text:
User:Bchethan

Simple Exercise
What is x2+2x+1 if x=1? Solution: 4

Sample Quiz
{What is Symmetric matrix + A matrix whose transpose matrix is same as the original matrix. - A matrix whose diagonal elements are non zero and other elements are zero - A zero matrix - None of those
 * type=""}

{ The determinant of transpose of $$\begin{bmatrix} 2&-1\\0&4\end{bmatrix}$$ is { 8_2 }.
 * type="{}"}

{
 * type="{}"}

$$ \displaystyle \ y_1 = $$ { 4 } $$ \displaystyle \ y_2 = $$ { -1 } $$ \displaystyle \ y_3 = $$ { 6 }

Next, we have Ux = y

$$ \left[\begin{array}{c c c}3 & 4 &2\\2 & 1 & 2\\3 & 4 & 1\end{array} \right]$$ X $$\left[\begin{array}{c}x_1\\x_2\\x_3\end{array} \right] $$ = $$\begin{bmatrix} y_1\\y_2\\y_3\end{bmatrix} $$

Use backward substitution we have:

$$ \displaystyle \ x_1 = $$ { 1 } $$ \displaystyle \ x_2 = $$ { 1 } $$ \displaystyle \ x_3 = $$ { 1 }

Final Project
1)Solve differential equation y' = 3t2y in [0,1] using Euler's method with n=10,y(0)=1. Solution: We need to find the solution ODE y' = 3t2y using Euler's method.

yn+1=yn+hf(tn,yn)

We divide time span with number points to find the step size h.

h=tmax-tmin/n=1-0/10=0.1

y1=y0+hf(t0,y0)

=1.000000+.1x3x02x1

=1.000000

y2=y1+hf(t1,y1)

=1.000000+.1x3x0.12x1.000000

=1.003000

y3=y2+hf(t2,y2)

=1.003000+.1x3x0.22x1.003000

=1.0150360

y4=y3+hf(t3,y3)

=1.01503600+.1x3x0.32x1.0150360

=1.0424420

y5=y4+hf(t4,y4)

=1.0424420+.1x3x0.42x1.0424420

=1.0924792

y6=y5+hf(t5,y5)

=1.0924792+.1x3x0.52x1.0924792

=1.1744151

y7=y6+hf(t6,y6)

=1.1744151+.1x3x0.62x1.1744151

=1.3012520

y8=y7+hf(t7,y7)

=1.3012520+.1x3x0.72x1.3012520

=1.4925360

y9=y8+hf(t8,y8)

=1.4925360+.1x3x0.82x1.4925360

=1.7791029

y10=y9+hf(t9,y9)

=1.77910290+.1x3x0.92x1.7791029

=2.2114249

2)Solve differential equation y' = 2ty in [0,1] using RK2 method yn+1=yn+h/4(k1+3K2) where k1=f(tn,yn),k2=f(tn+2/3h,yn+2/3hk1)with n=5,y(0)=1.

Solution: We need to find the solution ODE y' = 2ty using RK second order method.

yn+1=yn+h/4(k1+3K2)

k1=f(tn,yn)

k2=f(tn+2/3h,yn+2/3hk1)

y1=y0+h/4(k1+3K2)

k1=f(t0,y0)

=2x.0x1

=0

k2=f(t0+2/3h,y0+2/3hk1)

=2x2/3x.2x1

=.26667

y1=y0+h/4(k1+3K2)

=1+.2/4(0+3x.26667)

=1.04

y2=y1+h/4(k1+3K2)

k1=f(t1,y1)

=2x.2x1.04

=.416

k2=f(t1+2/3h,y1+2/3hk1)

=f(.2+.13333,1.04+.0554667)

=.730304

y2=y1+h/4(k1+3K2)

=1.04+.2/4(0.416+3x.730304)

=1.17035

y3=y2+h/4(k1+3K2)

k1=f(t2,y2)

=2x.4x1.17035

=.93648

k2=f(t2+2/3h,y2+2/3hk1)

=.730304

y2=y1+h/4(k1+3K2)

=1.04+.2/4(0.416+3x.730304)

=1.17035

3)Solve differential equation y' = 2ty in [0,1] using Two step Adams Bashforth method with n=5,y(0)=1.

Solution: We need to find the solution ODE y' = 2ty using Two step Adams Bashforth method.

yn+2 = yn+1 + 3/2 x hf(tn+1,yn+1)-1/2 x hf(tn,yn)

Calculating h=1-0/5=0.2

We need two approxmations for calculating y2

Calculating y1 using RK second order method.

y1=1.04

y2 = y1 + 3/2 x hf(t1,y1)-1/2 x hf(t0,y0)

=1.04+3/2(.2)f(0.2,1.04)-1/2(0.2)f(0.0,1)

=1.1648

y3 = y2 + 3/2 x hf(t2,y2)-1/2 x hf(t1,y1)

=1.1648+3/2(.2)f(0.4,1.1648)-1/2(0.2)f(0.2,1.04)

=1.40275

y4 = y3 + 3/2 x hf(t2,y2)-1/2 x hf(t2,y2)

=1.40275+3/2(.2)f(0.6,1.40275)-1/2(0.2)f(0.4,1.1648)

=1.81456

y5 = y4 + 3/2 x hf(t4,y4)-1/2 x hf(t3,y3)

=1.81456+3/2(.2)f(0.8,1.81456)-1/2(0.2)f(0.6,1.40275)

=2.21333

y6 = y5 + 3/2 x hf(t5,y5)-1/2 x hf(t4,y4)

=2.21333+3/2(.2)f(1,2.21333)-1/2(0.2)f(0.8,1.81456)

=3.25098

Introduction
My final project is about adding exercises for different ODE methods to Wikiversity page.I have added exercises for Euler method,Multistep method and Runge Kutta method.

Initial Experience
Prior to the final project I worked on small project as part of my homework.That was adding material to wikipidea page on Taylor's Approximation.I have gone through many books and decided to add few points to the existing information.I was corrected by Dr.Mohlenkamp on few of issues, after that I have modified the changes accordingly.After that I have realized that the changes were not required.So i have done more work for my final project and made sure that I won't repeat previous mistakes.

Motivation
I found useful material  on Wikipedia related to ODE methods but there were no solutions for examples.So I thought it will be useful to put some exercises and solution of it completely.I have gone through books and with the inspiration of it wrote few problems which are very easy but gives clear idea of method and solved it step by step.

Changes
I have added Wikipedia pages on ODE methods to Numerical Analysis Wikiversity page and after that created exercise for Euler Method, Multistep Method and Runge Kutta method.If the user is not able to get solution they can refer solution which covered each step in detail.I have also created quiz which covers error order of ODE methods and stability of ODE methods.

Reference
Guide to Numerical Analysis by Peter R. Turner

title: User:Bchethan


text:
User:Kadamsujit

= Name: Sujit Kadam =

Introduction
My final project is about Fixed point iteration. I got interested to Fixed point iteration when I learnt about Babylonian method. It’s a very old process but still used today and is powerful at the same time. I was amazed to know its application in Newton Raphson’s method and Secant method. I wanted to learn more about this iteration process. Hence, I opted for this process. This project is intended to get some more knowledge about Fixed point iteration and its application. The project explains about the different concepts and applications of Fixed point iteration using examples, exercises and quizzes.

Initial Experience
After reading wiki page of Fixed Point Iteration, I felt something’s missing. I started to think and search various explanations on Fixed point iteration. I read few books online. I found that many things can be added to improve Fixed point iteration on Wikipedia. After some initial research on topic I decided to write my project proposal that described about the things I will be adding. In fact, initially I was a little bit confused about Instructor's expectations. I thought that I need to add whatever I have learned and some extra information on Fixed point iteration. Accordingly, I made my project proposal.

I proposed to add points mentioned below

 * 1) Introductory definition and explanation about the iteration: Introduction, definition, formula and explanation about Fixed point iteration.
 * 2) Supporting theorems and derivations: Banach fixed point theorem, Babylonian method and any other important derivation.
 * 3) Rate of convergence: Proof and explain convergence speed of the iteration method.
 * 4) Examples to explain fixed point iteration: Some exercises on fixed point iteration based on different scenarios.
 * 5) Applications and usefulness of the iteration: Explain application of the iteration in Newton’s method and Secant method.
 * 6) Disadvantages or failure of this iteration: Explore and explain any cases of failure of this iteration method.
 * 7) Exercises and quizzes on fixed point iteration: Few exercises based on fixed point iteration.
 * 8) Important links and external study help materials: If I find any important interesting link related to the topic then I will post it in the project.

Instructor's input
My instructor pointed out that it would be much better if I don’t duplicate material and add something to the topic that is not present in Wikipedia or any online resources. The explanation of Fixed point iteration, derivation and theorems are already explained in Wikipedia pages are pretty good enough to understand. Instructor also pointed out that I should concentrate more on examples, exercises and quizzes. The examples should clear some basic and new concepts. Exercises should help readers to apply the concepts. Quizzes should test readers’ concept on Fixed point iteration. Instructor's comment were really helpful for me to know which points exactly I need to concentrate. It really add some good new information to the content.

Motivation
After thinking about the inputs from the instructor, I started some in-depth research on Fixed point iteration material. I checked out some books and online material and found that Wikipedia is missing on some parts in Fixed point iteration section. I thought to add algorithm of Fixed point iteration, a new concept related to derivative of function and example that can be used in application of Fixed point iteration i.e. Newton Raphson’s method, difficult exercises and quizzes. In our Numerical analysis course we studied many methods and iterations to find root. But I think Fixed point iteration is really a powerful yet simple tool because of which it was used new methods. It's accuracy is good, convergence rate is linear to quadratic (in some cases) and chances of failure is less compared to other methods. It offers really a good deal.

Proposed changes

 * 1) Introductory definition and explanation about the iteration: Introduction, definition, formula and explanation about Fixed point iteration.
 * 2) Supporting theorems and derivations: Banach fixed point theorem, Babylonian method and any other important derivation.
 * 3) Rate of convergence: Proof and explain convergence speed of the iteration method.
 * 4) Examples to explain fixed point iteration: Some exercises on fixed point iteration based on different scenarios.
 * 5) Applications and usefulness of the iteration: Explain application of the iteration in Newton’s method and Secant method.
 * 6) Disadvantages or failure of this iteration: Explore and explain any cases of failure of this iteration method.
 * 7) Exercises and quizzes on fixed point iteration: Few exercises based on fixed point iteration.
 * 8) Important links and external study help materials: If I find any important interesting link related to the topic then I will post it in the project.

