This textbook features the use of MATLAB® for solving problems and generating graphs of solutions. It includes a careful mathematical treatment of the central ideas of the subject and numerous applications, as well as historical preludes to each chapter. In addition to the standard topics, it contains a computational chapter that focuses on finite difference, finite element, and spectral numerical methods widely used by engineers. Although the book may be used without MATLAB, this software was used to generate many of the figures and tables. The code is provided, both in the book and for download from the Internet, and this code can be modified slightly to use in solving the MATLAB exercises.