Differential Equations
Catalog Description: Math 2120. Differential Equations.
Credit 3.
Prerequisites: "C" or better in Math 2110 . First order equations, linear
equations of higher order, power series solutions, Laplace transforms, and other
topics. It is recommended, but not required, that students take Math 2010
before taking Math 2120.
Textbook:
Dennis G. Zill, Differential Equations with Boundary-Value Problems, seventh
Edition, Brooks/Cole, 2009.
Goals:
This course is designed to provide instruction in techniques used in solving
ordinary differential equations commomly encountered in mathematical
physics and engineering.
Prerequisites by Topic:
Calculus sequence including differential and integral calculus, analytic
geometry, exponential and logarithmic functions, infinite series, and partial
differentiation.
| Chapter 1 | Introduction to Differential Equations | 2 class periods |
1.1 Basic Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
| Chapter 2 | First Order Differential Equations | 8 class periods |
2.1 Solution Curves Without a Solution
2.2 Separable Variables
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
| Chapter 4 | Higher-Order Differential Equations | 12 class periods |
4.1 Preliminary Theory-Linear Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients-Superposition Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equations
| Chapter 7 | The Laplace Transform | 12 class periods |
7.1 Definition of the Laplace Transform
7.2 Inverse Transforms and Transforms of Derivatives
7.3 Operational Properties I
7.4 Operational Properties II
7.5 The Dirac Delta Function [Optional]
7.6 System of Linear Differential Equations [Optional]
| Chapter 6 | Series Solutions of Linear Equations | 3 class periods |
6.1 Solutions about Ordinary Points
6.2 Solutions about Singular Points
6.3 Special Functions [Optional]
|
Chapter 8 |
Systems of Linear First-Order Differential Equations |
[Optional] selected sections as time permits |