Review List For Exam #3 (November 28, 2007)

The Exam will cover material in Text: Sections 6.1-6.5,   7.1,  7.4-7.6,  7.8  and 9.1.

Chapter 6

Concepts:

Laplace Transform

Theorem 6.2.1 and corollary 6.2.2

Step Function

Theorem 6.3.1

Dirac Delta Function

p.312 Ex. 5(a),(b);  p.322, Ex 11;  p.330, Ex 9;   P337, Ex 1.

Chapter 7

Concepts:

Systems of First Order Linear Equations.

Transforming a second order equation into a system of two first order equations.

Fundamental set of solutions of a homogeneous system.

Finding eigenvalues and eigenvectors of a 2 × 2 matrix.

Fundamental set of solutions in the case of real distinct eigenvlues.

Fundadental set of solutions in the case of complex eigenvalues

Fundamental set of solutions in the case of a repeated eigenvalue.

p.360, Ex. 5;  p.398, Ex.1;  p.410, Ex. 1;   p.428, Ex.1.

Concepts:

Phase plane

Node

Saddle point

Spiral point

Center

Stability of the origin

p.492, Ex. 2, 4, 5 (parts (a), (b), and (c) only).