User:Egm6341.s10.team3.sa/Mtg25

Mtg 25 (Lect 22): Thu, 25 Feb 10

 Typeset of transparencies, not lecture transcript. Subramanian Annamalai 13:55, 12 August 2010 (UTC)

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HW:
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(1)Install chebfun and practice sum command to do integration$$\displaystyle\color{blue} I = \int_{0}^{1}\frac{e^{x}-1}{x}dx$$, and record the computational time. Also practice using the tic/toc command in MATLAB.

(2)Compare the second column of Romberg Table Romberg to Simpson's rule and derive any relationship that exists.

(3)For $$\displaystyle\color{blue} I = \int_{0}^{1}\frac{e^{x}-1}{x}dx$$, compare $$\displaystyle\color{blue} I_{n}$$ to $$\displaystyle\color{blue} \theta(10^{-10})$$ and computational time for - Composite Trap rule, - Composite Simpson's rule and - Romberg table.

(4)For $$\displaystyle\color{blue} I = \int_{0}^{1}\frac{e^{x}-1}{x}dx$$, compare $$\displaystyle\color{blue} I_{n}$$ to $$\displaystyle\color{blue} \theta(10^{-10})$$ and computational time by using Matlab : trapz, quad and clencurt commands

(5)Compare the time for each of the above methods and comment on the results.


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Repeat the above HW for the integral, $$\displaystyle\color{blue} I = \int_{-5}^{5} \frac{1}{1+x^2} \,dx $$.


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APPLICATION: Orbital Mechanics Calculate the arc length of the orbit(ellipse) given,



Use all the above integration codes.
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