This book looks at a wide range of ordinary and partial differential equation (PDE) applications. Students using this text will actually solve many interesting science and engineering applications using PDE2D, an easy‐to‐use, general‐purpose PDE solver developed by the author over a 40‐year period, which is free with the purchase of this book. They will learn to derive and solve the ordinary or partial differential equations, with boundary and initial conditions, for many time‐dependent, steady‐state, and eigenvalue applications, including diffusion, heat conduction and convection, image processing, math finance, fluid flow, elasticity, and quantum mechanics, in one, two, and three space dimensions. That PDE2D can be used to solve a wide variety of applications is evidenced by the list of over 250 journal articles and books at, in which it has been used to generate some or all of the numerical results.

Much of the material in the book was developed for two graduate courses, “Seminar in Applied Mathematics” at Texas A&M University and “Advanced Scientific Computing” at the University of Texas El Paso, but the book could also be used as a supplementary text for a number of science or engineering courses in which PDE applications are studied. It could also be used as a reference by individual students or researchers interested in using PDE2D to solve their specific applications.

Some documentation on the mathematical algorithms used by PDE2D can be found ...

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