Course Outline

• Chapter 1, Introduction
• Chapter 2, First Order Equations:
  Separable Equations, Integrating Factor, Modeling, Phase Plane Technique
• Chapter3. Second Order Equations:
  IVP, Homogeneous Equations, Inhomogeneous equations, Method of Undetermined Coefficients, Variations of a Parameter, Oscillations, Euler equation
• Chapter 4 Linear Systems: $\dot {\bf x}(t) = {\bf A} {\bf x}(t)$.
• Chapter 5 Nonlinear Systems
• Chapter 6 Laplace Transforms:
  definition, inverse Laplace Transform, solving the ODE with Laplace transform
• Chapter 7 Partial Differential Equations:
  separation of variables, Sine and Cosine transforms, Wave Equations, BVP.

Table 1: Outline

Week	Pages	Title	Sections	Suggested Problems
1	13	Intro/First Order DFQ, Separable Eqn	1.1,1.2, 2.1	1.2.3-4 2.1.1-2 2.1.6
2	24	Integrating Factor and Modeling	2.2, 2.3	2.2.1-3 2.3.2-3 2.3.8
3	40	Steady State and Stability	2.4	2.4.2-6, 2.4.10
4	48	Second Order Linear Equation	3.1-3.5	3.2.4-5, 3.5.3-4,3.5.6-7
5	60	Inhomogeneous Eqn and MethUndetCoef	3.6-3.8	3.8.1-2, 3.8.4-5
6	76	Variation of a Parameter, Mechanical Vibrations, Euler Eq.	3.9-11	3.9.1-4,3.10.1-12,3.11.1-2
7	98	Linear Systems, General Solutions of HomogEqn, Review, Solving	4.1-4.4	4.1.1-3,4.3.1-4,4.5.1-3
8	108	Phase Plane Technique and Stability	4.6 4.7	4.6.1-2, 4.7.1-4
9	122	Nonlinear Systems and Stability	5.1 5.2	5.1.1-2, 5.2.1-2
10	138	Periodic Solutions and Central Force Field	5.3 5.4	5.3.1-3
11	155	Laplace Transform, Definition, Inverse, Properties, Solving DFQ	6.1-4

Here the problem are marked by a section number followed by a problem number. For example 2.2.1-3 means problems one, two and three in section 2.2.