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Part of: Synthesis digital library of engineering and computer science.

1. Introduction -- 1.1 Model equations -- 1.1.1 Advection equation -- 1.1.2 Diffusion equation -- 1.1.3 Laplace's equation -- 1.1.4 Wave equation -- 1.2 PDEs are everywhere -- 1.3 Exercises --

2. First-order PDEs -- 2.1 Constant coefficient equations -- 2.2 Linear equations -- 2.3 Method of characteristics -- 2.4 Quasilinear equations -- 2.5 Higher-dimensional equations -- 2.6 Fully nonlinear first-order equations -- 2.6.1 Method of characteristics -- 2.6.2 Charpit's method -- 2.7 Exercises --

3. Second-order linear PDEs -- 3.1 Introduction -- 3.2 Standard forms -- 3.2.1 Parabolic standard form -- 3.2.2 Hyperbolic standard form -- 3.2.3 Modified hyperbolic form -- 3.2.4 Regular hyperbolic form -- 3.2.5 Elliptic standard form -- 3.3 The wave equation -- 3.4 Exercises --

4. Fourier series -- 4.1 Fourier series -- 4.2 Fourier series on [-pi, pi] -- 4.3 Fourier series on [-L ,L] -- 4.4 Odd and even extensions -- 4.4.1 Sine series -- 4.4.2 Cosine series -- 4.5 Exercises --

5. Separation of variables -- 5.1 The heat equation -- 5.1.1 Nonhomogeneous boundary conditions -- 5.1.2 Nonhomogeneous equations -- 5.1.3 Equations with a solution-dependent source term -- 5.1.4 Equations with a solution-dependent convective term -- 5.2 Laplace's equation -- 5.2.1 Laplace's equation on an arbitrary rectangular domain -- 5.3 The wave equation -- 5.4 Exercises --

6. Fourier transform -- 6.1 Fourier transform -- 6.2 Fourier sine and cosine transforms -- 6.3 Exercises --

7. Solutions -- Author's biography.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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This book is an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject. The chapters include the following topics: First-order PDEs, Second-order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform. The reader is guided through these chapters where techniques for solving first- and second-order PDEs are introduced. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for any introductory course in PDEs typically found in both science and engineering programs and has been used at the University of Central Arkansas for over ten years.

Also available in print.

Title from PDF title page (viewed on December 31, 2017).