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