Introduction
The initial value problem y' = f(x, y); y(c) = d
Applications of the initial value problem y' = f(x, y); y(c) = d
N-th order linear differential equations
The Laplace transform method
Applications of linear differential equations with constant coefficients
Systems of first-order differential equations
Linear systems of first-order differential equations
Applications of linear systems with constant coefficients
Applications of systems of equations
Appendix A: CSODE user's guide
Appendix B: PORTRAIT user's guide
Appendix C: Laplace transforms
Answers to selected exercises

"Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Designed to be independent of any particular software package, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in solving various types of differential equations." "Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems." "The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions."