Topics Outline for MA211 - Differential Equations - 2010-11

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

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

4.4 Additional Operational Properties

4.4.1 Derivatives of Transforms

4.4.2 Transforms of Integrals

4.4.3 Transform of Periodic Function

4.5 The Dirac Delta Function

**6. Numerical Solutions of Ordinary Differential Equations**

6.1 Euler Methods and Error Analysis

6.2 Runge Kutta Methods