Ordinary and Partial Differential Equations / Edition 1

Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.