## Department of Mathematics - RHIT Topics Outline for MA211 - Differential Equations - 2010-11

last posted to site: 08/19/10

### Text and Text Materials

Text: Advanced Engineering Mathematics, 4th edition by Zill and Wright

### Approximate Timing and Pace

There should be 2 or 3 tests, perhaps a review day or two.
The topics break up into three main topics of about 3 weeks each, plus a short section on numerical methods.

• First order equations and modeling
• Linear second order equations including complex numbers
• Laplace transforms
• Numerical methods
 Topics Sections Time Chapter 1 - Ordinary Differential Equations 1.1-1.3 2 days Chapter 2 - First-Order Differential Equations 2.1-2.3 5 days Chapter 17 - Complex Numbers 17.1,17.2 2 days Chapter 3 - Higher-Order Differential Equations 3.1, 3.3, 3.4, 3.8 12 days Chapter 4 - Laplace Transforms 4.1-4.5 12 days Chapter 6 - Numerical Methods 6.1, 6.2 2 days Tests, Review and Spare days 5 days

1. Introduction to Differential Equations

1.1 Definitions and Terminology

1.2 Initial-Value Problems

1.3 Differential Equations as Mathematical Models

2. First-Order Differential Equations

2.1 Solution Curves Without a Solution
2.1.1 Direction Field
2.1.2 Autonomous First-Order DEs

2.2 Separable Equations

2.3 Linear Equations

17. Complex Numbers

17.1 Complex Numbers

17.2 Powers and Roots

3. Higher-Order Differential Equations

3.1 Theory of Linear Equations
3.1.1 Initial-Value and Boundary-Value Problems (boundary value problems optional)
3.1.2 Homogeneous Equations
3.1.3 Nonhomogeneous Equations

3.3 Homogeneous Linear Equations with Constant Coefficient

3.4 Undetermined Coefficients

3.8 Linear Models: Initial-Value Problems
3.8.1 Spring/Mass Systems: Free Undamped Motion
3.8.2 Spring/Mass Systems: Free Damped Motion
3.8.3 Spring/Mass Systems: Driven Motion
3.8.4 Series Circuit Analogue

4. Laplace Transform

4.1 Definition of Laplace Transform

4.2 Inverse Transform and Transforms of Derivatives
4.2.1 Inverse Transforms
4.2.2 Transforms of Derivatives

4.3 Translation Theorems
4.3.1 Translation on the s-axis
4.3.2 Translation of the t-axis