Actual changes

 * 1) Added Algorithm for Fixed point iteration that was not included in Wikipedia.
 * 2) Added a simple example that finds the square root of 2 correct till 3 decimal places.
 * 3) Added an example that proves a new concept not mentioned in Wikipedia: If |g'(x)| > 1 then sequence will not converge to desired value. If |g'(x)| < 1 then sequence will converge to desired value. This concept can be used in Newton Raphson method.
 * 4) Mentioned about the applications of Fixed point iteration: Newton Raphson’s method and Secant method.
 * 5) Added exercise that calculates the square root of 0.5 correct till 3 decimal places. The reason to choose this problem was to show that if a square root of a number near to zero is chosen then by using Babylonian method it first diverges and then converges to the desired value. The exercise displays the iteration steps.
 * 6) Added quizzes based on the concepts of Fixed point iteration.

Conclusion
Concluding, my project work I found that there are still many concepts to be learned in Fixed point iteration. I have tried to cover some concepts but there are still some concepts yet to be touched and learned. Its concepts are used in Newton Raphson and Secant method. Fixed point iteration is really an effective way of finding square root.

Exercise Template
Simple Exercise: What is 10*10? Solution: 100

Quiz template
{If x + 3x = -8, then x + 1 = - -2 + -1 - 1 - 2
 * type=""}

{ The determinant of $$\left[\begin{array}{c c}6 & 8 \\5 & 4\end{array} \right]$$ is { -16 _3 }.
 * type="{}"}

{
 * type="{}"}

$$ \displaystyle \ y_1 = $$ { 5 } $$ \displaystyle \ y_2 = $$ { -5 } $$ \displaystyle \ y_3 = $$ { 19 }

Next, we have Ux = y

$$ \begin{bmatrix} 1&10&-6\\0&5&-10\\0&0&19\end{bmatrix}$$ X $$\begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix} $$ = $$\begin{bmatrix} y_1\\y_2\\y_3\end{bmatrix} $$

Use backward substitution we have:

$$ \displaystyle \ x_1 = $$ { 1 } $$ \displaystyle \ x_2 = $$ { 1 } $$ \displaystyle \ x_3 = $$ { 1 }

Numerical Analysis
Topic Proposal: Fixed point iteration

I would like to propose to write on “Fixed point” iteration topic in Numerical analysis as my project. The goal of the project is to provide complete information about Fixed Point iteration on one single platform. I will be giving an introduction on Fixed point iteration with explanation. The project will first explain in detail about Fixed point iteration and its definition. Once the reader understands the definition then the project moves towards any supporting theorems or derivations of the formulas used in Fixed point iteration. Rate of convergence of the method will be explained to explain the speed of the method. The iteration will be illustrated by different examples to provide in-depth knowledge of the topic. At least two examples will be illustrated to explain the topic. The applications and usefulness of the iteration will be explained. I will also try to find examples or cases where fixed point may fail to converge to find square roots. At the end, the project will wrap asking some questions, exercises, quizzes and important links for external study.

List of topics I am planning to cover in my project:

 * 1) Introductory definition and explanation about the iteration: Introduction, definition, formula and explanation about Fixed point iteration.
 * 2) Supporting theorems and derivations: Banach fixed point theorem, Babylonian method and any other important derivation.
 * 3) Rate of convergence: Proof and explain convergence speed of the iteration method.
 * 4) Examples to explain fixed point iteration: Some exercises on fixed point iteration based on different scenarios.
 * 5) Applications and usefulness of the iteration: Explain application of the iteration in Newton’s method and Secant method.
 * 6) Disadvantages or failure of this iteration: Explore and explain any cases of failure of this iteration method.
 * 7) Exercises and quizzes on fixed point iteration: Few exercises based on fixed point iteration.
 * 8) Important links and external study help materials: If I find any important interesting link related to the topic then I will post it in the project.

What is Fixed Point Iteration?
http://en.wikipedia.org/wiki/Fixed_point_iteration

Algorithm
To find a solution to p = g(p) given an initial approximation p0.

INPUT: Initial approximation p0; tolerance TOL; maximum number of iterations N0. OUTPUT: approximate solution p or message of failure.

Step 1: Set i =1

Step 2: While $$i \leq No$$ Steps 3 - 6

Step 3: Set p = g(p0)

Step 4: If $$|p - po| \leq TOL$$ then OUTPUT (p); (The procedure was successful). STOP.

Step 5: Set i = i + 1

Step 6: Set p0 = p. (Update p0)

Step 7: OUTPUT ('The method failed after N0 iterations'). STOP.

Examples
1. Find square root of 2 accurate till third decimal (10-3). The initial point is 2.

Answer.

 * We know that,

 * x0 = 2

 * xn+1 = 0.5 * ( x0 + (2/ x0))

 * x1 = 0.5 * (2 + (2/2)) = 1.5

 * x2 = 0.5 * (1.5 + (2/1.5)) = 1.416

 * x3 = 0.5 * (1.416 + (2/1.416)) = 1.4142

 * We found out the square root of 2 accurate till 4th decimal in 3 steps.

2. Consider the iteration pn+1 = g(p0) when the function g(x) = 1 + x - x2/4 is used. The fixed points can be found by solving equations x = g(x). The two solutions (fixed points of g) are x = -2 and x = 2. The derivative of the function is g'(x) = 1 - x/2, and there are only two cases to consider

 * Case 1 (P = -2):
 * Start with P0 = -2.05
 * We get
 * P1 = -2.100625
 * P2 = -2.20378135
 * ..... $$\infty$$
 * Therefore, if |g'(x)| > 1 then sequence will not converge to P = -2

 * Case 2 (P = 2):
 * Start with P0 = 1.6
 * We get
 * P1 = 1.96
 * P2 = 1.9996
 * ..... 2
 * Therefore, if |g'(x)| < 1 then sequence will converge to P = 2

Applications
Two methods in which Fixed point technique is used:

1. Newton Raphson Method

 * Formula
 * $$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$

 * where,
 * xn - initial point
 * f(xn) is the value of the function at that point
 * f'(xn) is the value of the differentiated function at that point.

 * Plug all these values into the above equation to get xn+1. It becomes the next initial point. Repeat until you get a point within an acceptable degree of error

2. Secant Method

 * Used to avoid differentiated form in Newton Raphson's method. Only problem is you need two initial points for this method (xn and xn-1)

 * Formula
 * $$x_n=x_{n-1}-f(x_{n-1})\frac{x_{n-1}-x_{n-2}}{f(x_{n-1})-f(x_{n-2})}$$

 * Similar to Newton Raphson's method plug in all values to generate next approximation.

Exercises
If 'f' is continuous and 'x' is a fixed point on 'f' then what is 'f(x)'? Solution: f(x) = x

Find the square root of 0.5 using fixed point iteration? Initial point 0.1 and tolerance 10-3

Calculating x1 i.e. 1st Iteration Solution: x1 = 2.55

Calculating x2 i.e. 2nd Iteration Solution: x2 = 1.373

Calculating x3 i.e. 3rd Iteration Solution: x3 = 0.8685

Calculating x4 i.e. 4th Iteration Solution: x4 = 0.722

Calculating x5 i.e. 5th Iteration Solution: x5 = 0.707

In above problem, how many iterations or steps are needed to achieve an accuracy of 10-8 Solution: Iteration: 6

Quizzes
{Is there any possibility that the fixed point isn't unique -Yes +No
 * type=""}

{ Assuming g ε C[a,b], If the range of the mapping y = g(x) satisfies y ε [a,b], then} +g has a fixed point in [a,b] -g has no fixed point in [a,b] -Depends on some other condition

{ If |g'(x)| > 1, then the iteration xn+1 = g (x) produces a sequence } +that diverges away from P -that converges towards P -Depends

{The fixed point iteration will diverge unless x0 = 0. +True -False
 * type=""}

{Consider the following fixed point iteration; $$f(x)=\frac 12\left(\frac ax + x\right)$$. Rate (order) of convergence of this iteration is +Quadratic -Linear -Cubic
 * type=""}

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

title: User:Kadamsujit


text:
User:Mikesmith00

Martin's Page

http://en.wikiversity.org/wiki/User:Mjmohio

Exercise Template
Factor the polynomial $$ 4x^2 + 4x + 1 $$ completely Solution: $$ (2x+1)^2 $$

Quiz template
{Solve the inequality $$ 4x^2 + 4x + 1 < 0$$ - All real numbers + No Solution - $$ x < 1/4 $$ - $$ x > 1/4 $$
 * type=""}

{ Solve the system $$\left[\begin{array}{c c}3 & 4 \\2 & 1\end{array} \right]\left[\begin{array}{c}x \\ y\end{array} \right] = \left[\begin{array}{c}0 \\0\end{array}\right]$$
 * type="{}"}

$$ x =  $$ { 1 } $$ y =  $$ { 1 }

My final project
For my final project, I would like to do a more in depth analysis of Gaussian quadrature integration methods. I would do an example using the change of variables to [a, b] from [-1, 1]. I would also do a discussion and example on how we can make our error term as small as we want numerically by increasing the number of zeros used, instead of just two points. So I would add 4 or 5 examples, both of normal polynomials, and functions that are not polynomial in nature, and I would make a quiz on the subject.

