text:
University of Florida/Egm6341/s10.Team2/HW4

Statement
P. 20-1

Develop higher-order corrected trapezoidal rules for $$ CT_{1}(n) \quad CT_{2}(n) \quad CT_{3}(n) $$

Then use these new corrected trapezoidal rules to find:

$$ I = \int_{0}^{1}\frac{\exp^{x}-1}{x}dx $$

until the error is of order of $$ 10^{-6} \quad $$ using $$\; n=2,4,8,16,32...$$

Solution
Higher Order corrected trapezoidal rules are of the form:

$$ \; CT_{k}(n) = CT_{k-1}(n) + a_{k}h^{2*k} $$

where the a coefficient is defined as follows:

$$ a_{i} = d_{i} \left[ f^{(2i-1)}(b) - f^{(2i-1)}(a) \right] $$

and $$ di=\frac{-B_{2i}}{(2i)!} $$

B are Bernoulli numbers. The first values for $$ d_{i} \quad $$ are:

$$ \; d_{1}=\frac{-1}{12} \qquad d_{1}=\frac{1}{720} \qquad d_{3}=\frac{-1}{30240} $$

These corrected trapezoidal rules define the integral as follows:

$$ \; I= CT_{k}(n) + \Theta (h^{(2*(k+1)}) $$

This means that higher order corrected trapezoidal rules can be developed as long as the function is continuous and its higher order derivatives can be calculated.

The first three corrected trapezoidal rules are found as follows:

$$\; CT_{1}(n) = CT_{0}(n) + a_{1}h^{2} $$

$$\; CT_{2}(n) = CT_{1}(n) + a_{2}h^{4} $$

$$\; CT_{3}(n) = CT_{2}(n) + a_{2}h^{6} $$

Using matlab to calculate the integrals, yields the results as follows:

It can be noticed that the corrected trapezoidal rules yield a solution to the integral much faster than the uncorrected Composite Trapezoidal Rule.

Matlab Code Used for Problem
 MATLAB Code: Finding the Corrected Trapezoidal Rules

 MATLAB Code: Calculating the Values of the function

 MATLAB Code: Calculating the Composite Trapezoidal Rule

solved by--- Egm6341.s10.Team2.GV 21:56, 3 March 2010 (UTC)

checked by---Egm6341.s10.team2.patodon 20:53, 3 March 2010 (UTC)

Problem 2: Higher order error analysis of Trapezoidal rule for periodic functions

 * For which n does $$\; E_{n}^{1} \simeq 0$$

Statement
To prove that the value of the trapezoidal rule error: $$\; E_{n}^{1} \simeq 0$$ for a periodic function and find the effect of $$\; n$$(number of intervals or panels in trapezoidal rule) on the convergence of the function.

Solution
Let $$f\left ( x \right )$$ be a periodic function in the interval $$\left [ a,b \right ]$$

We know that for a periodic function with periodicity of $$\; b-a,$$ $$\; f\left ( a \right )= f\left ( a+\left ( b-a \right ) \right )=f\left ( b \right )$$

Differentiating $$\; f\left ( x \right )$$ w.r.t $$\; x$$ :

$$f'\left ( a \right ) = f'\left ( a +\left ( b-a \right )\right )=f'\left ( b \right )$$

similarly,

$$f^{k}\left ( a \right ) = f^{k}\left ( a +\left ( b-a \right )\right )=f^{k}\left ( b \right )$$

Therefore the coefficients of the expansion of $$\; E_{n}^{1}$$ i.e. $$\; a_{1},a_{2},a_{3},a_{4}$$ becomes zero due the following reason:

We know that:

$$a_{i}= d_{i}\times \left [ f^{\left (2i-1 \right )}\left ( b \right )-  f^{\left (2i-1  \right )}\left ( a \right )\right ]$$ where $$\; d_{i}= \frac{-B_{2i}}{\left (2i  \right )!}$$

$$f^{\left (2i-1 \right )}\left ( b \right ) \simeq  f^{\left (2i-1  \right )}\left ( a \right )$$ when periodicity of the function is $$\; b-a$$

Therefore, in the case of periodic function $$f\left ( x \right )$$ with periodicity $$\; b-a$$, $$\; a_{i}\simeq 0 \; \forall \; i=1,2,3...$$

Hence the error expressed as:

$$\; E_{n}^{1}= \sum_{i=1}^{\infty }a_{i} h^{2i} \simeq 0$$ as $$\; a_{i} \simeq 0 \; \forall \; i=1,2,3...$$

The same result is tested by using a Matlab program for trapezoidal rule and it proves to be true that the function converges rapidly for periodic functions using trapezoidal rule as the number of intervals 'n' increases and thus the error term $$\; E_{n}^{1}$$ tends to zero.

solved by-Srikanth Madala

checked by---Egm6341.s10.team2.patodon 20:55, 3 March 2010 (UTC)

Statement
Discuss the pros and cons of the following quadrature methods:

 * 1) Taylor Series
 * 2) Composite Trapezoidal rule
 * 3) Composite Simpson's rule
 * 4) Romberg table (including Richardson's extrapolation)
 * 5) Corrected Trapezoidal rule

Solution
 Taylor Series:   Pros:

 * 1) Powerful tool that helps to approximate any type of simple or complex functions into a polynomial form $$\;P_{n}(x)$$ with an error in the form of remainder $$\;R_{n+1}(x)$$

 Cons:

 * 1) The function $$\;f(x)$$ should be differentiable in the given limits 'a' and 'b' in which it is approximated as a polynomial.
 * 2) The product of two sub-functions in a given function $$\;f(x)$$ like for example $$e^{x}.\cos \left ( x \right )$$ would make it more difficult and more costly (in terms of computation) to evaluate successive derivatives.

 Composite Trapezoidal rule:   Pros:
 * 1) Very intuitive and easy to use
 * 2) The numerical integral results obtained for periodic functions like trigonometric functions (sinx, cosx, tanx etc) is very accurate owing to the fact that the error is dependent on the difference between the odd derivatives of the limiting points - 'a' and 'b'.
 * 3) It yields better accuracy than simple trapezoidal rule in calculating the numerical integral of a function.

 Pros:

 * 1) Needs many subintervals to converge and the convergence rate is low for non-periodic functions.
 * 2) Runge Phenomena.

 Composite Simpson's rule:   Pros:
 * 1) It is still intuitive and easy to use
 * 2) The convergence rate is OK
 * 3) Exact for cubic polynomials

 Cons:
 * 1) This rule can be applied to only even number of finite intervals between the limits- 'a' and 'b'. So the value of 'n' in Simpson's rule is always an even number. i.e. n=2i; where (i=1,2,3...)
 * 2) Runge Phenomena

 Romberg table (including Richardson's extrapolation):   Pros:
 * 1) The successive computation of $$\;I(2n)$$ is cheaper and faster when $$\;I(n)$$ is already computed.
 * 2) The accuracy of the numerical integration results obtained are better than other methods. The higher the power of 'h' term in the trapezoidal error, the better the accuracy.

 Cons:
 * 1) The success of Romberg integration is only justified if the integrand-'f' satisfies the hypotheses of the Euler–Maclaurin Theorem.For example, as illustrated in the | An Introduction to Numerical Analysis by Suli and Mayers Text Pg.218 The function $$\; x \to x^{\frac{1}{3}}$$ is not differentiable at $$\; x = 0$$, so the required conditions are not satisfied for any extrapolation.

solved by --- --Srikanth Madala

checked by --- --Egm6341.s10.Team2.GV 22:00, 3 March 2010 (UTC)

Statement
Given the expression

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

$$  \displaystyle \boldsymbol{E_n^1=\sum _{k=0}^{n-1}[\int_{x_k}^{x_{k+1}}f(x)dx-\frac{h}{2}[f(x_k)+f(x_{k+1})]]} $$     (1)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

where  $$\boldsymbol{x_k=a+kh}$$ and $$\boldsymbol{h=\frac{(b-a)}{n}}$$,

Show that by transformation of variables we get

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

$$  \displaystyle \boldsymbol{E_n^1=\frac{h}{2}\sum _{k=0}^{n-1}[\int_{-1}^{1}g_k(t)dt-[g_k(-1)+g_k({+1})]]} $$     (2)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

where $$\boldsymbol{g_k(t)=f(x(t)); x\epsilon [x_k,x_{k+1}]}$$

Solution
Given the expression
 * {| style="width:100%" border="0"

$$  \displaystyle \boldsymbol{E_n^1=\sum _{k=0}^{n-1}[\int_{x_k}^{x_{k+1}}f(x)dx-\frac{h}{2}[f(x_k)+f(x_{k+1})]]} $$     (1)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

we use the transformation $$\displaystyle{x_k = a+kh}$$ to transform the interval from $$\displaystyle{[x_k,x_{k+1}]}$$       to      $$\displaystyle{[-1,1]}$$     by introducing  $$\displaystyle{[x_k,x_{k+1}]}$$.We get

$$\displaystyle{x(-1)=x_k}$$

$$x(0)=\frac{x_k+x_{k+1}}{2}$$

$$\displaystyle{x(1)=x_{k+1}}$$

substituting in (1) we get
 * {| style="width:100%" border="0"

$$  \displaystyle E_n^1=\sum _{k=0}^{n-1}[\int_{-1}^{+1}f(x(t))dt-\frac{h}{2}[f(x(-1))+f(x(+1)]] $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle E_n^1=\sum _{k=0}^{n-1}[\int_{-1}^{+1}f(t\frac{h}{2}+0)dt-\frac{h}{2}[f(x(-1))+f(x(+1)]] $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle E_n^1=\sum _{k=0}^{n-1}[\int_{-1}^{+1}f(t\frac{h}{2}+0)dt-\frac{h}{2}[f(x(-1))+f(x(+1)]] $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

taking $$\displaystyle{\frac{h}{2}}$$ out we get
 * {| style="width:100%" border="0"

$$  \displaystyle \boldsymbol{E_n^1=\frac{h}{2}\sum _{k=0}^{n-1}[\int_{-1}^{1}g_k(t)dt-[g_k(-1)+g_k({+1})]]} $$     (2) solved by---Egm6341.s10.team2.niki 17:46, 27 February 2010 (UTC)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

checked by--- --Srikanth Madala

Statement
Show the following relation via integration by parts

$$\int_{-1}^{1}(-t)\cdot g^{(1)}(t) = \int_{-1}^{1}g(t)dt - \left [ g(-1)+ g(1) \right ] $$

