Schaum's outline of theory and problems of differential equations

Basic concepts

Classifications of first-order differential equations

Separable first-order differential equations

Exact first-order differential equations

Linear first-order equations

Applications of first-order differential equations

Linear differential equations : theory of solutions

Second-order linear homogeneous differential equations with constant coefficents

nth-order linear homogeneous differential equations with constant coefficients

The method of undetermined coefficients -

Variation of parameters

Initial-value problems

Applications of second-order linear differential equations

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

Matrices

e [superscript At]

Reduction of linear differential equations to a first-order system

Solutions of linear differential equations with constant coefficients by matrix methods

Linear differential equations with variable coefficients

Regular singular points and the method of Frobenius

Gamma and Bessel functions

Graphical methods for solving first-order differential equations

Numerical methods for solving first-order differential equations

Numerical methods for systems

Second-order boundary-value problems

Eigenfunction expansions

Appendix A. Laplace transforms.