Final Report
For my final project, I felt that it was necessary to add information to Wikiversity on numerical integration. This is a huge part of mathematics that was completely neglected previously. I added the entire page Gaussian Quadrature, and there has only been one edit, which I can't determine what they changed. I also felt that if I were to add an entire new section, I shouldn't assume prior knowledge at levels higher than being able to perform simple integrations, so as to make it available to the widest number of possible users, while making it technically advanced enough to be of use to high level students. Before I started on the final project, I had done some homework problems and also done the in class presentation on Gaussian Quadrature, and found that in my opinion, it is a very powerful tool for doing quick integration with very little cost computationally. I did some introductory work earlier in the quarter getting comfortable with posting on Wikipedia by making some changes to the condition number page on Wikipedia. I wanted to add some information the condition number rule of thumb, although my instructor said that it wasn't quite enough material, so I added a little bit more quantifiers related to the rule of thumb. I posted my proposal to the discussion page, and there were no comments, so I went ahead and added my change, and it has not been edited. At this point I moved forward with my final project. My goal for the page was to move from simple problems with a narrow reach of uses but simple application, to simple problems with a wider reach of uses. Then in the end I wanted my page to show the full scope of uses for Gaussian quadrature. I feel like my examples meet this. Then in examples, I wanted first to confirm that the reader understands and can apply the algorithm to their own problems, and finally be able to prove that the algorithm works exactly for any polynomial of degree less than $$2n$$. I want the reader to be able to complete this proof, as I feel it gives a deeper understanding of what is happening in the algorithm, and what could cause the algorithm to fail. I didn't understand until I completely understood the proof why continuity was important for approximation. At the end, I wanted to add a quiz that was primarily theoretical. I don't feel like being able to turn the crank on an algorithm imparts much knowledge at all, although it is a useful skill to have. For our purposes though, understanding the theoretical underpinning of the material is far more important than being able to use the algorithm.

title: User:Mikesmith00


text:
User:MountainMelody

User Name -
 * Mountain Melody

Education - Certifications -
 * bachelor of music education
 * working on masters
 * Kodaly Certification
 * Orff Certification
 * Suzuki Piano
 * Jr. Great Books training (taught 2 years)

Work History -
 * private music studio (over 20 years)
 * public music teacher (instrumental and general music - 9 years)
 * home school teaching (4 years)
 * composer/arranger (not published - more of a hobby)

title: User:MountainMelody


text:
Northern Arizona University/Environmental Ethics/Journals/McWane F.'s Journal

Leopold journal entrys


text:
Northern Arizona University/Environmental Ethics/Journals/Leopold

Journal Entry #1 9/6/2010  I was sitting here starring out the window looking at the trees while the wind blew on them. I slowly continued to get a since that nature needed me. The need for me to explore it and to enjoy it. I think that this feeling comes from my instincts. Or even the ethical standards I have built into my "human storage locker." It's almost like I have a beconing call to come to nature! In the beginning of feburary, Leopold speaks of avoiding spiritual dangers 1 danger is having a farm to plant one's own food. The other is to have your own heat that came from oak that you split and staked. Why would Leopold speak of these things? I think he is trying to tell the reader to get out of the city, go to the forest and live off the land. To let go of the modern inventions of man and embrace the love that we all have for the land.

Journal Entry #2 "Our lumberpile recruited entirely from the river, is thus not only a collection of personalities, but an anthology of human strivings in upriver farms and forests." He speaks of these lumberpiles as having "personalities." These lumber boards must have many things attached to them and/or a lot of markings? In order to have much personality. "Lakes have boats, and there is always a chance that one might land to pay you a visit." I wonder what he means by this? The sentance before this one spoke of solitude. Does he mean that solitude can be visited but not in a lake because there are boats? I guess so. He goes on to speak of aloneness. He mentions that the road in and out is covered with water. The only traffic in or out will be carp. I love how he goes to the nature in everything he says. This fills my heart with joy! Draba is a flower that is so small one must be looking for it or be very close to the ground to see it. He says "He who despairs of spring with downcast eye steps on it." This sentance impells me to go out and look for this flower named Draba. This sentance seems soo sad for one to ignore all of nature its wonderful beauty! "Draba plucks no heartstrings." What does Leopold mean by this? He must mean the flower is not pretty enough to be given as a gift to someone that enjoys it truelly in their heart. Leopold continues to speak of the Draba in a bad way then says it does a good job quickly and well.

Journal Entry #3 " Bur oaks were the shock troops sent by the invading forest to storm the praire; fire is what they had to fight." I love how Leopold says something sad and emotional then says something wonderful and good. This paints a picture in my mind of trees running across a prairie plain towards a fire. Leopold goes onto speak of how engineers got the idea of insulation from these bur oak trees. Leopold talks of how the oaks marched the entire prairie and took over the land. These oaks having thick cork wood would not burn. As a result the oaks stopped the prairies from burning up. He also states how if you look at the rings on the trees one can varify his claim because the rings will date back to the 1850s or 60s. As soon as the farmers took a hold of the prairie fires, the grubs or roots of oak grew up into trees and formed tall thickets so dense that it was difficult to walk through them. The person that owns a farm of oak owns a library of evolution. This is do to the way the land has grown and become healthy with every waking day/week/minute. "The drama of the sky dance is enacted nightly on hundreds of farms, the owners of which sigh for entertainment, but harbour the illusion that it is to be sought in theaters. They live on the land not by the land." This to me is an example of all those that live and we must embrace this place we live in for its beauty and love and wonder! I feel this is what Leopold is saying to us.


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User talk:Thrace~enwikiversity

 Hello Thrace, 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

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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.

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Renamed
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title: User talk:Thrace~enwikiversity


text:
User:Opriter/Haiti Reconstruction

HAITI RECONSTRUCTION

1. /INTRODUCTION/

2. '''/MOVEMENT OF THE EARTH/ '''

2.1 Historical perspective 2.2 Theory of continental drift 2.3 Theory of plate tectonics 2.4 Plate boundaries 2.5 Plate tectonics and the earth's magnetism 2.6 Movement of the earth's crust 2.7 Changes in the shape of the crust 2.7.1 Folding 2.7.1.1 Generalities 2.7.1.2 Classification of folds 2.7.2 Faulting 2.7.2.1 Definition 2.7.2.2 Slip, heave and throw 2.7.2.3 Types of faults 2.7.2.3.1 Categories 2.7.2.3.2 Dip slip fault 2.7.2.3.2.1 Normal fault 2.7.2.3.2.2 Thrust fault 2.7.2.3.2.3 Graben fault 2.7.2.3.2.4 Horst fault 2.7.2.3.2.5 Detachment fault 2.7.2.3.2.6 Reverse fault 2.8 Formation of Earthquakes 2.8.1 Tremor 2.8.2 Definition of an earthquake 2.8.3 Theory of elastic rebound 2.8.4 Where earthquakes happen 2.8.5 Focus and Epicenter 2.8.6 Seismic waves 2.8.6.1 Primary 2.8.6.2 Secondary 2.8.6.3 Surface 2.8.6.4 Raleigh 2.8.6.5 Love 2.8.7 Richter scale 2.8.8 Mercalli scale 2.8.9 Moment magnitude scale 2.9 Frequently asked questions 2.10 World earthquakes 2.11 Earthquake prediction 2.12 Tectonic weapons 2.13 Induced seismicity

3. /GEOLOGY OF HAITI/ 3.1 Context and problems

4. /HAITI JANUARY 12TH EARTHQUAKE/

4.1 Scientific records

4.2 Modelisation

4.3 News or sequence of events of the January 12th

4.4 Blog comments

4.5 Earthquake prediction before January 12th

4.6 Haiti's catastrophic earthquakes

4.6 Why the January 12th earthquake was catastrophic?

4.7 Key facts

5. /SCIENTIFIC FOLLOW-UP/

6. /PLAN OF THE RECONSTRUCTION/

7. /EXECUTION OF THE PLAN/

8. /ANALYSIS AND CRITICISMS/

9. /PREVENTION: REGULATION AND PARASEISMIC CONSTRUCTION/

10. /CONCEPT OF RISK: MANAGEMENT OF SEISMIC RISK/

11. /DISASTER MANAGEMENT/

12./NATURAL DISASTERS:CHOLERA AND HURRICANES/

13. /NATURAl DISASTER HAZARDS/

14. /ECONOMY/

15. '''/POLITICS AND ELECTIONS/ '''

title: User:Opriter/Haiti Reconstruction


text:
User talk:Larah~enwikiversity

 Hello Larah, 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

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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. --Mu301Bot 07:17, 12 October 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 12 October 2010 (UTC)

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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 Larah. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Larah~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 23:36, 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) 06:14, 19 April 2015 (UTC)

title: User talk:Larah~enwikiversity


text:
Turkish/Pronouns

Statement of learning goals for this resource
From this lesson you will understand the basic Turkish pronouns and how to use them in sentences.

To be
The verb "to be" in Turkish is always an ending added to the noun. These endings are either -im, -sin, -iz, -siniz, or -ler depending on the pronoun.

Below is an example using the Turkish word for pretty: güzel.

Dropping the Personal Pronoun
In Turkish, the personal pronoun is usually assumed in a sentence. Thus, most of the time it is dropped. For example:

Practice
Complete the following examples using the vocab provided below.

Vocab

iyi = good

beyaz = white

mutlu = happy

sıcak = hot

soğuk = cold

büyük = big

Two Vowels in a Row
When you add a "to be" suffix to a word, and the result has two vowels in a row, you add a -y- between them as a buffer. For example:

"iyi" means good. To say "I am good", you add the -im suffix. The result is iyiim but since you cannot have two "i"s together, you add the -y- which makes iyiyim, meaning "I am good".

title: Turkish/Pronouns


text:
User talk:Wleifbwilue~vanished

 Hello Abbatai, 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

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title: User talk:Wleifbwilue~vanished


text:
User talk:Janwe.dave

 Hello Janwe.dave, 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

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title: User talk:Janwe.dave


text:
User talk:Milljason22

 Hello Milljason22, 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

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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) 13:28, 12 October 2010 (UTC)

title: User talk:Milljason22


text:
User talk:Opriter

 Hello Opriter, 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.
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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) 13:28, 12 October 2010 (UTC)

Some other Haiti wiki efforts you may be able to coordinate with include: Sincerely, -- Jtneill - Talk - c 22:49, 12 March 2011 (UTC)
 * 2010 Haiti earthquake
 * http://sites.google.com/site/haitiearthquake/
 * https://failures.wikispaces.com/2010+Haiti+Earthquake
 * http://inventory.ict4peace.org/Haiti+Earthquake+-+January+2010

You can create draft pages in your user space e.g., User:Opriter/Draft page. This is not private, but gives a chance to develop content before putting into the main space. Please let me know if I can help more. -- Jtneill - Talk - c 23:31, 12 March 2011 (UTC)
 * I've userfied or moved the relevant resources that you've created to your subpages as User:Opriter/Haiti Reconstruction, User:Opriter/Haiti Reconstruction/INTRODUCTION and User:Opriter/Math, respectively. Please take the time given to properly develop the pages in your userspace before publishing them in the mainspace. TeleComNasSprVen 09:03, 13 March 2011 (UTC)
 * Thanks for doing this, TeleComNasSprVen. As requested, Opriter, I've restored the three pages I deleted from the main space to your user space and added links from User:Opriter.

title: User talk:Opriter


text:
User talk:Positron

You can write me here, but I'm more active in | in the English Wikipedia. --Positron 13:36, 12 October 2010 (UTC)

title: User talk:Positron


text:
Fluid Mechanics for MAP/Fluid Statics

>back to Chapters

Definitions
Fluid statics is the study of fluids which are either at rest or in rigid body motion  with respect to a fixed frame of reference. Rigid body motion means that there is no relative velocity between the fluid particles.

