Updated edition of Schaum's outline of theory and problems of modern introductory differential equations published in 1973.

Includes index.

Basic Concepts. Classification 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. Applications of Second-Order Linear Differential Equations. The Laplace Transform. The Inverse Laplace Transform. Convolutions and the Unit Step Function. Solutions of Linear Systems by Laplace Transform. Convolutions and the Unit Step Function. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transform. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transform. Solutions of Linear Systems by Laplace Transform. Matrices. eAt. 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: Laplace Transforms. Answers to Supplementary Problems.

This study guide outlines both the classic theory of differential equations and the newer solution procedures that practitioners favor. It includes hundreds of problems with fully worked out solutions to help students master the basics of this linchpin of modern mathematics. It also includes more than 800 supplementary problems with answers to challenge and reinforce comprehension.