An introduction to partial differential equations with MATLAB
著者
書誌事項
An introduction to partial differential equations with MATLAB
（Chapman & Hall/CRC applied mathematics and nonlinear science series）（A Chapman & Hall book）
CRC Press, c2013
2nd ed
- : hardback
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注記
Includes bibliographical references (p. 647-654) and index
内容説明・目次
内容説明
An Introduction to Partial Differential Equations with MATLAB (R), Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean's surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom.
Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text.
Each chapter's prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB's excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author's website.
目次
Introduction. The Big Three PDEs. Fourier Series. Solving the Big Three PDEs. Characteristics. Integral Transforms. Bessel Functions and Orthogonal Polynomials. Sturm-Liouville Theory and Generalized Fourier Series. PDEs in Higher Dimensions. Nonhomogeneous Problems and Green's Functions. Numerical Methods. Appendices. References. Index.
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