Differential Equations              Study Guide for Hour Quiz #5               C.S.Davis

You are responsible for the subject matter from Zill and Cullen (sixth edition)  in sections 8.1, 9.1, 9.2, 9.4, 11.1, 11.2, 11.3, 12.1 and 12.2. The following topics are notable in their importance.

8.1    1.  Convert from a higher order IVP (or a system of higher order IVP's) to a system of first order IVP's in normal form.   (P383Example2 and a step in the problems below in 9.4)

9.1, 9.2, and 9.4

          1. Use Numerical Methods for solving an  IVP:

        Method                                          1st order             System of 1st order IVP's 

        Euler, n times                                                              P385#1* 
        Improved Euler, n times                   P372#1,3            P385#1*  
        Taylor (second order), n times         P372#1,3            P385#1* 
        Runge-Kutta, 4th order, n times       P377#3,5            P385#3*,7

* Convert the given higher order IVP to a system of first order IVP's in normal form, then solve the system of IVP's.

11.1   1. Use the terms orthogonal function, orthogonal set, orthonormal set, square norm, norm, normalized, orthogonal w/r a weight function.   P434#1,4,7,9,13,14,12(12 look at only)

11.2   1. Determine the Fourier series for a given function.   P439#1,2,3,5

11.3   1. Describe and give examples of even and odd functions.   P446#1,3,5

          2. Determine Fourier cosine and sine series for a given function.   P446#11

          3. Give and explain periodic extensions.  (text)

          4.  Give half range expansions for given Fourier series (the three important ones).   P446#28

12.1    1. Solve PDE's by the method of separation of variables.   P468#1,3,5,7,13

12.2    1. Solve boundary value problems including the heat equation and/or the wave equation.   P474#1,5,9