**MATH 230 – Differential Equations**

**Course Description: **This course will introduce the student to the solution of
elementary differential equations and standard applications of differential
equations in science. It will include the solution of first order linear
differential equations with applications to exponential growth and decay
problems, mixture problems, orthogonal trajectories, etc., solutions to second
order differential equations with applications to harmonic motion, and the LaPlace transform

** **

**Textbook: **Edwards, C. H., Penney, D. E., & Calvis, D. T. (2019). *Differential
Equations and Boundary Value Problems: Computing and Modeling*, published by
Pearson

**Unit 1: Solving First Ordered Differential
Equations**

·
1.1 Differential
Equations

·
1.2 Integrals as General
and Particular Solutions

·
1.3 Slope Fields and
Solutions Curves

·
1.4 Separable Equations
and Applications

·
1.5 Linear First-Ordered
Equations

·
1.6a Homogeneous
Equations

·
1.6b Bernoulli Equations

·
1.6c Exact Equations

**Unit 2: Second Ordered
Differential Equations**

·
3.1 Second Ordered
Linear Equations

·
3.2 General Solutions of
Linear Equations

·
3.3 Homogeneous
Equations with Constant Coefficients

·
3.5a Nonhomogeneous
Equations and Undetermined Coefficients (or annihilation)

·
3.5b Variation of Parameters

**Unit 3: Applications of
Differential Equations**

·
2.1 Population Models

·
2.2 Equilibrium
Solutions and Stability

·
2.3
Acceleration-Velocity Models

·
3.4 Mechanical
Vibrations

·
3.7 Electric Circuits

**Unit 4: Laplace
Transforms and Series Solutions**

·
7.1a Laplace Transforms
by Definition

·
7.1b Laplace Transforms
by Table

·
7.1c Inverse Laplace
Transforms

·
7.1d Unit Step Function

·
7.2 Transformations of
Initial Value Problems

·
7.3 Translation and
Partial Fractions

·
8.1 Introduction and
Review of Power Series

·
8.2 Series Solutions
Near Ordinary Points