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.

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