In a fluid at rest, there is no shear stress, i. e. fluid does not deform, but fluid sustains normal stresses.

We can apply Newton's second law of motion to evaluate the reaction of the particle to the applied forces.

Force balance in $$ \displaystyle i^{th}$$ direction:

$$\displaystyle F_{i}^{net} = m\cdot a_{i}$$

We can also say,$$ \displaystyle F_{i}^{body} + F_{i}^{surf}= m\cdot a_{i}$$

Force created by pressure is :

$$ \displaystyle F^{surf} = F^{pressure} = -p\cdot \vec{A}$$

$$ \displaystyle \vec{A}$$ is the vector having the surface area as magnitude and surface normal as direction.

Thus,

$$ \displaystyle F^{pressure} = -p\cdot\vec{A} = -p\ A \ \vec{n}$$

Force caused by the pressures opposite to the surface normal.

For a differential fluid element: $$\displaystyle dF_{i}^{body} + dF_{i}^{surf} = dm\cdot a_{i}$$

Remember Taylor Series expansion: $$ \displaystyle F(x+\Delta x) = F + \frac{\partial F}{\partial x} + \frac{1}{2}\frac{\partial ^{2}F}{\partial x^{2}}\Delta x^{2} + \ldots$$

P is the pressure in the center of the fluid element, therefore the pressure on the surface in direction of $$x_i$$ is $$P + \frac{\partial P}{\partial x_{i}}\frac{dx_{i}}{2}$$.

Thus,
 * $$ \displaystyle dF_{2}^{pressure} = \left[P-\frac{\partial P}{\partial x_{2}}\frac{dx_{2}}{2}\right]dx_{1}\ dx_{3} - \left[P + \frac{\partial P}{\partial x_{2}}\frac{dx_{2}}{2}\right]dx_{1}\ dx_{3}$$:$$\displaystyle =-\frac{\partial P}{\partial x_{2}}dx_{1}dx_{2}dx_{3} = -\frac{\partial P}{\partial x_{2}}dV$$

$$ \displaystyle dF_{i}^{pressure} = -\frac{\partial P}{\partial x_{i}}dV$$

$$ \displaystyle dF_{i}^{body} = dm\ g_{i}$$

Thus,

$$ \displaystyle -\frac{\partial P}{\partial x_{i}}dV + dm\ g_{i} = dm\ a_{i}$$ or,$$ \displaystyle -\frac{\partial P}{\partial x_{i}}dV + \rho\ dV\ g_{i} = \rho\ a_{i}$$

or,$$ \displaystyle -\frac{\partial P}{\partial x_{i}} + \rho\ g_{i} = \rho a_{i}$$

or,$$ \displaystyle -\frac{\partial P}{\partial x_{1}} = \rho a_{1}\ ; \ -\frac{\partial P}{\partial x_{2}} = \rho a_{2}\ ; \ -\frac{\partial P}{\partial x_{3}} - \rho g = \rho a_{3}$$

for $$ \displaystyle a_{i}=0$$

$$ \displaystyle \frac{\partial P}{\partial x_{1}} = 0 \ ; \ \frac{\partial P}{\partial x_{2}} = 0 \ ; \ \frac{\partial P}{\partial x_{3}} = -\rho g$$

Pressure changes only in $$ \displaystyle x_{3}$$ direction.

Pressure variation in an incompressible and static fluid

$$ \displaystyle \frac{\partial P}{\partial x_{3}} = -\rho g \ ; \ x_{3} = z \rightarrow \frac{\partial P}{\partial z} = - \rho g $$ is constant since $$ \displaystyle \rho$$ and $$ \displaystyle g$$ are constants.

$$ \displaystyle \int^{p_{2}}_{p_{1}}{dP} = -\int^{z_{2}}_{z_{1}}{\rho g dz}$$

$$ \displaystyle p_{2} - p_{1} = -\rho g\ (z_{2}-z_{1})$$

If we take $$ \displaystyle p_{2}$$ at the surface, then:

$$ \displaystyle p_{atm}-p_{1} = -\rho g\ (z_{2}-z_{1})$$

$$ \displaystyle p_{1} = p_{atm} + \rho gh\ ; \ \ h = z_{2}-z_{1}$$

h is measured from the surface.

Other related topics
Buoyancy and calculation of forces on the submerged surfaces are topics related to fluid statics.

title: Fluid Mechanics for MAP/Fluid Statics


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Fluid Mechanics for MAP/Fluid Dynamics

>back to Chapters of Fluid Mechanics for MAP

>back to Chapters of Microfluid Mechanics

Introduction
Differential Approach: We seek solution at every point $$ \displaystyle (x_{1},x_{2},x_{3})$$, i.e describe the detailed flow pattern at all points.

Integral Approach: We focus on a control volume (CV), which is a finite region. It determines gross flow effects such as force or torque on a body or the total energy exchange. For this purpose, balances of incoming and outgoing flux of mass, momentum and energy are made through this finite region. It gives very fast engineering answers, sometimes crude but useful.

Lagrangian versus Eulerian Approach: Substantial Derivative
Let $$ \displaystyle \alpha$$ be any flow variable (pressure, velocity, etc.). Eulerian approach deals with the description of $$ \displaystyle \alpha$$ at each location $$ \displaystyle (x_{i})$$ and time (t). For example, measurement of pressure at all $$ \displaystyle x_{i}$$ defines the pressure field: $$ \displaystyle P(x_{1},x_{2},x_{3},t)$$. Other field variables of the flow are:

$$ \displaystyle U_{j}(x_{1},t), P(x_{1},t), \rho(x_{1},t), T(x_{1}), \tau_{jk}(x_{1},t) \Rightarrow \alpha(x_{i},t)$$

Lagrangian approach tracks a fluid particle and determines its properties as it moves.

$$ \displaystyle x_{i}|_{p}(t+\Delta t) = x_{i}|_{p}(t) + \int^{t+\Delta t}_{t}U_{i}|_{p}(t')dt'$$

Oceanographic measurements made with floating sensors delivering location, pressure and temperature data, is one example of this approach. X-ray opaque dyes, which are used to trace blood flow in arteries, is another example.

Let $$ \displaystyle \alpha_{p}$$ be the variable of the particle (substance) P, this $$ \displaystyle \alpha_{p}$$ is called "substantial variable".

For this variable:

$$ \displaystyle \alpha_{p}(\vec{x_{p}},t)$$ and $$ \displaystyle \vec{x_{p}} = \vec{x_{p}}(t) \rightarrow \alpha_{p}(\vec{x_{p}},t) = \alpha_{p}(t)$$

In other words, one observes the change of variable $$ \displaystyle \alpha$$ for a selected amount of mass of fixed identity, such that for the fluid particle, every change is a function of time only.

In a fluid flow, due to excessive number of fluid particles, Lagrangian approach is not widely used.

Thus, for a particle P finding itself at point $$ \displaystyle x_{i}$$ for a given time, we can write the equality with the field variable:

$$ \displaystyle \alpha_{p}(t) = \alpha \left[(x_{i})_{p},t\right]$$

Along the path of the particle:

$$ \displaystyle \alpha_{p}(t + \Delta t) = \alpha \left[(x_{i} + \Delta x_{i})_{p}, t + \Delta t\right]$$

Hence,

$$ \displaystyle d\alpha_{p} = \alpha \left[((x_{i} + \Delta x_{i})_{p}, t + \Delta t) - \alpha ((x_{i})_{p},t)\right]$$

$$ \displaystyle d\alpha_{p} = \frac{\partial \alpha}{\partial t}dt + \frac{\partial \alpha}{\partial x_{i}}dx_{ip}$$

$$ \displaystyle \frac{d\alpha_{p}}{dt} = \frac{\partial \alpha}{\partial t} + \left(\frac{\partial \alpha}{\partial x_{i}}\right)\left(\frac{dx_{i}}{dt}\right)_{p} = \underbrace{\frac{\partial \alpha}{\partial t}}_{Local\ change\ in\ time} + \underbrace{\frac{\partial \alpha}{\partial x_{i}}U_{i}}_{Change\ in\ space}$$

The local change in time is the local time derivative (unsteadiness of the flow) and the change in space is the change along the path of the particle by means of the convective derivative.

$$ \displaystyle \frac{d\alpha_{p}}{dt} = \frac{D\alpha}{Dt} = \left(\frac{\partial }{\partial t} + U_{i}\frac{\partial }{\partial x_{i}}\right)\alpha$$

The substantial derivative connects the Lagrangian and Eulerian variables.

System versus Control volume
In mechanics, system is a collection of matter of fixed identity (always the same atoms or fluid particles) which may move, flow and interact with its surroundings.

Hence, the mass is constant for a system, although it may continually change size and shape. This approach is very useful in statics and dynamics, in which the system can be isolated from its surrounding and its interaction with the surrounding can be analysed by using a free-body diagram.

In fluid dynamics, it is very hard to identify and follow a specific quantity of the fluid. Imagine a river and you have to follow a specific mass of water along the river.

Mostly, we are rather interested in determining forces on surfaces, for example on the surfaces of airplanes and cars. Hence, instead of system approach, we identify a specific volume in space (associated with our geometry of interest) and analyse the flow within, through or around this volume. This specific volume is called "Control Volume". This control volume can be fixed, moving or even deforming.

The control volume is a specific geometric entity independent of the flowing fluid. The matter within a control volume may change with time, and the mass may not remain constant.