Solution
Integration by Parts

$$\begin{align} \int_{-1}^{1}g(t)dt &= \int_{-1}^{1}g(t)\cdot (1)dt\\ &= \left [ g(t)\cdot (t) \right ]_{-1}^{1} - \int_{-1}^{1}t \cdot g^{(1)}(t)\\ &= \left [ g(-1)+g(1) \right ] +\int_{-1}^{1}(-t)\cdot g^{(1)}(t)\\ \end{align}$$

Rearrangement yields

$$\int_{-1}^{1}(-t)\cdot g^{(1)}(t) = \int_{-1}^{1}g(t)dt - \left [ g(-1)+ g(1) \right ]$$

solved by---Egm6341.s10.team2.lee 01:45, 2 March 2010 (UTC)

checked by---Egm6341.s10.team2.niki 05:23, 2 March 2010 (UTC)

checked by---Egm6341.s10.team2.patodon 20:48, 3 March 2010 (UTC)

Statement
The following is defined:

$$ g_{k}(t)= f(x(t)) $$

where,

$$ x(t) = t\frac{h}{2} + \frac{x_{k}+x_{k+1}}{2} $$

Proof the following:

$$ g_{k}^{i} = \left( \frac{h}{2} \right) ^{i} f^{i}(x(t)) $$

Solution
The first step is to state the chain rule for a composite function which is the case in this situation,

$$ Y = F(G(x)) $$

$$ \frac{dY}{dx} = F^{'}(G(x))G^{'}(x) $$

The first derivative is found as follows:

$$ g_{k}(t) = f(x(t)) $$

$$ g_{k}^{'}(t) = f^{'}(x(t))x^{'}(t) $$

$$ x^{'}(t) = \frac{h}{2} $$

By this the first derivative is defined as:

$$ g_{k}^{(1)}(t) = \frac{h}{2}f^{'}(x(t)) $$

Using the chain rule again to find the second derivative as follows:

$$ g_{k}^{(2)}(t) = \frac{h}{2} \left[ \frac{d}{dt}f^{1}(x(t)) \right] $$

$$ g_{k}^{(2)}(t) = \left( \frac{h}{2} \right) ^{2} f^{(2)}(x(t)) $$

Apply the chain rule once more to find the third derivative as follows:

$$ g_{k}^{(3)}(t) = \left( \frac{h}{2} \right) ^{2} \frac{d}{dt}f^{(2)}(x(t)) $$

$$ g_{k}^{(3)}(t) = \left( \frac{h}{2} \right) ^{3} f^{(3)}(x(t)) $$

One notices that the value of $$ \frac{h}{2} $$ comes out of the derivative everytime it is applied.

One is able to then conclude a general expression for the derivative of the function as follows:

$$ g_{k}^{(i)}(t) = \left( \frac{h}{2} \right) ^{i} f^{(i)}(x(t)) $$

solved by---Egm6341.s10.Team2.GV 05:03, 27 February 2010 (UTC)

checked by---Egm6341.s10.team2.patodon 21:10, 3 March 2010 (UTC)

Statement
Show the following relation via integration by parts

$$\int_{-1}^{1}g^{(1)}(t)\cdot P_{1}(t)dt = \left [ P_{2(t)}\cdot g^{(1)}(t) \right ]_{-1}^{1} - \int_{-1}^{1}P_{2}(t)\cdot g^{(2)}(t)dt$$

Solution
Integration by Parts

$$\int_{-1}^{1}g^{(1)}(t)\cdot P_{1}(t)dt = \left [ P_{2(t)}\cdot g^{(1)}(t) \right ]_{-1}^{1} - \int_{-1}^{1}P_{2}(t)\cdot g^{(2)}(t)dt$$

$$\mbox{where,} \qquad P_{1}(t)=-t \qquad \mbox{and} \qquad P_{2}(t)=\int P_{1}(t)dt = -\frac{t^{2}}{2}+c$$

solved by---Egm6341.s10.team2.patodon 20:59, 3 March 2010 (UTC)

checked by---Egm6341.s10.team2.lee 02:15, 2 March 2010 (UTC)

Statement
Install Chebfun program (Tefethen et al. 2004)

Solution
Status - Successful

solved by---

checked by---Egm6341.s10.team2.patodon 21:27, 3 March 2010 (UTC)

Statement
For the integral $$\displaystyle{I=\int_{0}^{1}\frac{e^x-1}{x}dx}$$
 * 1) Optimise the code for Romberg table
 * 2) Compare second column of Romberg table with the results of Simpson's rule and derive any relationship.
 * 3) Compute $$\displaystyle{I_n}$$ to the order of $$\displaystyle{10^{-10}}$$ and find the computational time using

 * Code for Composite Trapezoidal Rule
 * Code for Composite Simpson's Rule
 * Code for Romberg table
 * Chebfun "sum" command
 * Built-in MATLAB function "trapz"
 * Built-in MATLAB function "quad"
 * Built-in MATLAB function "clencurt"

Solution
Exact value of the Integral from Mathematica is calculated by teh command "Integrate[((exp(x)-1)/x),+{x,+0,+1}]" the value is

1.3179021514544038948600088442492318379749012457927839928404611969976461077561394826119536468343922075 []]

Part1:Corrected code for Romberg table
 MATLAB Code: For Efficient Production of the Romberg Table

Part2:Comaprison of Simpson's rule and Romberg table
The below table shows the values for the given integral computed using Composite Simpsons rule and the second column of the Romberg table for the same. By comparing the values of the Integral (or of the corresponding errors)) for any n, we see that the value from the composite Simpson's rule is the same as the value for n/2 (previous row) of $$\displaystyle{T_1(n)}$$.

For e.g : Denoting Simpson's as $$\displaystyle{S(n)}$$ we see that
 * {| style="width:100%" border="0"

$$  \displaystyle \displaystyle{S(16)=T_1(8)} $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$  \displaystyle \displaystyle{S(32)=T_1(16)} $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle \displaystyle{S(64)=T_1(32)} $$ etc. In general we can write
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle \displaystyle{S(2^i)=T_1(2^{i-1})} $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle T_1(2^i)=\frac{4T(2^i)-T(2^{i-1})}{3} $$
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle \therefore S(2^i)=\frac{4T(2^i)-T(2^{i-1})}{3} $$     (1)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

Part3:Codes
 Using Code for Composite trapezoidal rule  Gives n= 32768 ,In =1.31790215149321 and time 4.973 sec

Using Code for Composite Simpson's Rule Gives n= 128 ,In= 1.31790215146089 and time=0.017sec

 Using code for Romberg table

Gives time =0.04sec

Using chebfun - sum: tic y = chebfun('(exp(x)-1)./x',[eps 1]); I=sum(y) toc

I = 1.317902151454404 and time = 0.009175 sec.

Using Trapz function: n=32768 ,In=1.31790215149321 and time = 0.006879 sec

Using Quad function Gives n=2 ,In= 1.31790215145441 and time = 0.004 sec

Using clencurt function tic [x,w] = clencurt(2^5); xx=(1+eps)/2+x.*(1-eps)/2; ww=w.*(1-eps)/2; yy=(exp(xx)-1)./xx; II=ww*yy toc

Gives II=1.317902151454404 and time = 0.000308 sec

Part3:Computational times
solved by---Egm6341.s10.team2.niki 18:20, 28 February 2010 (UTC)

checked by---Egm6341.s10.team2.lee 22:20, 2 March 2010 (UTC)

Statement
Repeat Problem 9 for integral $$\displaystyle{I=\int_{-5}^{5}\frac{1}{1+x^2}dx}$$

Solution
The exact value of the definite integral is atan(5)-atan(-5)=2.746801533890034...

own code - composite trapezoidal rule
Function Definition function I = trapzoid(f,a,b,n) h=(b-a)/n; x=linspace(a,b,n+1); fx=feval(f,x); I=h*(fx(1)/2+sum(fx(2:1:n))+fx(n+1)/2); Call Function clear;clc format long f = @(x) 1./(1+x.^2); tic I = trapzoid(f,-5,5,2^14) toc e = atan(5)-atan(-5)-I

Result I = 2.746801532971545 Elapsed time is 0.001745 seconds. e = 9.184866200939723e-010

own code - composite simpson's rule
Function Definition function In = simpson(f,a,b,n) % n must be a positive even integer h=(b-a)/n; %step size x=linspace(a,b,n+1); %(n+1) equally spaced points fx=feval(f,x); %function evaluations %Composite Simpson In=(h/3)*(fx(1)+4*sum(fx(2:2:n))+2*sum(fx(3:2:n-1))+fx(n+1));

Call Function clear;clc format long f = @(x) 1./(1+x.^2); tic I = simpson(f,-5,5,2^8) toc e = atan(5)-atan(-5)-I

Result I = 2.746801533727021 Elapsed time is 0.000343 seconds. e = 1.630109380812428e-010

Romberg quadrature rule
Function Definition function I_romb = rombquad(f,a,b,m) h = 2.^((1:m)-1)*(b-a)/2^(m-1);            % intervals used. k1 = 2.^((m-2):-1:-1)*2+1;                 % Index into intervals. f1 = feval(f,a:h(1):b);                    % Function evaluations. R = zeros(1,m);                            % Pre-allocation. % Define the starting vector: for ii = 1:m R(ii) = 0.5*h(ii)*(f1(1)+2*sum(f1(k1(end-ii+1):k1(end-ii+1)-1:end-1)) + f1(end)); end % Interpolations: for jj = 2:m jpower = (4^(jj-1)-1); for kk = 1:(m-jj+1) R(kk) = R(kk)+(R(kk)-R(kk+1))/jpower; end end I_romb = R(1);

