Homework 1 -- Algebra Review

Purpose

• The study of differential equations is very difficult if the fundamental algebraic techniques and calculus concepts have not been mastered. This assignment, and a similar assignment you will receive on Wednesday, are intended to indicate a few of the basic skills that I expect you to have mastered.
• If you have forgotten how to work problems such as these, I suggest that you spend some time reviewing these techniques. (Note that even though I call this an algebra review, many of the methods needed to solve these problems can be found in your Calculus text.)
• If you have any questions about the assignment, please send them to me in an e-mail message.

Problems

1. Find all roots of the polynomials
   1. 
   2. 
   3. 
2. Find all numbers , , and that satisfy the three equations , , and .
3. Find the functions and that satisfy the two equations and .
4. Use trigonometric identities to write each of the following expressions in the form , i.e. solve for the constants A, , and . Express the angle in both degrees and in radians.
   1. 
   2. 
5. Convert each function into its equivalent partial fraction expansion
   1. 
   2. 
   3. 

• About this document ...