Fourier Series, Transforms, and Boundary Value Problems: Second EditionThis 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. |
Other editions - View all
Fourier Series, Transforms, and Boundary Value Problems J. Ray Hanna,John H. Rowland No preview available - 2012 |
Common terms and phrases
applied approximation assume becomes Bessel functions boundary conditions Chapter coefficients complete compute consider constant continuous converges coordinates corresponding cosine defined definition dependent derivative Determine differential equation discussion displacement eigenfunctions Example Exercises exists exponential expressed fails Figure Find finite follows force formula Fourier series Fourier transform function function f given heat homogeneous independent indicial initial integral interval inverse Laplace transform Legendre linear combination method multiplications obtain operator Original orthogonal partial periodic polynomial positive problem referred Related relative replaced represented result roots satisfies separation Show sin ax sine sinh solution solution set Solve square string substitution temperature Theorem uniformly value problem variable write written York zero