Basic concepts
An introduction to modeling and qualitative methods
Classifications of first-order differential equations
Separable first-order differential equations
Exact first-order differential equations
Linear first-order differential equations
Applications of first-order differential equations
Linear differential equations: theory of solutions
Second-order linear homogeneous differential equations with constant coefficients
nth-order linear homogeneous differential equations with constant coefficients
The method of undetermined coefficients
Variation of parameters
Initial-value problems for linear differential equations
Applications of second-order linear differential equations
Matrices
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Reduction of linear differential equations to a system of first-order equations
Graphical and numerical methods for solving first-order differential equations
Further numerical methods for solving first-order differential equations
Numerical methods for solving second-order differential equations via systems
The Laplace transform
Inverse Laplace transforms
Convolutions and the unit step function
Solutions of linear differential equations with constant coefficients by Laplace transforms
Solutions of linear systems by Laplace transforms
Solutions of linear differential equations with constant coefficients by matrix methods
Power series solutions of linear differential equations with variable coefficients
Series solutions near a regular singular point
Some classical differential equations
Gamma and Bessel functions
An introduction to partial differential equations
Second-order boundary-value problems
Eigenfunction expansions
An introduction to difference equations
Solving differential equations using Mathematica
Solving systems of differential equations via Eigenvalues using Mathematica
Qualitative methods
Euler's method using Microsofe Excel®
Some interesting modeling problems
Laplace transforms
Answers to supplementary problems

Schaum's Outline of Differential Equations, Fifth Edition is the go-to study guide for all students of science who need to learn or refresh their knowledge of differential equations. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. It supports the all major differential equations textbooks and is useful for study in Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations and Differential Equations. Chapters include an Introduction to Modeling and Qualitative Methods, Classifications of First-Order Differential Equations, Linear Differential Equations, Variation of Parameters, Initial-Value Problems for Linear Differential Equations, Graphical and Numerical Methods for Solving First-Order Differential Equations, Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms, and more