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(Solved) CHME 312, Spring 2017 Homework 5 Due Friday 03/13/17 Note: Please follow the submission guidelines properly. One SINGLE file submission. Name your...


I would like full solution for all the questions posted in the file.There is one part of it that requires matlab.Thank you

CHME 312, Spring 2017
Homework 5
Due Friday 03/13/17
Note: Please follow the submission guidelines properly. One SINGLE file
submission. Name your file in this format: <your last name>_<homework
number>.<doc/docx/pdf>. For example: smith_hw1.pdf. COPY your Matlab code
into your document. DO NOT take a screenshot of your code and paste it in your
document as image. Remember to include the outputs/plots/tables in your
submission. A wrong format or partial submission will affect your score.
Problem 1: (a) Fit the following dataset using Chebyshev polynomial as basis functions
of the form between [-1,1].
T0 (x) = 1
T1 (x) = x x f(x) -1 98.001 -0.5556 30.384 -0.1110 1.221 0.3333 11.038 0.7778 60.360 Decide and explain your choice of “n” based on the number of data points. Do not use
Matlab builtin functions (such as polyfit). You can perform the detailed steps by writing
Matlab code accordingly.
(b) Now use Matlab function polyfit and compare your results in (a) with it. Problem 2: Use Newton’s Forward and Backward approximation method to find the
function value at x = 1.72 by hand.
x
f(x)
1.7 0.3979849 1.8 0.3399864 1.9 0.2818186 2.0 0.2238908 If f(x=1.72) = 0.3864185, calculate your errors in both cases. Problem 3: The distance x of a runner from a fixed point is measured (in metres) at
intervals of half a second. The data obtained is (a) Use forward differences to approximate the runner’s velocity at t = 0.5s.
(b) Use backward difference to approximate the runner’s velocity at t = 1.25s.
(c) Use a central difference to approximate the runner’s acceleration at t = 1.5s.
Problem 4: Using Simpson’s 3/8 rule (n=10) and trapezoidal rule (n=10), integrate the
following and comment on the accuracy of the results compared to the analytical value.
! =
! ! !!

 


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