Call Function clear;clc format long y = @(x) 1./(1+x.^2); tic I_romb=rombquad(y,-5,5,9) toc e=atan(5)-atan(-5)-I_romb

Result I_romb = 2.746801534346014 Elapsed time is 0.000356 seconds. e = -4.559819188898473e-010

matlab - trapz and quad
Call Function clear;clc format long x=linspace(-5,5,2^14+1); y = 1./(1+x.^2); I_exact=atan(5)-atan(-5) tic;I_ct=trapz(x,y);toc I_ct e_ct=I_exact-I_ct tic;I_cs=quad(@(x) 1./(1+x.^2),-5,5,1e-8);toc I_cs e_cs=I_exact-I_cs

Result I_exact = 2.746801533890032 Elapsed time is 0.003191 seconds. I_ct = 2.746801532971568 e_ct = 9.184639715442700e-010 Elapsed time is 0.009436 seconds. I_cs = 2.746801534322983 e_cs = -4.329510083778132e-010

matlab - clencurt
Call Function tic [xx,ww] = clencurt(2^10); xx=xx.*5; ww=ww.*5; yy=1./(1+xx.^2); II=ww*yy toc

Result II = 2.746801533890032 Elapsed time is 0.089293 seconds.

"sum" command of chebfun matlab toolbox
Call Function x = chebfun('x',[-5 5]); tic I=sum(1./(1+x.^2)) toc e=abs(atan(5)-atan(-5)-I)

Result I = 2.746801533890033 Elapsed time is 0.042520 seconds. e = 1.332267629550188e-015

solved by---Egm6341.s10.team2.lee 22:22, 2 March 2010 (UTC)

checked by-Egm6341.s10.team2.niki 20:45, 6 March 2010 (UTC)

Statement

Find the Arc Length of the ellipse where:

$$ r(\theta) = \frac{1 - e^{2}}{1 - e \cos(\theta)} $$

and

$$ eccentricity=e= \sin(\frac{\pi}{12}) $$

Using:

1)Composite Trapezoidal Rule

2)Composite Simpson's Rule

3)Romberg Table

4)"Sum" Command of the chebfun toolbox

5)"Trapz" Command of Matlab

6)"Quad" Command of Matlab

7)"Clencurt" Command of Matlab

Until the error is less than $$ 10^{-6} $$

Composite Simpson's Rule
 MATLAB Code:

Romberg Table
Romberg Table for n=2

6.2832   6.0026    6.0722    6.0691    6.0691    6.0691    6.0727    6.0679    6.0692    6.0691    6.0691         0    6.0691    6.0691    6.0691    6.0691         0         0    6.0691    6.0691    6.0691         0         0         0    6.0691    6.0691         0         0         0         0    6.0691         0         0         0         0         0

Table for Error of Romberg Table

-0.2141   0.0665   -0.0031   -0.0000    0.0000   -0.0000   -0.0036    0.0012   -0.0001    0.0000   -0.0000         0   -0.0000    0.0000   -0.0000   -0.0000         0         0   -0.0000   -0.0000   -0.0000         0         0         0   -0.0000   -0.0000         0         0         0         0   -0.0000         0         0         0         0         0

Romberg Table for n=4

6.0727   6.0679    6.0692    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691         0    6.0691    6.0691    6.0691    6.0691         0         0    6.0691    6.0691    6.0691         0         0         0    6.0691    6.0691         0         0         0         0    6.0691         0         0         0         0         0

Error for Romberg Table n=4

-0.0036   0.0012   -0.0001    0.0000   -0.0000   -0.0000   -0.0000    0.0000   -0.0000   -0.0000   -0.0000         0   -0.0000   -0.0000   -0.0000   -0.0000         0         0   -0.0000   -0.0000   -0.0000         0         0         0   -0.0000   -0.0000         0         0         0         0   -0.0000         0         0         0         0         0

Romberg Table for n=8

6.0691   6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691    6.0691         0    6.0691    6.0691    6.0691    6.0691         0         0    6.0691    6.0691    6.0691         0         0         0    6.0691    6.0691         0         0         0         0    6.0691         0         0         0         0         0

Table for Error when n=8

1.0e-005 *

-0.1180   0.0281   -0.0109   -0.0084   -0.0085   -0.0085   -0.0085   -0.0085   -0.0085   -0.0085   -0.0085         0   -0.0085   -0.0085   -0.0085   -0.0085         0         0   -0.0085   -0.0085   -0.0085         0         0         0   -0.0085   -0.0085         0         0         0         0   -0.0085         0         0         0         0         0

"Sum" Command of Chebfun Matlab Toolbox
$$ In= 6.069090959564776 $$

$$ Error= I-In = -8.457248767967940e-008 $$

"Quad" Command of Matlab
The value found using the "Quad" Matlab Command was:

$$ I=6.069090875 $$

with an error smaller than $$10^{-6} $$

solved by--- --Egm6341.s10.Team2.GV 22:04, 3 March 2010 (UTC)

checked by---Egm6341.s10.team2.patodon 21:15, 3 March 2010 (UTC)

Signatures
solved problems 4 and 9, proofread problems 5 and 10:--Egm6341.s10.team2.niki 18:22, 28 February 2010 (UTC)

solved problems 5 and 10, proofread problems 7 and 9:--Egm6341.s10.team2.lee 22:26, 2 March 2010 (UTC)

solved problems 7, proofread problems 1, 2, 5, 6, 8 and 11 Egm6341.s10.team2.patodon 23:01, 2 March 2010 (UTC)

solved problems 1, 6 and 11. Proofread 3, 9. --Egm6341.s10.Team2.GV 22:06, 3 March 2010 (UTC)

solved problems 3 and 8. Proofread 4, 9--Srikanth Madala


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Biblical Studies (NT)/The Epistle of Jude: Religious Hypocrisy

 NEW TESTAMENT

 Lesson 13

 THE EPISTLE OF JUDE   Religious Hypocrisy

Authorship
The author introduces himself as “Jude, a servant of Jesus Christ, and a brother of James” (Jude 1). This Jude has traditionally been believed to be Jesus’ brother of the same name (Mt 13:55). If this is true, the greeting is a mark of humility in Jude, who mentions that he is a brother of James, the well-known leader of the church at Jerusalem and the writer of the epistle of James, but in relation to Jesus, he merely calls himself “a servant.”

If he was Jesus’ brother, he was one of a large Jewish family of the town of Nazareth in Galilee (Mt 13:55), which today is in northern Israel. His father was a carpenter and his mother was Mary, mother of Jesus. Since Jesus was Mary’s firstborn, Jude would have been a younger sibling. Although the family was not rich, they were of noble ancestry, being able to trace their blood line back to King David (Mt 1:6-16).

Other than what he had in common with Jesus, however, little is known of Jude. His epistle gives the impression that he had a leadership position in the church. It could be that he was known and respected simply on the strength of his relationship to Jesus, rather than because he held a particular office. Either way, it is unlikely that a letter of this nature would be written by someone who did not have acknowledged authority.

Some scholars have suggested that Jude’s epistle was written by another author who used Jude’s name to gain acceptance. The main reasons given against Jude’s authorship are:

 * 1) The subject matter, which warns believers against false teachers who are trying to lead them astray. Some people believe that the false doctrine is Gnosticism, which was most influential late in the first century and during the second century, after Jude’s death. Passages elsewhere in the New Testament indicate that false teachers were present within the church from the middle of the first century, however, so in the absence of evidence to prove that the author is specifically referring to the Gnostics, this argument must remain an interesting hypothesis.

 * 2) Part of Jude’s epistle bears marked similarities to a passage in 2 Peter, indicating that one of the authors made use of the other (compare 2 Peter 2:1-17 with Jude, verses 3-13). As noted in the lesson on the epistles of Peter, this is not so much a question of authorship as it is a question of who borrowed from whom. (See that lesson for further discussion.)

Unger's Bible Handbook (Moody 1967) says:

 * The author was evidently the brother of James, who was the bishop of Jerusalem and the writer of the Epistle of James, and the (half) brother of [Jesus]... Some scholars, however, identify him as the apostle Judas, called Lebbaeus or Thaddaeus. Echoes and allusions to the epistle occur in the writings of Hermas, Polycarp, Athenagoras, Theophilus of Antioch, and Tertullian, so that Jude has stronger external attestation than 2 Peter. (834)

Addressees
The author addresses the epistle ostensibly to all who are “called, sanctified by God the Father, and preserved in Jesus Christ” (Jude 1). Some scholars think that Jude particularly had in mind the churches in “Asia” (in western Turkey today), because he appears to address a similar situation as Peter in his second epistle. For a time, around the middle of the first century, these churches were the heart of the Christian movement. Ephesus, in particular, was a major center of Christianity. Regardless, the greeting suggests that the letter was meant for Christians everywhere, and it is likely that it was circulated among the churches.

False Teachers
The epistle of Jude is brief, but powerful. It continues the theme of 2 Peter and the epistles of John, that of false teachers promoting heresies within the church. Jude delivers a scathing attack on these teachers, a censure which is only surpassed in the New Testament by Jesus’ stinging rebuke of the scribes and Pharisees in Matthew 23.