Conservation of mass
The mass of a system do not change:

$$ \displaystyle \displaystyle \frac{dM}{dt}_{system}\bigg| = 0$$

where, $$ \displaystyle \displaystyle M = \int_{mass(system)}{dm} = \int_{V(system)}{\rho dV}$$

Newton's second law
For a system moving relative to a inertial reference frame, the sum of all external forces acting on the system is equal to the time rate of change of linear momentum ($$ \displaystyle \vec{P}$$) of the system:

$$ \displaystyle F_{i} = \frac{dP_{i}}{dt}\bigg|_{system}$$

$$ \displaystyle \displaystyle P_{i(system)} = \int_{mass(system)}{U_{i}dm} = \int_{V(system)}{U_{i}\rho dV}$$

The first law of Thermodynamics
$$ \displaystyle \underbrace{dQ}_{heat\ added\ on\ system} + \underbrace{dW}_{work\ done\ on\ system} = dE$$

in the rate form:

$$ \displaystyle \dot{Q} + \dot{W} = \frac{dE}{dt}\bigg|_{system}$$

where $$ \displaystyle \displaystyle E_{system} = \int_{mass(system)}{e dm} = \int_{V(system)}{e\rho dV}$$

and  $$ \displaystyle \displaystyle e = \underbrace{u}_{Intenral \ energy} + \underbrace{\frac{U_{i}U_{i}}{2}}_{Kinetic\ energy} + \underbrace{gz}_{Potential\ energy}$$

There are also other laws like the conservation of moment of momentum (angular momentum) and second law of thermodynamics, but they are not the subject of this course and will not be treated here.

Note that all basic laws are written for a system, i.e defined mass with fixed identity. We should rephrase these laws for a control volume.

One dimensional Reynolds Transport Theorem
Consider a flow through a nozzle.

If $$ \displaystyle B $$ is an extensive variable of the system.

$$ \displaystyle B_{sys}(t) = B_{cv}(t)$$

$$ \displaystyle \displaystyle B_{sys}(t + \Delta t) = B_{cv}(t + \Delta t) - B_{I}(t + \Delta t) +

B_{II}(t + \Delta t)$$

$$ \displaystyle \frac{\Delta B_{sys}}{\Delta t} = \frac{B_{sys}(t + \Delta t) - B_{sys}(t)}{\Delta t} = \frac{B_{cv}(t + \Delta t) - B_{cv}(t)}{\Delta t}\ -\ \frac{B_{I}(t + \Delta t)}{\Delta t}\ +\ \frac{B_{II}(t + \Delta t)}{\Delta t}$$

The first term for $$ \displaystyle \Delta t \rightarrow 0$$

$$ \displaystyle \lim_{\Delta t \rightarrow 0} \frac{B_{cv}(t + \Delta t) - B_{cv}(t)}{\Delta t} = \frac{\partial B_{cv}}{\partial t}$$

$$ \displaystyle B_{II}(t + \Delta t)$$ for $$ \displaystyle \Delta t \rightarrow 0$$

$$ \displaystyle B_{II}(t + \Delta t) = \rho_{2}b_{2}\Delta V_{2}$$

$$ \displaystyle \displaystyle B_{II}(t + \Delta t) = \rho_{2}b_{2}A_{2}l_{2} = \rho_{2}b_{2}A_{2}U_{2}\Delta t$$

$$ \displaystyle \displaystyle B_{out} = \rho_{2}b_{2}A_{2}U_{2}\Delta t$$

Similarly

$$ \displaystyle \displaystyle B_{I}(t + \Delta t) = \rho_{1}b_{1}\Delta V_{1} = \rho_{1}b_{1}A_{1}U_{1}\Delta t = B_{in}$$

Thus, for $$ \displaystyle \Delta t \rightarrow 0$$, the terms in the equality for the time derivative of the system are

$$ \displaystyle \frac{\Delta B_{sys}}{\Delta t} \rightarrow \frac{dB_{sys}}{dt}$$

$$ \displaystyle \frac{B_{in}}{\Delta t}=\dot{B}_{in}$$

$$ \displaystyle \frac{B_{out}}{\Delta t}=\dot{B}_{out}$$

so that, $$ \displaystyle \frac{dB_{sys}}{dt} = \frac{\partial B_{cv}}{\partial t} + \dot{B}_{out} - \dot{B}_{in}$$

This is the equation of 1 dimensional Reynolds transport theorem (RTT).

{| cellspacing="10" cellpadding="10" style="margin:0em 0em 1em 0em; width:100%"
 * rowspan="1" style="width:50%; vertical-align:top; border:1px white; background-color: white;" |

The three terms on the RHS of RTT are:

1. The rate of change of B within CV indicates the local unsteady effect.

2. The flux of B passing out of the CS.

3. The flux of B passing into the CS.

There can be more than one inlet and outlet.

Three Dimensional Reynolds Transport Theorem
Hence, for a quite complex, unsteady, three dimensional situation, we need a more general form of RTT. Consider an arbitrary 3-D CV and the outward unit normal vector $$ (\vec{n}) $$ defined at each point on the CS. The outflow and inflow flux of $$ B$$ across CS can be written as:

$$ \displaystyle \dot{B}_{out} = \int_{CSout}{dB_{out}} = \int_{CSout}{\rho b \vec{U}\cdot\vec{n}dA}$$

$$ \displaystyle \dot{B}_{in} = \int_{CSin}{dB_{in}} = -\int_{CSin}{\rho b \vec{U}\cdot\vec{n}dA}$$

$$ \displaystyle \dot{B}_{in}$$ and $$ \displaystyle \dot{B}_{out}$$ are positive quantities. Therefore, the negative sign is introduced into $$ \displaystyle \dot{B}_{in}$$, to compensate the negative value of $$ \displaystyle\vec{U}\cdot\vec{n}$$.

$$ \displaystyle \frac{dB_{sys}}{dt} = \frac{\partial B_{cv}}{\partial t} + \int_{CSout}{\rho b \vec{U}\cdot\vec{n}dA} + \int_{CSin}{\rho b \vec{U}\cdot\vec{n}dA}$$

$$ \displaystyle \frac{dB_{sys}}{dt} = \frac{\partial}{\partial t}\int_{cv}{\rho b dV} + \int_{cs}{\rho b \vec{U}\cdot\vec{n}dA}$$

Since $$ \displaystyle \rho \vec{u}\cdot \vec{n} dA = dm$$, RTT can be written as:

$$ \displaystyle \frac{dB_{sys}}{dt} = \frac{\partial B_{cv}}{\partial t} + \underbrace{\int_{CS}{bdm}}_{net\ flux\ of\ B\ across\ CS}$$

It is possible that CV can move with constant velocity or arbitrary acceleration.

This form of RTT is valid if the CV has no acceleration with respect to a fixed (inertial) reference frame. RTT is then valid for a moving CV with constant velocity when:

1. All velocities are measured relative to the CV.

2. All time derivative measure relative to the CV.

Thus for a CV moving with $$ \displaystyle \vec{U}_{s}$$

$$ \displaystyle \vec{U}_{r} = \vec{U} - \vec{U}_{s}$$

$$ \displaystyle \frac{dB_{sys}}{dt} = \frac{d}{dt}\left(\int_{cv}{b \rho dV}\right) + \int_{cs}{b \rho \vec{U_{r}}\cdot \vec{n}dA}$$

These issues will be covered again.

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Conservation of mass
$$ \displaystyle B = M, b = 1$$

$$ \displaystyle \frac{dM_{sys}}{dt} = \frac{\partial}{\partial t}\int_{cv}{b\rho dV} + \int_{cs}{b\rho \vec{U}\cdot\vec{n} dA} = 0$$

i.e

$$ \displaystyle \underbrace{\frac{\partial}{\partial t}\int_{cv}{\rho dV}}_{rate\ of \ change\ of\ mass\ in \ CV} + \underbrace{\int_{cs}{\rho \vec{U}\cdot \vec{n} dA}}_{net\ rate\ of\ mass\ flux\ through\ the\ CS} = 0$$

Assume $$ \displaystyle \rho$$ = constant (incompressible)

$$ \displaystyle 0 = \rho\frac{\partial}{\partial t} \int_{cv}{dV} + \rho\int_{cs}{\vec{U}\cdot\vec{n}dA}$$

As $$ \displaystyle V $$ of CV is also constant, the time derivative drops out:

$$ \displaystyle 0 = \rho \int_{cs}{\vec{U}\cdot\vec{n}dA}\rightarrow\underbrace{\int_{cs}{\vec{U}\cdot\vec{n}dA}}_{volume\ flow\ rate} = 0$$

The net volume flow rate should be zero through the control surfaces.

Note that we did not assume a steady flow. This equation is valid for both steady and unsteady flows.

If the flow is steady,

$$ \displaystyle 0 = \int_{cs}{\rho \vec{U}\cdot\vec{n}dA} \rightarrow \text{Net mass  flow rate is equal to zero} $$

there is no-mass accumulation or deficit in the control volume.

Linear Momentum equation for inertial control volume
$$ \displaystyle B = \vec{P}$$, $$ \displaystyle b  =  \vec{U}$$

$$ \displaystyle \frac{d\vec{P}}{dt}_{system} = \frac{\partial}{\partial t}\int_{cv}{\vec{U}\rho dV} + \underbrace{\int_{cs}{\vec{U}\rho \vec{U}\cdot\vec{n}dA}}_{momentum\ flux}$$

$$ \displaystyle \frac{d\vec{P}}{dt}_{system} = \vec{F}_{on\ system}$$

This equation states that the sum of all forces acting on a non-accelerating CV is equal to the sum of the net rate of change of momentum inside the CV and the net rate of momentum flux through the CS.

