Assignment 1

Assignment 1 - AM351 Spring 08 Due Monday, June 9...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
AM351 Spring 08 Due Monday, June 9 Assignment 1 Instructions: write your solutions clearly, explain your steps carefully and refer to the- orems and lemmas when needed. The assignment is due either in class or in the as- signments drop box (4th Foor) by 2pm. 1. ( 3 marks ) Consider the following initial value problem involving Legendre’s equation (1 - x 2 ) y - 2 xy ± + α ( α + 1) y =0 , y (0) = 1 ,y ± (0) = 5 . On what interval does the existence and uniqueness theorem stated in class pre- dict that a unique solution to the problem will exist? Justify your answer. 2. ( 3 marks ) (a) Use the deFnition to show that the functions f 1 ( x ) = 1 ,f 2 ( x )= x, f 3 ( x )= x 2 are linearly independent on the real line. (b) The above result can be generalized to show that the set of functions f 1 ( x ) = 1 ,f 2 ( x )= x, f 3 ( x )= x 2 , ..., f n +1 ( x )= x n are linearly independent on the real line. Use this result to prove that, for any constant r f 1 ( x )= e rx ,f 2 ( x )= xe
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/28/2009 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.

Page1 / 3

Assignment 1 - AM351 Spring 08 Due Monday, June 9...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online