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The first two editions of An Introduction to Partial Differential Equations with MatLAB gained popularity among instructors and students at various universities throughout the world. Plain mathematical language is used in a friendly manner to provide a basic introduction to partial differential equations (PDEs). Suitable for a one- or two-semester introduction to PDEs and Fourier series, the book strives to provide physical, mathematical, and historical motivation for each topic. Equations are studied based on method of solution, rather than on type of equation. This third edition of this popular textbook updates the structure of the book by increasing the role of the computational portion, compared to previous editions. The redesigned content will be extremely useful for students of mathematics, physics, and engineering who would like to focus on the practical aspects of the study of PDEs, without sacrificing mathematical rigor. The authors have maintained flexibility in the order of topics. In addition, students will be able to use what they have learned in some later courses (for example, courses in numerical analysis, optimization, and PDE-based programming). Included in this new edition is a substantial amount of material on reviewing computational methods for solving ODEs (symbolically and numerically), visualizing solutions of PDEs, using MatLAB's symbolic programming toolbox, and applying various schemes from numerical analysis, along with suggestions for topics of course projects. Students will use sample MatLAB or Python codes available online for their practical experiments and for completing computational lab assignments and course projects.
Preface.
Acronyms and Abbreviations.
Author Biographies.
Introduction.
The Big Three PDEs.
Using MatLAB for Solving Differential Equations and Visualizing Solutions.
Fourier Series.
Solving the Big Three PDEs on Finite Domains.
Review of Numerical Methods for Solving ODEs.
Solving PDEs Using Finite Difference Approximations.
Integral Transforms.
Using MatLAB’s Symbolic Math Toolbox with Integral Transforms.
PDEs in Higher Dimensions.
Overview of Spectral, Finite Element, and Finite Volume Methods.
A Important Definitions and Theorems.
B Bessel’s Equation and the Method of Frobenius.
C A Menagerie of PDEs.
D Review of Math with MatLAB.
E Answers to Selected Exercises.
Bibliography.
Index