MTH 142/URI

Summer 2003

Maple Assignment 2

Due date: 7/15/2003

Use worksheet  Taylor Polynomials and Taylor Series to solve Problem 1.

Problem 1. Consider the function [Maple Math]  

(a)  Find the 7, 11, and 20-th degree Taylor polynomial  at x = 0. Find the longest interval [-d,d] about x = 0 in which the polynomial stays within 0.1 of [Maple Math] .

(b)   Plot them together with the graph of g(x) on the interval  [-1, 1].


Use worksheet  Fourier Polynomials and Series to solve Problem 2.

  Problem 2 Consider the function g(x) = [Maple Math] for x between [Maple Math] and [Maple Math] repeated periodically.

 (a)  Compute and have Maple print the Fourier polynomials of degrees 5,7, and 11.

 (b)  Plot them together with the graph of g(x) on the interval [- [Maple Math] , [Maple Math] ] .

Use worksheet  Differential Equations to solve Problem 3.

Problem 3. Consider the following ODE 

 dy/dx = y x/(1 + x2) + y2  .

(a) Find the general solution to the equation.

(b) Plot the slope field corresponding to the equation for x and y between -2 and 2.

(c) Solve the initial value problems

  dy/dx = y x/(1 + x2) + y2 ,   y(1) = 2.