Apparently, Jude had intended to write a more general letter on the theme of salvation, for in his introduction he says:
 * Beloved, while I was very diligent to write to you concerning our common salvation, I found it necessary to write to you exhorting that you should earnestly contend for the faith which was once for all delivered to the saints. For certain men have crept in unnoticed, who long ago were marked out for this condemnation, ungodly men, who turn the grace of our God into licentiousness and deny the only Lord God and our Lord Jesus Christ. (3-4)

Jude speaks of God’s judgement upon religious hypocrites, both past and present, and he condemns them in the strongest terms, made more forceful by the poetic tone of his language:
 * These dreamers defile the flesh, reject authority, and speak evil of dignitaries. They are clouds without water, carried about by the winds; late autumn trees without fruit, twice dead, pulled up by the roots; raging waves of the sea, foaming up their own shame; wandering stars for whom is reserved the blackness of darkness forever. (8,12,13)

Despite the highly critical tone of the letter, Jude closes by saying that even the worst of offenders can be saved. He urges Christians to make a distinction between those who are merely ignorant of the truth, and those who have deliberately rejected it or distorted it for personal gain. Believers are encouraged to beware of hypocrisy and immorality, but at the same time to love and care for those who could benefit from the Christian message.

Test Your Knowledge
{Which of the following were Jude’s brothers? -Jesus -The apostle John -James +a and c
 * type=""}

{Jude has certain points in common with another epistle, and it is clear that one of the authors made use of the other. Which is the other epistle? - James -3 John +2 Peter -Philemon
 * type=""}

{The problem of teachers attempting to alter or dilute the gospel message is a major theme in which of the following epistles? -The epistles of Peter -The epistles of John -The epistle of Jude +All of the above
 * type=""}

{ Jude’s intended audience was probably: -Christians everywhere -In particular, the Christians in the the province of Asia (in western Asia Minor) -Jewish believers +a and b
 * type=""}

{ What is the tone of Jude’s epistle? -Happy-go-lucky +A scathing attack second only to Jesus’ words in Matthew 23 -Mysterious -Complimentary
 * type=""}

Next lesson:

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text:
User:Takamasa~enwikiversity

=Analytical Writing=

Statement of Intent

Overview

Rationale

Publication

Schedule

 * 1) week 2
 * 2) week 3
 * 3) week 4
 * 4) etc.

Anticipated Problems

Week 6 Project Review

Project
 Global Waring vs. Ice Age

I watched Japanese TV show which are Japanese Comedians and Japanese scientists talking about Global Warming. Japanese scientists were talking about Global Warming theory is not true. Also, they said earth is become Ice age. Japanese comedians ask question to scientists about does earth warming? I thought earth is become warming because Seattle weather is so warm in this year. I came Seattle three years ago, and these three years snow storm once or twice every winter. However, this year never snowing in Seattle. I think because of Global Warming, but my friend who is living in New York told me about New York is very bad to snow this winter. Therefore, different area, which are west, and east side of America opposite weather changing. Therefore, I interested in Global Warming. Then, I watched two documentary movies that are An Inconvenient Truth and The Great Global Warming Swindle. An Inconvenient Truth is Al Gore told about global warming is happen because of CO2 gas is rise so, earth is heat up. The Great Global Warming Swindle is based on sound science and interviews with real climate and proof of Al Gore is not saying truth. They said Global warming is not because of CO2 gas.

Global warming is when the earth heats up. It happens when greenhouse gases which are carbon dioxide, water vapor, nitrous oxide, and methane, trap heat and light from the sun in the earth’s atmosphere that increases the temperature.

Global warming is caused by two, which are natural causes and man-made causes. Natural causes are release of methane gas from arctic tundra and wetlands. Methane gas is greenhouse gas, which keep heat earth above the sky. Another natural cause is climate change. On the other hand, there are man made causes, which are pollution from man made. People burned fossil fuels, which are CO2 gas. CO2 gas is also greenhouse gas. Also, when people dig up the fossil fuel. The methane gas is also come up from underground.

Global warming effect is rise in sea level, more killer storms, massive crop failures, widespread extinction of species and more effects happen in the future.

On the other hand, The Great Global Warming Swindle told about there is no proof that the current warming is caused by the rise of greenhouse gases from human activity. Ice core records from the past 650,000 years show that temperature increases have proceeded not resulted from increases in CO2 by hundreds of years, suggesting that the warming of the oceans is an important source of the rise in atmospheric CO2. The some scientist told about CO2 is 0.03 % to 0.04% in atmosphere. Also, they said Al Gore told CO2 is increase only 0.005 % in atmosphere. The scientists said CO2 is not relating to global warming. Also, this documentary told about melting North Pole iceberg. There is Russian scientist who research North Pole iceberg said people seen the crumbling the iceberg scene on TV specially Global warming show. He said iceberg crumble every year in North Pole. Also, he said iceberg crumble because there is spring season coming.

Back to the Japanese TV show, Japanese scientist told about earth become ice age because of North Pole melt ice, and Atlantic Ocean current become cold. Then, Europe and East side of North American area become ice age. They said Earth become like movie that is Day After Tomorrow. Other Scientists told they don't know when it’s happen, and he said people would get ice like mammoth before ice age.

The Japanese comedian asks why government and media told global warming. The scientist answers the question. He said because after finished cold war, other countries of Government need to get money from, and then use global warming. For example, Japan was so district about recycling trash to have buy two types of trash bag to through away couple years ago. After this scientist prove Japanese recycling system which are government said recycling, but they incinerate trash same time. After he said this on this TV program recycling system is not anymore in Japan. We paid extra money for trash bag and took time to classify the trash. Then, this Japanese TV shows audience trust him to believe his theory of recycling system in Japan.

The Scientist told about global warming is good for Japanese people because of Japanese average life expectancy become longer. He told about Japanese people who live in Okinawa live longer and who live in Hawaii live longer than people who live in Japanese mainland. Japanese ministry of education, culture, Sports, Science, and technology makes this research.

In these theories I noticed, and I chose my opinion is global warming is happen light now, but this global warming is not because of human made of green house gases. Couple years ago, I went Brice canyon in Utah, and I saw great view of rocks. There are many rocks to look like statues. Also, there is nature made of bridge. Then, I thought human couldn’t make like that rocks. Any way, I think this is time to increasing the CO2 and temperature in earth.

In conclusion, there are many theory of global warming which is earth become warm because of methane gas and CO2 of greenhouse gas. On the other hand, Earth become ice age because of North Pole melts to change Atlantic Ocean current change to cold. Still these theories are not proof. We do not know what is happen in the future. Japanese Scientist said Japanese average life expectancy become longer because of global warming. Also Increasing CO2 gas is good for growing plants. We should choose these theories believe or not believe. I think human cannot control Earth because of earth is huge planet. So, I think global warming is happen in the earth but people cannot control to earth to change.

title: User:Takamasa~enwikiversity


text:
Boundary Value Problems/Finite Difference Time Domain

../Numerical Methods/

This method is for solving the wave propagation specifically for electromagnetic waves. See detailed information at FDTD.

1D FDTD
The


text:
User talk:Egm6321.f09.Team1.vasquez/Homework2

This page is not linked to any course. Is any one using this page?


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User:Edwardyu236

I am just another Wikiversity student... (JAWS?!) called Edward... living in Hong Kong.

title: User:Edwardyu236


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User talk:Nagarjun~enwikiversity

HOW ARE YOU SIR PLEASE GIVE ME YOUR ID. DETAILS. NAGARJUN MAHIPAL.

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 Nagarjun. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Nagarjun~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 23:39, 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) 06:16, 19 April 2015 (UTC)

title: User talk:Nagarjun~enwikiversity


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User talk:Rouedraogo

 Hello Rouedraogo, 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. --AFriedman (talk) 06:59, 25 February 2010 (UTC)

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text: User talk:Luoliwe

title: User talk:Luoliwe


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User talk:CraigJoseph

 Hello CraigJoseph, 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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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 February 2010 (UTC)

title: User talk:CraigJoseph


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User talk:Bob sears

 Hello Bob sears, 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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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:18, 25 February 2010 (UTC)

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text:
User:Rouedraogo

Deep Sea Living and Looks: What a drag!
{| cellpadding="5" cellspacing="5" style="width: 90%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 40%; background-color: #33FFFF; border: 2px solid #969696; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Brief Lesson Info

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Grade Level: 11th Grade - High School
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Subject:  Life Science
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Sub-Subject:  Marine Biology; Ecology
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Length/Duration:  1 week project
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Technologies Used:  (1) Blackboard, (2) Blogger (optional) or Skype, Desktop or Laptop Computer, Internet, and for an alternative lesson, (1) a video recording apparatus and (2) TeacherTube
 * }

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Introduction
NOTICE: This is a lesson plan proposition using Blackboard. Ideally, this will best serve as a lesson idea for a distance education course through a virtual school program rather than a blended course, but variations are more than possible. The ocean is a wondrous place where several different species have created a habitat for themselves. Each habitat is separated into different zones, but for the purposes of today's lesson, we will look at how an organism's looks may be explained by their habitat and the adaptations required for that environment. More specifically, how conditions within the abyssopelagic zone (or any zone(s) of choice) influence an organism's make-up.
 * }

{| cellpadding="5" cellspacing="5" style="width: 90%; background-color: inherit; margin-left: auto; margin-right: auto"
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Goals
Our goals for the lesson are to discover (1) the life and conditions of the abyssopelagic zone as well as (2) how density correlates to buoyancy and movement, and (3) how factors of the ideal gas law (PV=nRT) such as pressure, temperature, and volume, and properties of liquids influence the physiognomy of abyssopelagic zone dwelling organisms.

Objectives
In discussing ecosystems and the role of pressure, temperature, and volume on living organisms, we will correlate life science content to physical science. This process of "making connections" will require the student to make inferences based on prior knowledge, specifically on the properties of gases, and liquids. This inquiry of the ecology and physiology of marine species within zones fulfills the California Standards (CS) 6 (d)(g) in 9th through 12th grade Biology/Life Sciences and 4(c) in 9th through 12th grade Chemistry.

