Math 1070 Matlab exercise 1

This is an alternative exercise for those familiar with matlab.

To access the files needed for this assignment, in the class web page

http://www.pitt.edu/~trenchea/Math1070_Fall_Semester_2016.html

click on

A collection of matlab codes accompanying the text 

and then on Chapter1

Copy the files plot_exp.m and polyeval.m into your working directory.

The routine plot_exp plots several Taylor polynomials and their errors
for increasing degrees.  The particular function being approximated is
exp(x) and it is being expanded about x = 0.

The function polyeval evaluates a Taylor polynomial. It is used by plot_exp.

Read the comments in the beginning of the two files to better understand
what the code is doing.

Run plot_exp. You will be asked to input a value for b for the
interval [-b,b]. Two plots will be created. The first one plots the
function and four approximating Taylor polynomials. The second one
plots the errors in the approximations. Note that you need to press
any key to produce the second plot.

Create a new routine plot_geom.m similar to plot_exp.m but for the 
function 1/(1-x). To do so perform the following steps.

- copy plot_exp.m into plot_geom.m and modify plot_geom.m
- change the comments to reflect the change in the function
- modify the part that produces the Taylor coefficients to compute the
  coefficients for 1/(1-x)
- change the line 
    true = exp(x);
    true = 1./(1-x); % pay attention to the dot before /
- modify the titles and legends of the two plots

Run the code for different values of b < 1. Also try b >= 1. What happens
in this case?

Submit the following:

1. The two plots created by plot_geom for b = .5. You can save the plots 
into .eps files by commenting out the print statements.

2. A discussion of how the accuracy depends on the degree of the Taylor
polynomial and the distance from x = 0.

3. A discussion of why the program crashes for b >= 1.