Math 212 Differential Equations
Oxford College of Emory University, Spring 2021
Oxford College of Emory University, Spring 2021
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.
MATLAB
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