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Fourier Series, Transforms, and Boundary Value Problems (Dover Books on Mathematics) (Paperback)
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This introduction to Fourier and transform methods emphasizes basic techniques rather than theoretical concepts. It explains the essentials of the Fourier method and presents detailed considerations of modeling and solutions of physical problems. All solutions feature well-drawn outlines that allow students to follow an appropriate sequence of steps, and many of the exercises include answers. The chief focus of this text is the application of the Fourier method to physical problems, which are described mathematically in terms of boundary value problems. Problems involving separation of variables, Sturm-Liouville theory, superposition, and boundary complaints are addressed in a logical sequence. Multidimensional Fourier series solutions and Fourier integral solutions on unbounded domains are followed by the special functions of Bessel and Legendre, which are introduced to deal with the cylindrical and spherical geometry of boundary value problems. Students and professionals in mathematics, the physical sciences, and engineering will find this volume an excellent study guide and resource.