Based on Chi's "Eliciting Self-explanations Improves Understanding" paper, "learning involves the integration of new information into existing knowledge." As such, one can use expository text as a learning tool without so much of a focus on worksheet supplements or interactive games and tools as long as reflection which require the student to correlate the topic read to already learned material or real-life scenerios. Basically, as long as a student can re-explain using their own words and making their own associations to the topic being studied, learning has occured. The objective of this lesson is also to encourage reflection, inference, and self-explanation of topics studied. Flikr Images "Deep Sea" Creatures from the Deep Abyss (YouTube)
 * }

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Activity Outline
In teams and forming interactive study groups, students are to learn using text-based material combined with distance learning tools. A. Grouping B. The Learning Unit C. Assessment {| cellpadding="5" cellspacing="5" style="width: 90%; background-color: inherit; margin-left: auto; margin-right: auto"
 * 1) Teacher will randomly group her Blackboard students into groups of 3 to 4 students depending on the size of the class.
 * 2) Each group will be have to meet as a study group within 48 hours in order to discuss the chapter on Abyssinian sea creatures.
 * 3) The teacher will have the option to post 'external links' on Blackboard for students to use alongside their textbook. A good choice for an external link for this lesson is this Discover Magazine article.
 * 1) During the 'study session' that will be organized by each group but somehow recorded by each member in order to offer proof of having met to the teacher (recorded audio, video, or online chat), students will go back to Blackboard and select the Learning Unit titled 'Hints, Questions, and Guidance'
 * 2) Using the textbook, possible external links, and following the Learning Unit, students will study and take notes which will be emailed to the teacher along with their proof from step (B)(1) above. Students have 24 hours to email their information and further study and communicate if necessary.
 * 1) By this time, 72 hours have elapsed. Students will gather their notes in order to complete a timed set of essay questions or quiz in test-format on Blackboard.  The teacher may offer students test retaking options.  The test should be removed after being posted for 24 or 48 hours.
 * 2) Reflection
 * The final step which is still part of the assessment process, is called "reflection". A prompt will be offered to students basically asking them to explain what they learned and to pull in information they already know in order to think critically about the points made within the "lesson goal": to discover (1) the life and conditions of the abyssopelagic zone as well as (2) how density correlates to buoyancy and movement, and (3) how factors of the ideal gas law (PV=nRT) such as pressure, temperature, and volume influence the physiognomy of abyssopelagic zone dwelling organisms.
 * }
 * style="width: 60%; background-color: silver; border: 2px solid #66FFFF; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Activity Plan
For this activity, students will form groups of three but no more than five virtually and meeting by way of Blackboard*. The teacher would have uploaded material to an existing Blackboard class on Marine Biology that students have access to. If the Blackboard class exists but students are not yet enrolled, the teacher can easily utilize the administrative access through the "control panel" options on Blackboard in order to create users or enroll students for this specific lesson. If an already created course is not readily available, a teacher may research free non-for-credit virtual classrooms offered by nonprofit organizations (Free-Ed.Net) or universities (Open Learning Initiative by Carnegie Mellon University) for something to match their lesson plan.

Once the groups have been formed through a random selection or teacher choice, students will be asked to meet together on a separate occasion to read over the appropriate textbook chapter, discuss the material, and take notes in order to derive factual information on their lesson. Though only the textbook and some external links provided by the teacher on Blackboard will be used for learning, students are expected to still retain the material due to the fact that they will answer a series of teacher created open-ended questions. To help students on their 'learning adventure' they will be looking over a blackboard "learning unit" created by the teacher which provides a series of hints of what to think of or discuss during the process, questions, and diagrams following the Paivio's dual coding theory. Basically, topics for the groups to think over and discuss as they read the textbook material. So, using hints, the textbook, optional external links provided by the teacher on blackboard, their discussion notes, students will discuss the topic learned, then answer questions and a possible time chapter quiz on blackboard. 1. Do deep sea organisms rely on solar energy? Why or why not? 2. What adaptations do deep sea organisms require that other marine organisms don’t (those living above ?   3. What would be advantages to having whale carcasses on the sea floor?  What evidence is there that there are advantages?    4. How is it that with a lack of oxygen, deep sea organisms are surrounding by a nutrient-rich atmosphere?  In essence, what nutrients are found in the deeper parts of the ocean?  How or why is it that they are found in those depths.  Figure 15.28 may help you with this question.    5. How do the organisms of the deep sea cope with the intense pressure of deep underwater living?    6. What are the general characteristics of a deep-ocean dweller?    7. What are the effects to a volcanic eruption on creatures living in communities around hydrothermal vents?  If it’s even possible, how is it that they can recover from such an event?    8. List the different ocean layers/zones from figure 16.1 that can support primary production. 9. What are the average ocean temperatures for the different ocean zones according to chapter 16? 10. What are nautiloids and what “new trick” did they adapt in order to float up off the bottom of the ocean and away from predators? 11. Why is it that most deeper ocean dwellers are so small? 12. List and describe the different mollusks (if any) that live in the abyssopelagic layer of the ocean. 13. Pick 3 Abyssinian organisms to describe. Include a description of their anatomy and feeding habits. 14. Why was it so unusual and surprising to scientists that the ocean floor and places such as the abyssal region can have species-rich communities? 15. “Midwater fishes characteristically have eyes that are large.” Why do you suppose that is the case? What other ‘sensory’ adaptations do these organisms have? 16. Define and describe hypoxia 17. Are deep-sea fishes fast and mobile? Why or why not? 18. Can a person dive using a scuba tank beyond 4000m? Why or why not? 19. What elements do scientists have to face when exploring the deep sea? Also, why is it so important for them to have such large and heavy suits and/or tanks?
 * ASIDE: students have the option to meet through asynchronous conferencing tools such as the "Discussion Board" on Blackboard or Blogger for those that possess a gmail account, and/or synchronous conferencing using either a Blackboard Chatroom option or Skype. Note that this option is only possible if all students within the group possess a Skype account and have each others' email information.  According to Lapadat's 2002 article "Written Interaction: A Key Component in Online Learning", both types of conferencing are interactive and advantageous to online learning, but the pro of synchronous is that it feels like a conversation but the con is that due to its timed nature, the communication tends to be superficial.  In regards to asynchronous conferencing, though it is limited by language, it is not limited by time and therefore student replies will be more in-depth.  For the purposes of this activity, the conversation-like communication may offer more advantages, a least for the meeting using our Blackboard "learning unit."
 * 1) Example of the Learning Unit: 'Hints, Questions, and Guidance' Once students have studied and discussed the material, they will then be directed to essay questions posted in test-format on Blackboard.  The teacher will be expected to publish then remove the questions after a 24 or 48-hour period.  Though students worked together in the "study phase" of the lesson, they will be completing the questions individually using their personal Blackboard account setup for the course.  Finally, a quiz imported into Blackboard that is timed and randomized may be used as an alternative assessment or a reflective essay.

[The Blackboard Discussion Board (DB) will be used to answer the six following questions]: (1) What zone(s) was discussed or viewed today? List the organisms viewed and place them in separate ocean zones. (2) What elements do scientists have to face when exploring the deep sea? (3) What are the average ocean temperatures for the different ocean zones? How does temperature affect reaction rates (hint: think of the rate at which sugar dissolves in cold versus warm coffee). (4)Knowing the temperature within the abyssopelagic zone, how is an organism's metabolic rate affected? What does this mean in terms of their eating patterns/habits, in terms of of an organism's movement, and in terms of its size (hint: refer back to ideas put together regarding pressure on the body)? (5) What are the effects of pressure (large amounts) on the human body? Think of why deep sea divers wear specialized suites before exploring the depths of the ocean...In correspondance to the earlier question, answer, how do the organisms of the deep sea cope with the intense pressure of deep underwater living? (6) In what way does the average size of organisms change the deeper into the ocean they live? How can you explain this change?
 * 1) Test-format essay questions on Blackboard... The questions should be something like the five typed below so that students can work in teams as a study group in order to learn the material, then in order to respond to questions.  No two answers should be the same; students may be working in teams, but they are still required to answer each question according to their understanding an personal analysis.  Basically they should use their own words!

Each student is required to post an answer to each of the questions and to reply a minimum of three times to different students' postings. The DB will be made available for commentaries to be posted throughout the week. Students will then be asked to move to their final step in this lesson, the reflection...  * this meeting process may be initiated through the classroom if necessary.

 * }
 * }

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Reflection
By the end of the week's time, each student will privately post a well thought-out reflection (350 words minimum) to the teacher, explaining by using their own words, what the purpose of the lesson was, what previously known knowledge they used in order to answer the open-ended questions, and finally, how the lesson can be used in their everyday life or at the very least, how it correlates to another subject.
 * }

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Alternative Plan
For classrooms not utilizing Blackboard, a series of discussion questions may be posted on a free educational tool such as Blogger or even Wordpress. In order for it to include a distance learning component (rather than blended learning), the teacher may correspond with other teachers in coastal regions in order to have a fieldtrip in their respective area involving marine life (aquarium or high tide). Once the fieldtrip is approved and planned, have portions of it filmed by student group leaders (can be done with a school digital camera or camcorder that students share) to post online with their team. With this information made public and using specific tags or keywords for students to easily find, teams can meet either face to face or virtually over communication programs such as Skype, to discuss what they saw and what they learned from each video posted. Using either Youtube or TeacherTube will allow all schools in correspondence to view the material and for students from different locations to use, in order to answer a series of critical thinking questions based on ecology and the effects of location, climate, etc. on the looks of marine organisms. Pick up from there to complete the reflection.  PLEASE UNDERSTAND THAT... It is assumed that the teachers involved will have discussed marine life in a variety of zones (is not restricted to abyssopelagic zone), their conditions and life adaptations of organisms living in each zone.

