis) and n for each cell and for the marginal and overall cells. Usually, this is best done in a table.
 * 2) e.g., for a 2 x 2 design, there are four cells (2 x 2 table). The marginal means are also of interest, so a 3 x 3 table is needed.
 * 3) Obtain the descriptive statistics using SPSS:
 * 4) If you have a within-subjects factor, then compute a total score via Transform - Compute e.g., totalscore = mean(factor1,factor2, etc.)
 * 5) Analyze - Means - Compare Means - Put factor1, factor2, and totalscore (if you have one) into the first box, and your between-subjects variable in the between-subjects variable box. In Options, request M, SD, Skewness, Kurtosis, and N. This provides a better output than via Analyze - Explore.
 * 6) To obtain histograms for each cell, use Analyze - Frequencies - switch off statistics and switch on histograms via Charts with normal distribution curve. When there is a between-subjects variable, first split the file, then run Frequencies. Remember to switch the split file off afterwards.
 * 7) Examining the normality assumption:
 * 8) Examine the histograms for each cell:
 * 9) If there is a between-subjects IV, then split the file so that output is sorted by groups
 * 10) Analyze - Frequencies - Put the DV or all within-subjects variables into the r.h. box, then Charts - Histograms - Normal Curve - and run
 * 11) Examine the skewness and kurtosis for each cell - are they between -1 and +1? If so and you have at least 20 per cell, ANOVA should be quite robust to these relatively minor departures from normality. This is quite a conservative guideline. Some texts suggest robustness for skewness of between -2 and +2. If the sample data is outside these guidelines, consider whether ANOVA is appropriate.
 * 12) Shapiro-Wilk tests of normality can also be used to help examine whether a variable is normally distributed. If the test is significant, it would seem to be unlikely that the data is drawn from a population which has a perfectly normal distribution. However, ANOVA is robust to violation of normality assumptions with large cell sample sizes. Shapiro-Wilk statistics are often significant even when the data is appropriate for ANOVA. So, be aware that Shapiro-Wilks is a particularly sensitive test, especially with large sample sizes. If using this test, accompany the interpretation with your own examination of the skewness and kurtosis for each of the cells. Remember also that the ANOVA assumption is about normality for the data within each cell, thus it would be important to obtain Shapiro-Wilk tests of normality for each cell separately, such as by using split file.


text:
Survey research and design in psychology/Tutorials/Qualitative analysis

Contents

 * 1) /Overview/
 * 2) /Thematic analysis/
 * 3) /Multiple response analysis/

Recordings

 * 1) Screencasts


text: File:L1 reaction.png

title: File:L1 reaction.png


text: File:L2 lrng.png

title: File:L2 lrng.png


text:
Analysis of variance/Types

The main types of ANOVA are listed below. They are all part of the general linear model.

title: Analysis of variance/Types


title: File:15.7.jpg


text: File:Acfigure.png

title: File:Acfigure.png


text:
User talk:Mildlywild

Hello! My name is Phatcharapan, also known as Mildly. Some people do call me Wild ... depends. I am a 2nd year college student and my major is Social Science.I am just like you, a complex human being. I smile, cry, whine, laugh, love and hope. At times I fear, and most of the time I try. I know you do the same things too. So we are not really that different

title: User talk:Mildlywild