Force on the system is the sum of surface forces and body forces.

$$ \displaystyle \vec{F}_{on\ system} = \vec{F_{S}} + \vec{F_{B}}$$

The surface forces are mainly due to pressure, which is normal to the surface, and viscous stresses, which can be both normal or tangential to the surfaces.

$$ \displaystyle \vec{F}_{pressure} = -\int_{A}{P\vec{n}dA}$$

$$ \displaystyle \vec{F}_{v.stresses} = \int_{A}{\tau dA}$$

The body forces can be due to gravity or magnetic field.

at the initial moment $$ \displaystyle t$$

$$ \displaystyle \vec{F}_{on\ system} = \vec{F}_{on\ CV}$$

i.e. in component form:

$$ \displaystyle F_{Si} + F_{Bi} = \frac{\partial}{\partial t}\int_{cv}{U_{i}\rho dV} + \int_{cs}{U_{i}\rho U_{j}n_{j} dA}$$

First law of Thermodynamics
$$ \displaystyle B = E, b = e$$

$$ \displaystyle \frac{dE}{dt}_{system} = \frac{\partial}{\partial t}\int_{cv}{e\rho dV} + \int_{cs}{e\rho \vec{U}\cdot\vec{n}dA}$$

at the initial moment $$ \displaystyle t $$, the following equality is valid:

$$ \displaystyle \frac{dE}{dt}_{system} = [\dot{Q} + \dot{W}]_{system} = [\dot{Q} + \dot{W}]_{cv}$$

thus, the integral form of energy equation is:

$$ \displaystyle [\dot{Q} + \dot{W}]_{cv}= \frac{\partial}{\partial t}\int_{cv}{e\rho dV} + \int_{cs}{e\rho \vec{U}\cdot\vec{n}dA}$$

Examples
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Example 1
Consider the mass balance in a stream tube by using the integral form of the conservatin of mass equation.

Let $$ \displaystyle A_{1}$$ and $$ \displaystyle A_{2}$$ be too small such that the velocities $$ \displaystyle \vec{U}$$ at position 1 and 2 are uniform across $$ \displaystyle A_{1}$$ and $$ \displaystyle A_{2}$$.

$$ \displaystyle \frac{\partial}{\partial t}\int_{cv}{\rho dV} + \int_{cs}{\rho \vec{U}\cdot\vec{n}dA} = 0$$

The first term is zero and the second term can be analyzed by decomposing the integration area.

$$ \displaystyle \int_{CS_I}{\rho \vec{U}\cdot\vec{n}dA} + \int_{CS_{III}}{\rho \vec{U}\cdot\vec{n}} dA + \int_{CS_{II}}{\rho\vec{U}\cdot\vec{n}dA} = 0$$

where the integration over $$ \displaystyle CS_{III}$$ is zero, because there is no flow across the streamtube. Thus,

$$ \displaystyle \displaystyle -\rho U_{1}A_{1} + 0 + \rho U_{2}A_{2} = 0$$

$$ \displaystyle \rho U_{1}A_{1} = \rho U_{2}A_{2} \rightarrow U_{2} = \frac{U_{1}A_{1}}{A_{2}}$$

$$ \displaystyle \dot{m}_{1} = \dot{m}_{2}$$

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Example 4

Water from a stationary nozzle strikes to a plate. Assume that the flow is normal to the plate and in the jet velocity is uniform. Determine the force on the plate in $$ \displaystyle x_{1}$$ direction.

Independent from the selected CV.

$$ \displaystyle 0 = \int_{cs}{\rho U_{i}n_{i}dA}\ (mass)$$

$$ \displaystyle F_{i} = F_{Si} + F_{Bi} = \int_{cs}{U_{i}\rho U_{j}n_{j}dA}\ (momentum)$$

No body force in $$ \displaystyle x_{1}$$ direction.

$$ \displaystyle \displaystyle F_{1} = F_{S1} = \int_{cs}{U_{1}\rho U_{j}n_{j}dA}$$

$$ \displaystyle \displaystyle F_{S1} = p_{a}A - p_{a}A + R_{1}$$

$$ \displaystyle R_{1} = \int_{cs}{U_{1}\rho U_{j}n_{j}dA} = \int_{CS1}{U_{1}^{1}\rho U_{j}^{1}n_{j}dA} + \underbrace{\int_{CS2}{U_{1}^{2}\rho U_{j}^{2}n_{j}dA}}_{0} + \underbrace{\int_{CS3}{U_{1}^{3}\rho U_{j}^{3}n_{j}dA}}_{0}$$

$$ \displaystyle U_{1} = 0$$ at 2 and 3.

$$ \displaystyle R_{1} = -U_{1}\rho U_{1}A_{Jet}$$

The force which acts on the plate (action-reaction) is $$ \displaystyle K_{1} = -R_{1} = U_{1}\rho U_{1}A_{Jet}$$

It is also possible to solve the problem with $$ \displaystyle CV_{2}$$

$$ \displaystyle F_{S1} = p_{a}A + R_{1} = - U_{1}^{2}A_{jet}\rho$$

$$ \displaystyle R_{1} = -p_{a}A - U_{1}^{2}A_{Jet}\rho$$

Hence, the force exerted on the plate by the CV is

$$ \displaystyle K_{1} = - R_{1}$$

$$ \displaystyle \displaystyle F_{net} = -R_{1} - p_{a}A$$

$$ \displaystyle F_{net} = p_{a}A + U_{1}^{2}A\rho - p_{a}A$$

$$ \displaystyle F_{net} = U_{1}^{2}A\rho$$

Example 5
Consider the plate exposed to uniform velocity. The flow is steady and incompressible. A boundary layer builds up on the plate. Determine the Drag force on the plate. Note that $$ \displaystyle U_{1}$$ can be approximated at L.

$$ \displaystyle U_{1}(L, x_{2}) = U\left(2\frac{x_{2}}{\delta} - \left(\frac{x_{2}}{\delta}\right)^{2}\right)$$

Apply conservation of mass

$$ \displaystyle \displaystyle \rho\int_{cs}{U_{i}n_{i}dA} = 0$$

$$ \displaystyle \rho\int_{0}^{h}{-U_{0}\ w\ dx_{2}} + \rho\int_{0}^{\delta}{U\ w\ dx_{2}} = 0$$

$$ \displaystyle U_{0}h = \int_{0}^{\delta}{Udx_{2}}$$

$$ \displaystyle F_{i} = \underbrace{\frac{\partial}{\partial t}\int{U_{i}\rho dV}}_{=0\ steady\ state} + \int_{cs}{U_{i}\rho U_{j}n_{j}dA}$$

$$ \displaystyle F_{1} = -D = \int_{0}^{h}{U_{1}\rho U_{j}n_{j}dA} + \underbrace{\int_{CS2}{U_{1}\rho U_{j}n_{j}dA}}_{= 0\ streamline} + \int_{0}^{\delta}{U_{1}\rho U_{j}n_{j}dA} + \underbrace{\int{U_{1}\rho U_{j}n_{j}dA}}_{= 0\ wall}$$

$$ \displaystyle -D = -U_{0}\rho U_{0}\ h\ w + \int{U_{1}\rho U_{1}\ w\ dx_{2}}$$

$$ \displaystyle D = U_{0}^{2}\rho \ h\ w - \rho\ w\int_{0}^{\delta}{U_{1}^{2}dx_{2}}= \rho U_{0}\int_{0}^{\delta}{U_{1}dx_{2}}-\rho\ w\int_{0}^{\delta}{U_{0}U_{1}dx_{2}}$$

Insert the mass conservation result into the momentum equation.

$$ \displaystyle D = \rho w \int_{0}^{\delta}{U_{1}(U_{0} - U_{1})dx_{2}}|_{x_{1} = L}$$

$$ \displaystyle U_{1}$$ is known.Here,using $$ \displaystyle \frac{x_{2}}{\delta} = \eta$$

$$ \displaystyle D = \rho\ w\ U_{0}^{2}\delta \int_{0}^{1}{(2\eta - \eta^{2})(1 - 2\eta + \eta^{2})d\eta} = \frac{2}{15}\rho U_{0}^{2}w\ \delta$$

Momentum Equation for CV with rectilinear acceleration
For an inertial CV the following transport equation for momentum holds:

$$ \displaystyle \vec{F} = \frac{\partial}{\partial t}\int_{cv}{\vec{U}\rho\ dV} + \int_{cs}{\vec{U}\rho\vec{U}\cdot\vec{n}dA} $$

However, not all CV are inertial: for example a rocket must accelerate if it is to get off the ground.

Denote an inertial reference frame with $$ \displaystyle X_{1},X_{2},X_{3}$$ and another reference frame moving with the system $$ \displaystyle x_{1},x_{2},x_{3}$$. Hence, $$ \displaystyle x_{1},x_{2},x_{3}$$ becomes the non-inertial frame of reference. Let the system to move with a velocity and an acceleration $$ \displaystyle \vec{U}_{rf}$$ and $$ \displaystyle \vec{a}_{rf}$$ respectively. Here $$\displaystyle \overrightarrow U_{X}= \overrightarrow U_{x}+\overrightarrow U_{rf}$$ and accordingly with time derivative dt, $$\displaystyle \frac{d\overrightarrow U_{X}}{dt}= \frac{d\overrightarrow U_{x}}{dt}+\frac{d\overrightarrow U_{rf}}{dt} \Rightarrow \frac{d\overrightarrow U_{X}}{dt} \ne \frac{d\overrightarrow U_{x}}{dt}$$ or,$$ \displaystyle \vec{a}_{X} = \vec{a}_{x} + \vec{a}_{rf}\Rightarrow \frac{d\overrightarrow P_{X}}{dt} \ne \frac{d\overrightarrow P_{x}}{dt}$$ These above relationship implies that the velocity and the acceleration is not same when considered from inertial and moving reference frame. The Newton's second law states that:

$$ \displaystyle \left.\vec{F}\right|_{system} = \left.\frac{d\vec P_X}{dt}\right|_{system} $$

Thus the following relation holds for the fluid velocity in the system

$$ \displaystyle \vec{U}_{x} = \vec{U}_{X} - \vec{U}_{rf}$$

Where $$ \displaystyle \vec{U}_{x}$$ is the velocity of the fluid in the system with respect to a non-inertial reference frame, $$ \displaystyle \vec{U}_{X}$$ is the velocity of the fluid in the system with respect to the inertial reference frame. Accordingly, the acceleration reads:

$$ \displaystyle \frac{d\vec{U}_{x}}{dt} = \frac{d\vec{U}_{X}}{dt} - \frac{d\vec{U}_{rf}}{dt} (1) $$

$$ \displaystyle \vec{a}_{x} = \vec{a}_{X} - \vec{a}_{rf}$$

For a control volume moving with $$ \displaystyle \vec{U}_{rf}$$ and $$ \displaystyle \vec{a}_{rf}$$

$$ \displaystyle \frac{d\vec{U}_{CV}}{dt}=\frac{d\vec{U}_{rf}}{dt}$$

Thus for cases, where $$ \displaystyle \frac{dU_{cv}}{dt} \neq 0$$, the time derivative of $$ \displaystyle \vec{P}_{X}$$ and $$ \displaystyle \vec{P}_{x}$$ are not equal for a system accelerating relative to an inertial reference frame, i.e. RTT is not valid for an accelerating control volume.