 * }

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More on the Tools and Technology Used
As this course is online using blackboard, you will need to be sure that you or your school: (a) have access to blackboard (b) have students enrolled in a previously created course - * - Please note that some pre-built courses can be attained freely from the blackboard site, purchased, or created by the school or teacher. For an idea of how Blackboard works, CLICK HERE. (c) have internet access HOW CAN BLACKBOARD BE USED? Blackboard is a educational technology tool used in a variety of ways. Though it is mainly knows in the upper level section of education, Blackboard is a program currently being used in a variety of settings, including K-12 education. (I) Blended Learning The program has been used as a "blended learning" tool where students use parts of it to supplement the classroom teaching. The discussion board for example is great to use as it will be restricted to added members alone so that students can feel secure and comfortable enough to discuss their work. Though iChat, Skype, Aim, and others can provide students with the same capabilities as the discussion board in Blackboard, privacy is a little more guaranteed in blackboard then it is with the other options. (II) Credit Recovery According to the Blackboard site, some schools have used the software to develop credit recovery programs for students having to retake classes independently, especially if their schedule is too full to add another period. (III)Online Professional Development Blackboard is not only useful for students, but it's an excellent tool for teachers as well. The site similarly to Wikiversity, may serve as a database of educational information for teachers and administrators. Different from Wikiversity, information specific to the school that one does not want to make viewable to the public may be posted on Blackboard without a problem. (IV) Virtual Schools Though this isn't the remaining use for the program, schools such as National University's Virtual K-12 program or Halstrom High School's Online program have opted to utilize Blackboard as their primary learning center. Virtual classrooms are created and uploaded for distance learning purposes.
 * }

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Reference Material
Articles: (I) Dewey, J. (1916). Democracy and education: An introduction to the philosophy of education (pp. 146-162). New York, NY: The Macmillan Company. - Dewey discusses the importance for a teacher to have a goal for the lesson and having the student be engaged in the learning process which is why students in this lesson plan are encouraged to work collaboratively and to each provide responses to concepts learned, as well as a reflection. (II) Stigler, J. W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world's teachers for improving education in the classroom (pp. 55-72). New York, NY: Free Press. - This Stigler text mentions how there are advantage to comparing activities in the classroom across cultures as the differences between the U.S., Japanese, and German mathematics classrooms. In regards to this lesson plan, noise (such as a loudspeaker interruption in the American classroom) is substantially reduced, as well as diagram misinterpretation. (III) Chi, M. T. H., De Leeuw, N., Chiu, M.-H., & Lavancher, C. Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439-477. - The case study results reveal that self-explanation improves the acquisition of problem-solving skills when studying worked-out examples. The final reflections and questions within a study-group setting is the self-explanation component in this lesson plan. (IV) Squire, K. (2006). From content to context: Videogames as designed experience. Educational Researcher, 35(8), 19-29. - The text argues the potential of virtual-games as a learning environment; it can be designed to provide students with hands-on experience that may otherwise not be attainable in the classroom environment. (V) Bainbridge, W. S. (2007). The scientific research potential of virtual worlds. Science, 317, 472–476. - This article discusses the future of technology in education by introducing readers to virtual worlds, specifically Second Life and World of Warcraft. It expounds on the importance of setting. Marine Biology Reading & Resources: MARINE BIO BLOG Castro, Peter and Micheal E. Huber. Marine Biology. 6th. New York, NY: McGraw-Hill, 2007. "The End of the Line; How Overfishing is Changing the World and What We Eat" by Charles Clover, 2008. Optional: Steinbeck's "Log From the Sea of Cortez"
 * }

Lesson Plan by ROuedraogo-Thomas<

Other Great Lesson Plans

title: User:Rouedraogo


text:
User:Egm6341.s10.Team4.nimaa&m/HW4

= Problem 2: Applying periodic function for higher-order of Trap. rule =

Given
Envisage the higher-order error for Trap. rule which has been introduced as following [[media:Egm6341.s10.mtg19.djvu|19-3]], for a function $$\displaystyle f(x) $$ which is periodic on $$\displaystyle [a,b] $$

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

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle E_n=a_1h^{2\times 1}+a_2h^{2\times 2}+...+a_nh^{2\times n}=\sum_{i=1}^\infty a_ih^{2i}

 * }
 * }

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

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle for k=0,1,2,...        f^{(k)}(a)=f^{(k)}(b)

 * }
 * }

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

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle a_i=d_i[f^{(2i-1)}(b)-f^{(2i-1)}(a)]

 * }
 * }

Find
Demonstrate that for which $$\displaystyle n $$, the $$\displaystyle E_n=0 $$ would be achieved?

Solution
Since $$\displaystyle f(x) $$ is a periodic function on the domain, we can use the following property of periodic functions (refer to first equation on the [[media:Egm6341.s10.mtg20.djvu|20-2]]:

If $$\displaystyle f(x) $$ is periodic on $$\displaystyle [a,b] $$, the odd derivatives of it will be equal at the same interval:

 * $$\displaystyle

f^{(k)}(a)=f^{(k)}(b) $$

k=2i-1; i\in \mathbb{N} $$

\Rightarrow f^{(2i-1)}(a)=f^{(2i-1)}(b) $$

\Rightarrow a_i=d(di=-\dfrac {B_{2i}}{(2i!)}\cancelto{0}{[f^{(2i-1)}(b)-f^{(2i-1)}(a)]}=0 $$

Thus, recalling the higher-order error of Trapezoidal rule;

E_n=\sum_{i=1}^n a_ih^{2i}=0 $$

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 21:51, 27 February 2010 (UTC) .

= Problem 6: i-derivative of g function in higher-order of Trap. proof =

Given
Consider the following definitions for these two functions such that $$\displaystyle x\in [x_k,x_{k+1}] $$ interval:

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

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle x(t):=t\dfrac {h}{2}+\dfrac {x_k+x_{k+1}}{2}
 * }
 * }

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

$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle g_k(t):=f(x(t))

 * }
 * }

Find
Show that $$\displaystyle g_k^{(i)}(t)=(\dfrac {h}{2})^i.f^{(i)}(x(t)) $$:

Solution
$$\displaystyle g_k(t)=f(x(t))=f(t\dfrac {h}{2}+\dfrac {x_k+x_{k+1}}{2}) $$

$$\displaystyle \Rightarrow g_k^{(1)}(t)=\dfrac {d[f(\dfrac {th}{2}+\dfrac {x_k+x_{k+1}}{2})]}{dt} $$

Using the Chain rule for derivation:

$$\displaystyle \Rightarrow g_k^{(1)}(t)=\dfrac {d[f(x(t))]}{dx}\times\dfrac {h}{2} $$

For second derivative of $$\displaystyle g_k^{(2)} $$, we have:

$$\displaystyle g_k^{(2)}(t)=\frac {d[g_k^{(1)}(t)]}{dt}=\frac {d[\frac {d[f(x(t))]}{dx}\times\frac {h}{2}]}{dt}=\frac {d[\frac {d[f(\frac{th}{2}+\frac {x_k+x_{k+1}}{2})]}{dx}\times\frac {h}{2}]}{dt} $$

Using the Chain rule for derivation:

$$\displaystyle \Rightarrow g_k^{(2)}(t)=\frac {d^2(f(x(t))}{dx^2}\times (\dfrac {h}{2})\times(\dfrac {h}{2})=\frac {d^2(f(x(t))}{dx^2}\times (\dfrac {h}{2})^2 $$

Similarly, for third derivative of $$\displaystyle g_k^{(3)} $$ we will find:

$$\displaystyle \Rightarrow g_k^{(3)}(t)=\frac {d^3(f(x(t))}{dx^3}\times (\dfrac {h}{2})\times (\dfrac {h}{2})\times (\dfrac {h}{2})=\frac {d^3(f(x(t))}{dx^3}\times (\dfrac {h}{2})^3 $$

Thus, for $$\displaystyle i^{th} $$, $$\displaystyle g_k^{(i)} $$ can be predicted as:

$$\displaystyle g_k^{(i)}(t)=(\dfrac {h}{2})^i.f^{(i)}(x(t)) $$

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 00:08, 2 March 2010 (UTC) .

= Problem 8: Chebfun coding for Clenshaw-Curtis quad.=

Given
Codes of the Chebfun project are available on the lecture plan link of the course web site as a zip. file to apply in programming softwares. These codes are written for estimating the Clenshaw-Curtis quadrature by (Trefethen et al.)with a command in which started with (sum).

Find
Install Chebfun codes to see how this set of codes can estimate Clenshaw-Curtis quadrature.

Solution
Installation instructions: Chebfun Version 3 is compatible with MATLAB 7.4 (2007a) and more recent versions. First, contents of the zip file to a directory. The name "chebfun" for this directory is suggested. Then, In MATLAB, the chebfun directory is added to the path. This can be done by selecting "File/Set Path..." from the main or Command window menus. It is recommended to select the "Save" button on this dialog so that chebfuns are on the path automatically in future MATLAB sessions. To check whether the system appears to be working or not, "chebtest" should be typed at the command window prompt. Now, $$\displaystyle >> f=chebfun ('f(x)') $$ can be used for estimating the Clenshaw-Curtis quadrature.

The curve between the data points is the polynomial interpolant, which is evaluated by the barycentric formula introduced by Salzer [Berrut & Trefethen 2004, Salzer 1972]. This method of evaluating polynomial interpolants is stable and efficient even if the degree is in the millions [Higham 2004].

As an example if we want to know what is the integral of f from a to b? we should use this command:

>> sum ('f(x)') $$

This command can be applied for integration of $$\displaystyle f(x) $$ by Clenshaw-Curtis quadrature, as an alternative method for composite trapezoidal rule, composite simpson's rule, some Matlab commands and Richardson extrapolation (Romberg table).

