Math 112: MATLAB Assignment 2

   TAYLOR SERIES AND POLYNOMIALS         Due Date: November 30, 2018

The sample program below calculates 2nd and 4th degree Taylor polynomials for the function

about the point

The polynomials are plotted, together with the function, over the interval

Contents

Sample program

Lines beginning with a percent sign (%) are comments construct Taylor polynomials.

figure(1);clf; %open figure one and clear any plots
x=[-1: .01:1];
y=(1+x.^2).^(-1);  %the function
P2=1-x.^2;         %the second-order Taylor polynomial (calculated by hand)
P4=1-x.^2+x.^4;    %the 4th order Taylor polynomial
% annotating the graph is always important
figure(1);clf; %open and clear the 1st figure
plot(x,y,x,P2,'--',x,P4,'-.')
legend('1/(1+x^2)','P_2','P_4')
xlabel('x')
title('The function and the 2^{nd} and 4^{th} order Taylor Polynomials')
figure(2);clf; %open and clear the 2nd figure
plot(x,abs(y-P2),x,abs(y-P4),'--') % abs is the absolute value
legend('|1/(1+x^2)-P_2|','|1/(1+x^2)-P_4|')
xlabel('x')
title('Errors in the two Taylor Polynomials')
% Program output:

New Matlab Ideas

the Legend command generates a legend for your graph. If there are two curves in your graph, the legend command should consist of two strings (defined using single quotation marks). Note that the underscore ('_') is used to make subscripts and the caret ('^') is used to make superscripts. if you want to create a superscript with more than one character in it, enclose the superscripted text in braces ('{}')

For example, to type

you would use the string 'e^{ix}'.

Variables used

Your Assignment

After running the above example, do the following to hand in: (Consult the MATLAB TA's if you have any questions.)

Calculate the 2nd and 3rd degree Taylor polynomials for the function

about the point

     

Plot these polynomials and the function on the interval

    

Please be sure to turn in your hand calculation as well as your code and your clearly labeled plot.