To develop momentum equation for an accelerating CV, it is necessary to relate $$ \displaystyle \vec{P}_{X}$$ to $$ \displaystyle \vec{P}_{x}$$.

Previously we have seen that in a non-inertial reference frame having rectilinear acceleration, i.e. (translational acceleration).

$$ \displaystyle \vec{a}_{X} = \vec{a}_{x} + \vec{a}_{rf}$$ and also

$$ \displaystyle \vec{F} = \int_{mass\ (system)}{ \vec a_{X}dm}$$

$$ \displaystyle =\int_{mass\ (system)}{(\vec{a}_{x} + \vec{a}_{rf})dm}$$

$$ \displaystyle \vec{F} - \int_{mass\ (system)}{\vec{a}_{rf}dm} = \int_{mass\ (system)}{\vec{a}_{x}dm}$$

$$ \displaystyle \vec{F} - \int_{mass\ (system)}{\vec{a}_{rf}dm} = \int_{mass\ (system)}{\frac{d\vec{U}_{x}}{dt}dm} = \frac{d}{dt}\int_{mass\ (system)}{\vec{U}_{x}dm}$$

$$ \displaystyle \vec{F} - \int_{V\ (system)}{\vec{a}_{rf}\rho\ dV} = \frac{d\vec{P}_{x}}{dt}|_{system}$$

For a moving CV we know that

$$ \displaystyle \frac{d\vec{P}_{x}}{dt}|_{system} = \frac{\partial}{\partial t}\int_{cv}{\vec{U}_{x}\rho\ dV} + \int_{cs}{\vec{U}_{x}\rho\vec{U}_{x}\cdot\vec{n}dA}$$

Let system and CV coincides at an instant $$ \displaystyle t_0$$:

$$ \displaystyle \vec{F}_{on\ system} -\int_{V\ system}{\vec{a}_{rf}\rho dV} = \vec{F}_{on\ cv} - \int_{cv}{\vec{a}_{rf}\rho dV}$$

$$ \displaystyle \vec{F}_{on\ cv} - \int_{cv}{\vec{a}_{rf}\rho dV} = \frac{\partial}{\partial t}\int_{cv}{\vec{U}_{x}\rho\ dV} + \int_{cs}{\vec{U}_{x}\rho \vec{U}_{x}\cdot \vec{n}dA}$$

Extension of Energy equation for CV
$$ \displaystyle \left[\dot{Q} + \dot{W}\right]_{on\ system} = \left[\dot{Q} + \dot{W}\right]_{on\ cv} = \frac{\partial}{\partial t}\int{e\rho\ dV} + \int_{cs}{e\rho \vec{U}\cdot\vec{n}dA} $$

where $$ \displaystyle e = U + \frac{\left|\vec{U}\right|^{2}}{2} + g\ z$$

$$ \displaystyle \dot{W}_{on\ cv} = \dot{W}_{body} + \dot{W}_{surface}$$

here $$ \displaystyle z = x_{2}$$

$$ \displaystyle \dot{W}_{body} = \dot{W}_{shaft} + \dot{W}_{elec} + \dot{W}_{other} $$

$$ \displaystyle \dot{W}_{surface} = \dot{W}_{normal} + \dot{W}_{shear} $$

$$ \displaystyle \vec{\tau}_{s}$$ is the stress in the plane of dA.

Special form of the Energy equation
For a CV with one inlet 1, one outlet 2 and steady uniform flow through it.

$$ \displaystyle \underbrace{\dot{Q} + \dot{W}_{shaft} + \dot{W}_{shear}}_{K} = \int_{cs}{\left(u + \frac{p}{\rho} + \frac{\left|\vec{U}^{2}\right|}{2} + gz\right)\rho\vec{U}\cdot\vec{n}dA}$$

For uniform flow properties at the inlet and outlet.

$$ \displaystyle K = \left(u_{1} + \frac{p_{1}}{\rho_{1}} + \frac{\left|\vec{U}_{1}^{2}\right|}{2} + gz_{1}\right)\underbrace{\int_{1}{\rho_{1}\vec{U}_{1}}\cdot\vec{n}dA}_{-\dot{m}} + \left(u_{2} + \frac{p_{2}}{\rho_{2}} + \frac{\left|\vec{U}_{2}^{2}\right|}{2} + gz_{2}\right)\underbrace{\int_{2}{\rho_{2}\vec{U}_{2}}\cdot\vec{n}dA}_{\dot{m}}$$

$$ \displaystyle K = \dot{m}\left[(u_{2} - u_{1}) + \left(\frac{p_{2}}{\rho_{2}} - \frac{p_{1}}{\rho_{1}}\right) + \left(\frac{\vec{U}_{2}^{2}}{2} - \frac{\vec{U}_{1}^{2}}{2}\right) + g(z_{2} - z_{1})\right]$$

Reform:

$$ \displaystyle \frac{p_{1}}{\rho_{1}} + \frac{\left|\vec{U}_{1}^{2}\right|}{2} + gz_{1} = \frac{p_{2}}{\rho_{2}} + \frac{\left|\vec{U}_{2}^{2}\right|}{2} + gz_{2} + (u_{2} - u_{1}) - \frac{\dot{Q}}{\dot{m}} - \frac{\dot{W}_{shaft}}{\dot{m}} - \frac{\dot{W}_{shear}}{\dot{m}}$$

For $$ \displaystyle \dot{W}_{shaft} = 0$$, $$ \displaystyle \dot{W}_{shear} = 0$$ and incompressible flow:

$$ \displaystyle \underbrace{\frac{p_{1}}{\rho} + \frac{\left|\vec{U}_{1}^{2}\right|}{2} + gz_{1}}_{mechanical\ evergy\ per\ unit\ mass\ at\ flow\ cross\ section} = \frac{p_{2}}{\rho} + \frac{\left|\vec{U}_{2}^{2}\right|}{2} + gz_{2} + (u_{2} - u_{1}) - \frac{\dot{Q}}{\dot{m}}$$

$$ \displaystyle \frac{p}{\rho} + \frac{U^{2}}{2} + gz$$: Mechanical energy per unit mass.

$$ \displaystyle u_{2} - u_{1} - \frac{\dot{Q}}{\dot{m}}$$: Irreversible conversion of mechanical energy to unwanted thermal energy $$ \displaystyle (u_{2} - u_{1})$$ and loss of energy via heat transfer $$ \displaystyle \left(-\frac{\dot{Q}}{\dot{m}}\right)$$.

Thus with this equation I can calculate the loss of energy through a device.

$$ \displaystyle h_{loss} = \left[u_{2} - u_{1} -\frac{\dot{Q}}{\dot{m}}\right]\frac{1}{g}$$

i.e.

$$ \displaystyle \frac{p_{1}}{\rho g} + \frac{U_{1}^{2}}{2g} + z_{1} = \frac{p_{2}}{\rho g} + \frac{U_{2}^{2}}{2g} + z_{2} + h_{loss}$$

One can add the work done by a pump or a turbine.

$$ \displaystyle \frac{p_{1}}{\rho g} + \frac{U_{1}^{2}}{2g} + z_{1} = \frac{p_{2}}{\rho g} + \frac{U_{2}^{2}}{2g} + z_{2} + h_{loss} - h_{pump} + h_{turbine}$$

Differential Control Volume Analysis:Bernoulli Equation
Integrate between 1 and 2 along a streamline:

$$ \displaystyle \frac{p_{1}}{\rho} + \frac{U_{1}^{2}}{2} + gz_{1} = \frac{p_{2}}{\rho} + \frac{U_{2}^{2}}{2} + gz_{2} = constant$$

Bernoulli equation is clearly related to the steady flow energy equation for a stream line. This form of the Bernoulli equation, when the following conditions are satisfied:

1. Steady flow. Note that theres is also an unsteady Bernoulli equation.

2. Incompressible flow. For example, in aerodynamics, flow can be accepted to be incompressible for Mach number $$ \displaystyle (M =\frac{\text{speed of flow}}{\text{speed of sound}}) $$ less than 0.3.

3. Frictionless flow, e.g. in the absence of solid walls.

4. Flow along a single streamline. Different streamline has a different constant.

5. No shaft work between 1 and 2.

6. No heat transfer between 1 and 2.

Example 3
 Find a relationship between the flow rate and the pressure difference inside a pipe which could be measured by venturimeter

title: Fluid Mechanics for MAP/Fluid Dynamics


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text:
User:Mjmohio/Final Report Template

Project Report for User:Mjmohio
For Introduction to Numerical Analysis, Fall 2012.

Introduction
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title: User:Mjmohio/Final Report Template


text:
Category:Disambiguation pages

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User talk:Timir~enwikiversity

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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.

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title: User talk:Timir~enwikiversity


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User talk:Mikesmith00

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 * 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) 21:38, 12 October 2010 (UTC)

title: User talk:Mikesmith00


text:
User talk:Raghu~enwikiversity

 Hello Raghu, 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) 21:38, 12 October 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 Raghu. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Raghu~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 23:41, 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) 06:18, 19 April 2015 (UTC)

title: User talk:Raghu~enwikiversity


text:
Laboratory on Mathematics and Mathematics Education/WebQuests

Task 1: Exploring WebQuests

 * Explore the following WebQuest: Let's Take a Trip! What are the learning objectives? (That means, what are the students intended to learn in this WebQuest?)
 * Have a look at some other WebQuests. What is the structure of a WebQuests? What are the different parts good for?

Task 2: Write a WebQuest!

 * Write a simple WebQuest about a topic of your choice. You may also choose the grade. Write your WebQuest in Wikipedia. You may use Portuguese.

Links & Materials

 * List of WebQuests
 * About WebQeusts (article by Bernie Dodge)
 * Five rules for writing a great webquest (article by Bernie Dodge)


text:
Proving Pythagorean Theorem Using SAS

On the picture of the triangle with the segment of ab cut in the middle of the triangle, we see that the small triangle with sides bc, b^2 and ab were multiplied by b. If we divide this triangle by b again, the sides would become side c, side b and side a. The other small triangle that is attached was multiplied by a, forming sides ab, ac, and a^2. Again if we divide these triangles up by a, the sides would be side b, side c and side a. The angle across from Side length of b should both have the same angle. Same goes for the angle across from side length a, and c. For example, the angles across from sides b in both the small triangles should have the same angle. The angle across from sides a in both the triangles should also have the same angles. Same goes for angles across from side c.