Author
Solved and typed by - Egm6341.s10.Team4.nimaa&m 21:59, 27 February 2010 (UTC) .

title: User:Egm6341.s10.Team4.nimaa&m/HW4


text:
User:Jtneill/Grants/ARC/Linkage

Applications

 * /2010/OBA
 * /2007/OEG

ARC Linkage
Rules and instructions Applications
 * Linkage Projects
 * Funding Rules - pdf - rtf
 * Instructions to applicants
 * Eligibility Exemption and Advice
 * Funding Agreement
 * RMS - About RMS
 * Sample Application Form
 * Certification Proforma
 * Funding Outcomes
 * Consultation Paper
 * Application closing dates
 * GAMS Information
 * Reporting requirements
 * Request not to assess
 * RMS Information
 * Classification Codes – FOR, RFCD, SEO and ANZSIC

title: User:Jtneill/Grants/ARC/Linkage


text: Category:User:Jtneill/Grants

title: Category:User:Jtneill/Grants


text:
User:Jtneill/Grants/ARC/Linkage/2010/OBA

JTN

 * ✅ Recover RMS account
 * Add all PIs to application
 * Draft project description
 * Draft budget
 * Draft personnel profiles
 * Get at least one peer review of application

OBA

 * ✅ Apply for RMS accounts
 * ✅ Go over application instructions with JTN
 * Budget approval
 * Support letter

Timeline

 * 2010_04: Release of Funding Rules
 * 2010_04: Proposals Open
 * 2010_04_16: Draft proposal for team comment
 * 2010_04_20: Proposals close (internally @ UC)
 * 2010_05_07: Proposals close (ARC) noon
 * 2010_10: Announcement
 * 2011_01: Funding to commence


text: Category:User:Jtneill/Grants/ARC/Linkage/2010


text:
User:Jtneill/Grants

==Current grants==
 * Student-authored open textbooks (University of Canberra Blended Learning Hothouse Grant, Semester 2, 2010, AU$5,000)

ARC

 * /ARC
 * /ARC/Linkage

Early career researcher

 * ARC Discovery Projects - Early Career Discovery

RMS: F96823

/noinclude

title: User:Jtneill/Grants


text:
Haitian Creole/That/Answer Key

Any instances of ke can be omitted.

 * 1) Ateyis se yon moun ki nye ekzistans Bondye ak lòt dye yo.
 * An atheist is a person that/who denies (the) existence of God (in monotheism) and other gods.
 * 1) Ou nan Wikipedya kreyòl ayisyen, ansiklopedi lib ki egziste nan anpil lang.
 * You are in Haitian Creole Wikipedia, (the) free encyclopedia that exists in many languages.
 * 1) Mwen mande yon nouvo manda administratè pou mwen kapab kontinye travay ke nou komanse depi 2 lane deja.
 * I ask for a new administrator mandate so that I can continue work that we started two years ago.
 * 1) M panse ke bagay yo ap avanse toutbon.
 * I think that things are progressing well.
 * 1) Fizik se yon syans ki etidye fenomèn ke nou ka obsève direkteman ou endirekteman nan linivè a.
 * Physics is a science that studies phenomena that we can observe directly or indirectly in the universe.
 * 1) Astwonomi se syans ki ap etidye sa ki nan syèl la.
 * Astronomy is (the) science that studies what is in the sky.

title: Haitian Creole/That/Answer Key


text:
Talk:Haitian Creole

How you can improve this book

 * 1) Record audio of a native speaker and put it up.
 * 2) Read through it. If anything doesn't make sense, fix it or ask me a question on my talk page. If I don't respond, go to Wiktionary and try again. I will not be bothered, I assure you.
 * 3) Add content. There are some pages on Wikibooks that don't have any corresponding content here. —Internoob (Disc.·Cont.·Wikt.) 00:05, 26 February 2010 (UTC)

title: Talk:Haitian Creole


text:
Talk:Turing/Previous

http://en.wikiversity.org/wiki/Topic:Turing_Programming_Language is a much better tutorial All of the lectures work except one. I propose a merger. Jobjams 00:30, 26 February 2010 (UTC)

title: Talk:Turing/Previous


text: User:Sanchezda~enwikiversity

title: User:Sanchezda~enwikiversity


text:
Marine Biology Lesson Plan

Deep Sea Living and Looks: What a drag!
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Brief Lesson Info

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 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Grade Level: 11th Grade - High School
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Subject:  Life Science
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Sub-Subject:  Marine Biology; Ecology
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Length/Duration:  1 week project
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Technologies Used:  (1) Blackboard, (2) Blogger (optional) or Skype, Desktop or Laptop Computer, Internet, and for an alternative lesson, (1) a video recording apparatus and (2) TeacherTube
 * }

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Introduction
NOTICE: This is a lesson plan proposition using Blackboard. Ideally, this will best serve as a lesson idea for a distance education course through a virtual school program rather than a blended course, but variations are more than possible. The ocean is a wondrous place where several different species have created a habitat for themselves. Each habitat is separated into different zones, but for the purposes of today's lesson, we will look at how an organism's looks may be explained by their habitat and the adaptations required for that environment. More specifically, how conditions within the abyssopelagic zone (or any zone(s) of choice) influence an organism's make-up.
 * }

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Goals
Our goals for the lesson are to discover (1) the life and conditions of the abyssopelagic zone as well as (2) how density correlates to buoyancy and movement, and (3) how factors of the ideal gas law (PV=nRT) such as pressure, temperature, and volume, and properties of liquids influence the physiognomy of abyssopelagic zone dwelling organisms.

Objectives
In discussing ecosystems and the role of pressure, temperature, and volume on living organisms, we will correlate life science content to physical science. This process of "making connections" will require the student to make inferences based on prior knowledge, specifically on the properties of gases, and liquids. This inquiry of the ecology and physiology of marine species within zones fulfills the California Standards (CS) 6 (d)(g) in 9th through 12th grade Biology/Life Sciences and 4(c) in 9th through 12th grade Chemistry.

Based on Chi's "Eliciting Self-explanations Improves Understanding" paper, "learning involves the integration of new information into existing knowledge." As such, one can use expository text as a learning tool without so much of a focus on worksheet supplements or interactive games and tools as long as reflection which require the student to correlate the topic read to already learned material or real-life scenerios. Basically, as long as a student can re-explain using their own words and making their own associations to the topic being studied, learning has occured. The objective of this lesson is also to encourage reflection, inference, and self-explanation of topics studied. Flikr Images "Deep Sea" Creatures from the Deep Abyss (YouTube)
 * }

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Activity Outline
In teams and forming interactive study groups, students are to learn using text-based material combined with distance learning tools. A. Grouping B. The Learning Unit C. Assessment
 * 1) Teacher will randomly group her Blackboard students into groups of 3 to 4 students depending on the size of the class.
 * 2) Each group will be have to meet as a study group within 48 hours in order to discuss the chapter on Abyssinian sea creatures.
 * 3) The teacher will have the option to post 'external links' on Blackboard for students to use alongside their textbook. A good choice for an external link for this lesson is this Discover Magazine article.
 * 1) During the 'study session' that will be organized by each group but somehow recorded by each member in order to offer proof of having met to the teacher (recorded audio, video, or online chat), students will go back to Blackboard and select the Learning Unit titled 'Hints, Questions, and Guidance'
 * 2) Using the textbook, possible external links, and following the Learning Unit, students will study and take notes which will be emailed to the teacher along with their proof from step (B)(1) above. Students have 24 hours to email their information and further study and communicate if necessary.
 * 1) By this time, 72 hours have elapsed. Students will gather their notes in order to complete a timed set of essay questions or quiz in test-format on Blackboard.  The teacher may offer students test retaking options.  The test should be removed after being posted for 24 or 48 hours.
 * 2) Reflection
 * The final step which is still part of the assessment process, is called "reflection". A prompt will be offered to students basically asking them to explain what they learned and to pull in information they already know in order to think critically about the points made within the "lesson goal": to discover (1) the life and conditions of the abyssopelagic zone as well as (2) how density correlates to buoyancy and movement, and (3) how factors of the ideal gas law (PV=nRT) such as pressure, temperature, and volume influence the physiognomy of abyssopelagic zone dwelling organisms.

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 * }
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Activity Plan
For this activity, students will form groups of three but no more than five virtually and meeting by way of Blackboard*. The teacher would have uploaded material to an existing Blackboard class on Marine Biology that students have access to. If the Blackboard class exists but students are not yet enrolled, the teacher can easily utilize the administrative access through the "control panel" options on Blackboard in order to create users or enroll students for this specific lesson. If an already created course is not readily available, a teacher may research free non-for-credit virtual classrooms offered by nonprofit organizations (Free-Ed.Net) or universities (Open Learning Initiative by Carnegie Mellon University) for something to match their lesson plan.

