{"product_id":"fourier-series-and-numerical-methods-for-partial-differential-equations-9780470617960","title":"Fourier Series and Numerical Methods for Partial Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eUnable to find a suitable coursebook for an introductory PDE course, the author wrote one that combines the needed foundation and theory with tangible applications in physics and other disciplines. Since many practical applications are non-linear, numerical solution techniques are required.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\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","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515418108247,"sku":"9780470617960","price":90.86,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/fourier-series-and-numerical-methods-for-partial-differential-equations-9780470617960","provider":"Book Curl","version":"1.0","type":"link"}