Math 212 Differential Equations

Textbook: 

• A First Course in Differential Equations with Modeling Applications by Dennis G. Zill, 11th Edition.

• Differential Equations with MATLAB by Brian Hunt, Ronald Lipsman, John Oxborn, and Jonathan Rosenberg, 3rd Edition.

Software:

MATLAB

Topics:

Chapter 1 Introduction to Differential Equations

1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models

Chapter 2 First-Order Differential Equations

2.1 Solution Curves Without a Solution
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions

Chapter 3 Modeling with First-Order Differential Equations

3.1 Linear Models
3.2 Nonlinear Models

Chapter 4 Higher-Order Differential Equations

4.1 Preliminary Theory-Linear Equations
4.2 Reduction of Orders
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients-Superposition Approach
4.6 Variation of Parameters
4.7 Cauchy--Euler Equations
4.8 Green's Functions
4.10 Nonlinear Differential Equations

Chapter 6 Series Solutions of Linear Equations

6.1 Review of Power Series
6.2 Solutions About Ordinary Points
6.3 Solutions About Singular Points

Chapter 7 The Laplace Transform

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