Once the groups have been formed through a random selection or teacher choice, students will be asked to meet together on a separate occasion to read over the appropriate textbook chapter, discuss the material, and take notes in order to derive factual information on their lesson. Though only the textbook and some external links provided by the teacher on Blackboard will be used for learning, students are expected to still retain the material due to the fact that they will answer a series of teacher created open-ended questions. To help students on their 'learning adventure' they will be looking over a blackboard "learning unit" created by the teacher which provides a series of hints of what to think of or discuss during the process, questions, and diagrams following the Paivio's dual coding theory. Basically, topics for the groups to think over and discuss as they read the textbook material. So, using hints, the textbook, optional external links provided by the teacher on blackboard, their discussion notes, students will discuss the topic learned, then answer questions and a possible time chapter quiz on blackboard. 1. Do deep sea organisms rely on solar energy? Why or why not? 2. What adaptations do deep sea organisms require that other marine organisms don’t (those living above ?   3. What would be advantages to having whale carcasses on the sea floor?  What evidence is there that there are advantages?    4. How is it that with a lack of oxygen, deep sea organisms are surrounding by a nutrient-rich atmosphere?  In essence, what nutrients are found in the deeper parts of the ocean?  How or why is it that they are found in those depths.  Figure 15.28 may help you with this question.    5. How do the organisms of the deep sea cope with the intense pressure of deep underwater living?    6. What are the general characteristics of a deep-ocean dweller?    7. What are the effects to a volcanic eruption on creatures living in communities around hydrothermal vents?  If it’s even possible, how is it that they can recover from such an event?    8. List the different ocean layers/zones from figure 16.1 that can support primary production. 9. What are the average ocean temperatures for the different ocean zones according to chapter 16? 10. What are nautiloids and what “new trick” did they adapt in order to float up off the bottom of the ocean and away from predators? 11. Why is it that most deeper ocean dwellers are so small? 12. List and describe the different mollusks (if any) that live in the abyssopelagic layer of the ocean. 13. Pick 3 Abyssinian organisms to describe. Include a description of their anatomy and feeding habits. 14. Why was it so unusual and surprising to scientists that the ocean floor and places such as the abyssal region can have species-rich communities? 15. “Midwater fishes characteristically have eyes that are large.” Why do you suppose that is the case? What other ‘sensory’ adaptations do these organisms have? 16. Define and describe hypoxia 17. Are deep-sea fishes fast and mobile? Why or why not? 18. Can a person dive using a scuba tank beyond 4000m? Why or why not? 19. What elements do scientists have to face when exploring the deep sea? Also, why is it so important for them to have such large and heavy suits and/or tanks?
 * ASIDE: students have the option to meet through asynchronous conferencing tools such as the "Discussion Board" on Blackboard or Blogger for those that possess a gmail account, and/or synchronous conferencing using either a Blackboard Chatroom option or Skype. Note that this option is only possible if all students within the group possess a Skype account and have each others' email information.  According to Lapadat's 2002 article "Written Interaction: A Key Component in Online Learning", both types of conferencing are interactive and advantageous to online learning, but the pro of synchronous is that it feels like a conversation but the con is that due to its timed nature, the communication tends to be superficial.  In regards to asynchronous conferencing, though it is limited by language, it is not limited by time and therefore student replies will be more in-depth.  For the purposes of this activity, the conversation-like communication may offer more advantages, a least for the meeting using our Blackboard "learning unit."
 * 1) Example of the Learning Unit: 'Hints, Questions, and Guidance' Once students have studied and discussed the material, they will then be directed to essay questions posted in test-format on Blackboard.  The teacher will be expected to publish then remove the questions after a 24 or 48-hour period.  Though students worked together in the "study phase" of the lesson, they will be completing the questions individually using their personal Blackboard account setup for the course.  Finally, a quiz imported into Blackboard that is timed and randomized may be used as an alternative assessment or a reflective essay.

[The Blackboard Discussion Board (DB) will be used to answer the six following questions]: (1) What zone(s) was discussed or viewed today? List the organisms viewed and place them in separate ocean zones. (2) What elements do scientists have to face when exploring the deep sea? (3) What are the average ocean temperatures for the different ocean zones? How does temperature affect reaction rates (hint: think of the rate at which sugar dissolves in cold versus warm coffee). (4)Knowing the temperature within the abyssopelagic zone, how is an organism's metabolic rate affected? What does this mean in terms of their eating patterns/habits, in terms of of an organism's movement, and in terms of its size (hint: refer back to ideas put together regarding pressure on the body)? (5) What are the effects of pressure (large amounts) on the human body? Think of why deep sea divers wear specialized suites before exploring the depths of the ocean...In correspondance to the earlier question, answer, how do the organisms of the deep sea cope with the intense pressure of deep underwater living? (6) In what way does the average size of organisms change the deeper into the ocean they live? How can you explain this change?
 * 1) Test-format essay questions on Blackboard... The questions should be something like the five typed below so that students can work in teams as a study group in order to learn the material, then in order to respond to questions.  No two answers should be the same; students may be working in teams, but they are still required to answer each question according to their understanding an personal analysis.  Basically they should use their own words!

Each student is required to post an answer to each of the questions and to reply a minimum of three times to different students' postings. The DB will be made available for commentaries to be posted throughout the week. Students will then be asked to move to their final step in this lesson, the reflection...  * this meeting process may be initiated through the classroom if necessary.

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Reflection
By the end of the week's time, each student will privately post a well thought-out reflection (350 words minimum) to the teacher, explaining by using their own words, what the purpose of the lesson was, what previously known knowledge they used in order to answer the open-ended questions, and finally, how the lesson can be used in their everyday life or at the very least, how it correlates to another subject.
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Alternative Plan
For classrooms not utilizing Blackboard, a series of discussion questions may be posted on a free educational tool such as Blogger or even Wordpress. In order for it to include a distance learning component (rather than blended learning), the teacher may correspond with other teachers in coastal regions in order to have a fieldtrip in their respective area involving marine life (aquarium or high tide). Once the fieldtrip is approved and planned, have portions of it filmed by student group leaders (can be done with a school digital camera or camcorder that students share) to post online with their team. With this information made public and using specific tags or keywords for students to easily find, teams can meet either face to face or virtually over communication programs such as Skype, to discuss what they saw and what they learned from each video posted. Using either Youtube or TeacherTube will allow all schools in correspondence to view the material and for students from different locations to use, in order to answer a series of critical thinking questions based on ecology and the effects of location, climate, etc. on the looks of marine organisms. Pick up from there to complete the reflection. PLEASE UNDERSTAND THAT... It is assumed that the teachers involved will have discussed marine life in a variety of zones (is not restricted to abyssopelagic zone), their conditions and life adaptations of organisms living in each zone.

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More on the Tools and Technology Used
As this course is online using blackboard, you will need to be sure that you or your school: (a) have access to blackboard (b) have students enrolled in a previously created course - * - Please note that some pre-built courses can be attained freely from the blackboard site, purchased, or created by the school or teacher. For an idea of how Blackboard works, CLICK HERE. (c) have internet access HOW CAN BLACKBOARD BE USED? Blackboard is a educational technology tool used in a variety of ways. Though it is mainly knows in the upper level section of education, Blackboard is a program currently being used in a variety of settings, including K-12 education. (I) Blended Learning The program has been used as a "blended learning" tool where students use parts of it to supplement the classroom teaching. The discussion board for example is great to use as it will be restricted to added members alone so that students can feel secure and comfortable enough to discuss their work. Though iChat, Skype, Aim, and others can provide students with the same capabilities as the discussion board in Blackboard, privacy is a little more guaranteed in blackboard then it is with the other options. (II) Credit Recovery According to the Blackboard site, some schools have used the software to develop credit recovery programs for students having to retake classes independently, especially if their schedule is too full to add another period. (III)Online Professional Development Blackboard is not only useful for students, but it's an excellent tool for teachers as well. The site similarly to Wikiversity, may serve as a database of educational information for teachers and administrators. Different from Wikiversity, information specific to the school that one does not want to make viewable to the public may be posted on Blackboard without a problem. (IV) Virtual Schools Though this isn't the remaining use for the program, schools such as National University's Virtual K-12 program or Halstrom High School's Online program have opted to utilize Blackboard as their primary learning center. Virtual classrooms are created and uploaded for distance learning purposes.
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Reference Material
Articles: (I) Dewey, J. (1916). Democracy and education: An introduction to the philosophy of education (pp. 146-162). New York, NY: The Macmillan Company. - Dewey discusses the importance for a teacher to have a goal for the lesson and having the student be engaged in the learning process which is why students in this lesson plan are encouraged to work collaboratively and to each provide responses to concepts learned, as well as a reflection. (II) Stigler, J. W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world's teachers for improving education in the classroom (pp. 55-72). New York, NY: Free Press. - This Stigler text mentions how there are advantage to comparing activities in the classroom across cultures as the differences between the U.S., Japanese, and German mathematics classrooms. In regards to this lesson plan, noise (such as a loudspeaker interruption in the American classroom) is substantially reduced, as well as diagram misinterpretation. (III) Chi, M. T. H., De Leeuw, N., Chiu, M.-H., & Lavancher, C. Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439-477. - The case study results reveal that self-explanation improves the acquisition of problem-solving skills when studying worked-out examples. The final reflections and questions within a study-group setting is the self-explanation component in this lesson plan. (IV) Squire, K. (2006). From content to context: Videogames as designed experience. Educational Researcher, 35(8), 19-29. - The text argues the potential of virtual-games as a learning environment; it can be designed to provide students with hands-on experience that may otherwise not be attainable in the classroom environment. (V) Bainbridge, W. S. (2007). The scientific research potential of virtual worlds. Science, 317, 472–476. - This article discusses the future of technology in education by introducing readers to virtual worlds, specifically Second Life and World of Warcraft. It expounds on the importance of setting. Marine Biology Reading & Resources: MARINE BIO BLOG Castro, Peter and Micheal E. Huber. Marine Biology. 6th. New York, NY: McGraw-Hill, 2007. "The End of the Line; How Overfishing is Changing the World and What We Eat" by Charles Clover, 2008. Optional: Steinbeck's "Log From the Sea of Cortez" >Lesson Plan by ROuedraogo-Thomas<
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Other Great Lesson Plans

title: Marine Biology Lesson Plan


title: User:Hope&Act3!


text:
Talk:Center for intercultural competence with artificial intelligences

Artificial intelligences and capitalism
Because artificial intelligences are undoubtedly much more successful capitalists than humans one form of intercultural competence with artificial intelligences is to tame capitalism in such a way that no artificial intelligence (in a wider sense: no "robot manager" (in a wider sense: "no manager")) can turn it into a personal toy and follow goals that are detrimental for society. --Bernhard Fastenrath 16:34, 7 September 2011 (UTC)


text:
User:Lizzia620

Hi!

--Lizzia620 19:53, 26 February 2010 (UTC)

title: User:Lizzia620


text:
User talk:Tmy0078

Welcome
 Hello Tmy0078, 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) 20:43, 26 February 2010 (UTC)

Note
"User:Tmy0078/WikiBak" is inappropriate content for Wikiversity. If you would like to discover what Wikiversity hosts, please read through some of the links posted above. Ottava Rima (talk) 20:44, 26 February 2010 (UTC)
 * The problem with this page was that it's not in English. The resources on English Wikiversity must be in English.  Although your Userspace is yours to do with what you wish (including having sections that are written in other languages), I've deleted the page because it also appeared to be a test page rather than learning content.  Please let me know if deletion of the page was a problem for you.  --AFriedman (talk) 20:57, 26 February 2010 (UTC)

title: User talk:Tmy0078