Differential equations and boundary value problems
MATH 386

Spring 2007
d r USI r X FQiitG l i p q D E k G r P X D E r S E k X l S r QVI l QTtTD l F&t7Y7itFG l FG f sk S P r E r Ew G q g tsr l "sYir l E l V tRiVhQFWTFG S l FvTVY&FRT&hG l $y ES y S X r IIS y X U G D p n w
Differential equations and boundary value problems
MATH 386

Spring 2012
SEC. 9.39.4 OVERVIEW SOLVING ODES WITH FOURIER SERIES
[Read this in conjunction with the examples in class and homework.]
Section 9.3
We solve the boundary value problem
x (t) + ax(t) = f (t),
0<t<L
u
Differential equations and boundary value problems
MATH 386

Spring 2012
3.8 (SUPPLEMENT) ORTHOGONALITY OF EIGENFUNCTIONS
We now develop some properties of eigenfunctions, to be used in Chapter 9 for Fourier
Series and Partial Dierential Equations.
1. Denition of Orthogona
Differential equations and boundary value problems
MATH 386

Spring 2012
3.2 (SUMMARY) GENERAL SOLUTIONS OF LINEAR EQUATIONS
[Compare all this material with the second order case, in Section 3.1.]
Consider the nth order linear equation
(1)
y (n) + pn1 (x)y (n1) + + p1 (x)
Differential equations and boundary value problems
MATH 386

Spring 2012
FAMOUS SECOND ORDER LINEAR EQUATIONS
In Math 385 we concentrate on constant coecient equations. But when using separation
of variables to solve heat and wave and Schrdinger equations in disks, balls o
Differential equations and boundary value problems
MATH 386

Spring 2012
Project IV Fourier Series
Robert Jerrard
Goal of the project
To develop understanding of how many terms of a Fourier series are required in order to
wellapproximate the original function, and of the
Differential equations and boundary value problems
MATH 386

Spring 2012
Math 285 Spring 2003 Final Exam Answers
Total points: 200. Do only two of #9, 10, 11, 12. (Cross out the
two you are not doing.) Explain all answers. No notes, books, calculators or
computers.
1. [20
Differential equations and boundary value problems
MATH 386

Spring 2012
THE FIRST ORDER LINEAR METHOD
Call a Dierential Equation rst order linear if it can be put in the form
dy
(1)
+ P (x)y = Q(x)
dx
for some functions P and Q.
First Order Linear Solution Method.
Step 0.
Differential equations and boundary value problems
MATH 386

Spring 2012
UNDETERMINED COEFFICIENTS SUMMARY SHEET
Goal: to solve Ly = f where L is a constant coecient linear dierential operator and f
has the form
f (x) = Pm (x)erx cos(kx)
or
= Pm (x)erx sin(kx)
or
= Pm (x)e
Differential equations and boundary value problems
MATH 386

Spring 2007
NAME:
Math 285 Spring 2003  Test 2
Total points: 100. Do all questions. Explain all answers. No notes, books, calculators or computers. 1. [6 points] For the following differential equation, write do
Differential equations and boundary value problems
MATH 386

Spring 2012
SEC. 9.5 HEAT EQUATION AND SEPARATION OF VARIABLES
You should learn everything on this handout, and should also learn how to come up with
these solutions by using Separation of Variables, as covered i