{"product_id":"fourier-series-and-numerical-methods-for-partial-differential-equations-hardback-9780470617960","title":"Fourier Series and Numerical Methods for Partial Differential Equations (Hardback) 9780470617960","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFourier Series and Numerical Methods for Partial Differential Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eRichard Bernatz (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470617960, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 20 August 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e332 pages, Drawings: 15 B\u0026amp;W, 0 Color; Graphs: 85 B\u0026amp;W, 0 Color\u003cbr\u003e24.4 x 16.3 x 2.1 cm, 0.599 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.\" (\u003ci\u003eMathematical Reviews,\u003c\/i\u003e 2011)\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, \u003ci\u003eFourier Series and Numerical Methods for Partial Differential Equations\u003c\/i\u003e presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs.  \u003cp\u003eThe book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: \u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs\u003c\/li\u003e \u003cli\u003eThe concept of completeness, which introduces readers to Hilbert spaces \u003c\/li\u003e \u003cli\u003eThe application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions\u003c\/li\u003e \u003cli\u003e The finite element method, using finite dimensional subspaces\u003c\/li\u003e \u003cli\u003e The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFourier Series and Numerical Methods for Partial Differential Equations\u003c\/i\u003e is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Terminology and Notation.\u003c\/p\u003e \u003cp\u003e1.2 Classification.\u003c\/p\u003e \u003cp\u003e1.3 Canonical Forms.\u003c\/p\u003e \u003cp\u003e1.4 Common PDEs.\u003c\/p\u003e \u003cp\u003e1.5 Cauchy–Kowalevski Theorem.\u003c\/p\u003e \u003cp\u003e1.6 Initial Boundary Value Problems.\u003c\/p\u003e \u003cp\u003e1.7 Solution Techniques.\u003c\/p\u003e \u003cp\u003e1.8 Separation of Variables.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fourier Series.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vector Spaces.\u003c\/p\u003e \u003cp\u003e2.2 The Integral as an Inner Product.\u003c\/p\u003e \u003cp\u003e2.3 Principle of Superposition.\u003c\/p\u003e \u003cp\u003e2.4 General Fourier Series.\u003c\/p\u003e \u003cp\u003e2.5 Fourier Sine Series on (0, \u003ci\u003ec\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e2.6 Fourier Cosine Series on (0, \u003ci\u003ec\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e2.7 Fourier Series on (–\u003ci\u003ec\u003c\/i\u003e; \u003ci\u003ec\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e2.8 Best Approximation.\u003c\/p\u003e \u003cp\u003e2.9 Bessel's Inequality.\u003c\/p\u003e \u003cp\u003e2.10 Piecewise Smooth Functions.\u003c\/p\u003e \u003cp\u003e2.11 Fourier Series Convergence.\u003c\/p\u003e \u003cp\u003e2.12 2\u003ci\u003ec\u003c\/i\u003e-Periodic Functions.\u003c\/p\u003e \u003cp\u003e2.13 Concluding Remarks.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Sturm–Liouville Problems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Basic Examples.\u003c\/p\u003e \u003cp\u003e3.2 Regular Sturm–Liouville Problems.\u003c\/p\u003e \u003cp\u003e3.3 Properties.\u003c\/p\u003e \u003cp\u003e3.4 Examples.\u003c\/p\u003e \u003cp\u003e3.5 Bessel's Equation.\u003c\/p\u003e \u003cp\u003e3.6 Legendre's Equation.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Heat Equation.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Heat Equation in 1D.\u003c\/p\u003e \u003cp\u003e4.2 Boundary Conditions.\u003c\/p\u003e \u003cp\u003e4.3 Heat Equation in 2D.\u003c\/p\u003e \u003cp\u003e4.4 Heat Equation in 3D.\u003c\/p\u003e \u003cp\u003e4.5 Polar-Cylindrical Coordinates.\u003c\/p\u003e \u003cp\u003e4.6 Spherical Coordinates.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Heat Transfer in 1D.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Homogeneous IBVP.\u003c\/p\u003e \u003cp\u003e5.2 Semihomogeneous PDE.\u003c\/p\u003e \u003cp\u003e5.3 Nonhomogeneous Boundary Conditions.\u003c\/p\u003e \u003cp\u003e5.4 Spherical Coordinate Example.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Heat Transfer in 2D and 3D.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Homogeneous 2D IBVP.\u003c\/p\u003e \u003cp\u003e6.2 Semihomogeneous 2D IBVP.\u003c\/p\u003e \u003cp\u003e6.3 Nonhomogeneous 2D IBVP.\u003c\/p\u003e \u003cp\u003e6.4 2D BVP: Laplace and Poisson Equations.\u003c\/p\u003e \u003cp\u003e6.5 Nonhomogeneous 2D Example.\u003c\/p\u003e \u003cp\u003e6.6 Time-Dependent BCs.\u003c\/p\u003e \u003cp\u003e6.7 Homogeneous 3D IBVP.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Wave Equation.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Wave Equation in 1D.\u003c\/p\u003e \u003cp\u003e7.2 Wave Equation in 2D.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Methods: an Overview.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Grid Generation.\u003c\/p\u003e \u003cp\u003e8.2 Numerical Methods.\u003c\/p\u003e \u003cp\u003e8.3 Consistency and Convergence.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Finite Difference Method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Discretization.\u003c\/p\u003e \u003cp\u003e9.2 Finite Difference Formulas.\u003c\/p\u003e \u003cp\u003e9.3 1D Heat Equation.\u003c\/p\u003e \u003cp\u003e9.4 Crank–Nicolson Method.\u003c\/p\u003e \u003cp\u003e9.5 Error and Stability.\u003c\/p\u003e \u003cp\u003e9.6 Convergence in Practice.\u003c\/p\u003e \u003cp\u003e9.7 1D Wave Equation.\u003c\/p\u003e \u003cp\u003e9.8 2D Heat Equation in Cartesian Coordinates.\u003c\/p\u003e \u003cp\u003e9.9 Two-Dimensional Wave Equation.\u003c\/p\u003e \u003cp\u003e9.10 2D Heat Equation in Polar Coordinates.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Finite Element Method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 General Framework.\u003c\/p\u003e \u003cp\u003e10.2 1D Elliptical Example.\u003c\/p\u003e \u003cp\u003e10.3 2D Elliptical Example.\u003c\/p\u003e \u003cp\u003e10.4 Error Analysis.\u003c\/p\u003e \u003cp\u003e10.5 1D Parabolic Example.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Finite Analytic Method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 1D Transport Equation.\u003c\/p\u003e \u003cp\u003e11.2 2D Transport Equation.\u003c\/p\u003e \u003cp\u003e11.3 Convergence and Accuracy.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eAppendix A: FA 1D Case.\u003c\/p\u003e \u003cp\u003eAppendix B: FA 2D Case.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52276369654040,"sku":"9780470617960","price":89.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470617960.jpg?v=1781368101","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/fourier-series-and-numerical-methods-for-partial-differential-equations-hardback-9780470617960","provider":"Freshly Printed Books","version":"1.0","type":"link"}