Since the angles across from sides a, and the angles across from sides b are the same, the angles across from side C should be 90 degrees. This means that there are angles of 30, 60 and 90 degrees in each of the small triangles, which proves that this that the segment ab splitting the whole triangle is actually cutting a 90 degrees angle. This proves that the triangle is 90 degrees. Then we can assume that the sides of the whole triangle are equal to the triangle of the big triangle. There for the hypotenuse of the triangle with the segment ab, should be a^2 + b^2, which should be equal to the hypotenuse of the other large triangle which is c^2. So a^2+b^2=c^2

Completed by: Joe Delinski joe.delinski, Cynthia Gonzalez cgnozal4, Suzie Moon smoo1244, Charmaine Ramos cramos2, Susan Zurawski sue652

title: Proving Pythagorean Theorem Using SAS


text:
User talk:Kingkeal

 Hello Kingkeal, 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) 02:29, 13 October 2010 (UTC)

title: User talk:Kingkeal


text: Exercise and metabolic disease/assessment overview


text:
Exercise and metabolic disease/Activity 1

You have been allocated a group, and the group allocated a metabolic condition. The ultimate goal is to create a well researched resource that you can use to assist in your professional life. Additionally, the resource is shared with the world, creating an open education resources and tool. The initial activity requires you to search for, evaluate and make judgements on the use of existing research. You will need to initially work as a team to make decisions about how to cover the relevant literature and complete the task of an annotated bibliography. Remember that the resource that you will need to create from the groups combined annotated bibliography is described in Activity 2.

Task

 * 1) As a group, decide how you are going to cover the relevant literature so that you can create the resource in Activity 2. Each person in the group should be responsible for creating an annotated bibliography on 10-15 references (at least 75% of these should be original references).
 * 2) Each individual in the group creates an annotated bibliography on their references. The annotated bibliography will be shared with everyone in the unit as a future resource.

Timeline
The activity will be introduced in week 2 and discussed in the tutorial. In week 3 we can discuss an example of an annotated bibliography of one reference from any students wanting to bring one in. **The activity should be complete by the end of week 4.**

What is an annotated bibliography?

 * Video by Youtube user janiesantoy, 2009: Writing an Annotated Bibliography. 6:22 minutes.

This video provides a good first reference to what is in an annotated bibliography, there are a number of other references posted below. In the video annotated bibliographies are described formally, but you may choose to create a fairly informal version. For the purposes of this activity, you will need to include enough information so that the annotations can be understood by others in the unit, but you may choose to include dot points rather than formal sentences. You do need to include your own summary of the research and critique. You will probably find it useful to include annotations about how or where this may contribute to the resource created in Activity 2. See the assessment overview to gain further insight in to how this will be assessed.

Bibliographic tools
Often its a good idea to use an electronic bibliographic tool/reference manager to keep your references and annotations. Examples include Endnote and Refworks. If you annotate directly into a tool such as this it is often easy to search for certain words and quickly format your references in a document. But this doesnt apply to formatting online documents (at present at least) and is not ideal for sharing annotations when it comes to creating the resource in Activity 2. So you may also want to consider using tools such as delicious, an electronic document, a wiki or even pen and paper.

More links and resources
See Ben Rattray's bookmarks for website resources around annotated bibliographies

The critique

 * /Tips for reading a research article/


text:
Exercise and metabolic disease/Activity 1/Tips for reading a research article

 * 1) Read the Abstract. It consists of a brief summary of the research questions and methods. It may also state the findings. Because it is short and often written in dense jargon, you may need to read it a couple of times. Try to restate the abstract in your own nontechnical language.
 * 2) Read the Introduction. This is the beginning of the article, appearing first after the Abstract. This contains information about the authors' interest in the research, why they chose the topic, their hypothesis, and methods. This part also sets out the operational definitions of variables.
 * 3) Read the Discussion section. Skip over the Methods section for the time being. The Discussion section will explain the main findings in great detail and discuss any methodological problems or flaws that the researchers discovered.
 * 4) Read the Methods section. Now that you know the results and what the researchers claim the results mean, you are prepared to read about the Methods. This section explains the type of research and the techniques and assessment instruments used.
 * 5) Read the Results section. This is the most technically challenging part of a research report. But you already know the findings (from reading about them in the Discussion section). This section explains the statistical analyses that led the authors to their conclusions. It will test your knowledge of statistics, as well as research terms such as correlation coefficient, dependent and independent variables, subject variables, main effect, interaction, and interrater reliability, to name a few.
 * 6) Read the Conclusion. The last section of the report summarizes the findings, but, more importantly it sets out what the researchers think is the value of their research for real-life application. This section often contains suggestions for future research, including issues that the researchers became aware of in the course of the study.
 * 7) Is the article up to date? Old and irrelevant? Timeless?
 * 8) Is the article original research? Supporting previous findings? A review of the literature?

Title

 * 1) Does the title give you insight as to what the article is about?
 * 2) Does the title tell you what, whom and how?
 * 3) Does the title entice you to read furter?

Abstract

 * 1) Does the abstract contain a brief statement about the purpose, method, results, conclusion and clinical relevance?
 * 2) After reading the abstract did you learn the essence of the article without the details?

Introduction

 * 1) Is the problem clearly stated?
 * 2) Is the literature complete, current and appropriate and is the review objective?
 * 3) Are alternative views acknowledged?
 * 4) Are statements appropriately supported?
 * 5) Are there unsupported assumptions (especially contributing to the articles research question)?
 * 6) Did the author identify a “gap”?
 * 7) Is the purpose clearly stated?
 * 8) Is there a hypothesis?

Method

 * 1) Are subjects well-described?
 * 2) How was the sample selected?
 * 3) How large was the sample?
 * 4) Was a control group used?
 * 5) Is the instrumentation well-described? Calibrated?
 * 6) Is the procedure laid out in detail?
 * 7) Could someone replicate the study?
 * 8) Is there internal validity?
 * 9) Is the data analysis well-described? Appropriate?
 * 10) What p-value was used? (or how were the stats presented?)

Results

 * 1) Are the measreued data summarised?
 * 2) Are results statistically significant?
 * 3) Are results clinically/practically significant?

Discussion

 * 1) Was the hypothesis accepted? Rejected?
 * 2) Does the author identify weakness/limitations of the experiment?
 * 3) Are statements appropriately supported?
 * 4) Is further literature cited to address the findings? Are alternative views acknowledged?
 * 5) Are the results applied clinically/practically?
 * 6) Are suggestions for further research indicated?

Conclusion

 * 1) Are the results briefly restated?
 * 2) Do conclusions follow from the results?

Formatting and clarity

 * 1) Is the article clear? Is it formatted appropriately?
 * 2) Are the main points arranged in logical sequence?
 * 3) Do you have difficulty following the argument? Is the case made?

Referencing

 * 1) Are all references precise and clear?
 * 2) About the Author
 * 3) Is the article (or authors work in general) well cited (cite lists of central articles are generally very important to your research, Google scholar has a good function for keeping up to date this way)?
 * 4) Where is it published?
 * 5) Is the author well established in the field?

Potential conflicts of interest

 * 1) Are there Sponsors of the research (often a statement near the end of the article)?
 * 2) Employer of the research team (e.g. Gatorade research)?
 * 3) Publisher of the research (e.g. ASCM publishes MSSE, NSCA publishes J Strength Conditioning Research)?


text:
Exercise and metabolic disease/Activity 2

You are now familiar with a number of resources in the area you have been allocated. It's now time to put it all together in a useful resource, like a good textbook but online and dynamic. Afterall, you can't know everything all of the time, so its useful to know where to access information quickly that can help you work with clients and their condition.

Task

 * 1) Each group has been allocated a wiki. You will need to create an account if you don't have one already (you may create an alias but you will need to tell me praivately what it is). Go to your wiki and log-in (I will initially need to approve this and at the end of Activity 3 the wiki will become open). Get a feel for editing the site and discuss with your group your own project management. The created wiki's are: hypertension, dyslipidemia and hyperlipidemia and end-stage renal disease.
 * 2) Using your annotated bibliographies, develop your group's wiki to form an online practioner's resource. You will need to synthesize your resources into a coherent and succinct site. The resource should be fully supported by research in a similar way to a literature review. The resource however will be more practical and offers the opportunity for multi and social media to be incorporated. The resource will also be an open resource, so anyone on the web will have potential access not only to view the resource, but also to develop and edit it.

Here is an idea of sections that you may want to include in the resource.
 * Scope of the AEP
 * Pathophysiology of the disease
 * Diagnosis (tests) and normal ranges
 * Medical and Clinical Considerations (typical complications)
 * Exercise Prescription (prevention/treatment)
 * Exercise Training (and monitoring)

Have a look at the Reflection Activity to see how the resource will eventually be used in this unit (though you will have as long as it stays online). You can create the wiki as the group decides. It is suggested however that separate categories (as listed above) appear on separate pages of the wiki.

Although this activity task will not be assessed directly, at the end of Activity 3, the resource will be assessed. This activity aims to ensure you cover key elements of the resource that will be assessed under the assessment overview. The elements that you should be seeking to ensure during this activity include:
 * coverage of literature - well researched and critiqued information, statements supported and any alternative views presented
 * synthesis of ideas and application
 * referencing included

Timeline
It is expected that this activity will be **completed by the start of week 9** if not earlier. There is no formal submission for this activity but progress will be discussed in week 9.

Resources
Exercise Physiology scope of practice and position stands

http://www.delicious.com/benrattray/ucniss-MExSci

Existing Static Resources
Textbooks that act as a static resource for practioners in this area include: Human Kinetics' Clinical Exercise Physiology ACSM's Resource Manual for Guidelines for Exercise Testing and Prescription 6th ed ACSM's Resources for Clinical Exercise Physiology 2nd ed.

What are wikis? (this is one!)
Video by Youtube user leelefever 2007: Wikis in Plain English

How do I edit a wiki like this one?
Video by Youtube user Howcast 2010: How to Edit a Wikipedia Article (while this video refers to Wikipedia, the same techniques are for this wiki.