{"product_id":"solutions-manual-to-accompany-beginning-partial-differential-equations-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9781118630099","title":"Solutions Manual to Accompany Beginning Partial","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSolutions Manual to Accompany\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  \u003cp\u003e1 First Ideas 1\u003c\/p\u003e \u003cp\u003e1.1 Two Partial Differential Equations 1\u003c\/p\u003e \u003cp\u003e1.2 Fourier Series 4\u003c\/p\u003e \u003cp\u003e1.3 Two Eigenvalue Problems 12\u003c\/p\u003e \u003cp\u003e1.4 A Proof of the Convergence Theorem 14\u003c\/p\u003e \u003cp\u003e2 Solutions of the Heat Equation 15\u003c\/p\u003e \u003cp\u003e2.1 Solutions on an Interval [0, L] 15\u003c\/p\u003e \u003cp\u003e2.2 A Nonhomogeneous Problem 19\u003c\/p\u003e \u003cp\u003e3 Solutions of the Wave Equation 25\u003c\/p\u003e \u003cp\u003e3.1 Solutions on Bounded Intervals 25\u003c\/p\u003e \u003cp\u003e3.2 The Cauchy Problem 32\u003c\/p\u003e \u003cp\u003e3.2.1 d’Alembert’s Solution 32\u003c\/p\u003e \u003cp\u003e3.2.2 The Cauchy Problem on a Half Line 36\u003c\/p\u003e \u003cp\u003e3.2.3 Characteristic Triangles and Quadrilaterals 41\u003c\/p\u003e \u003cp\u003e3.2.4 A Cauchy Problem with a Forcing Term 41\u003c\/p\u003e \u003cp\u003e3.2.5 String with Moving Ends 42\u003c\/p\u003e \u003cp\u003e3.3 The Wave Equation in Higher Dimensions 46\u003c\/p\u003e \u003cp\u003e3.3.1 Vibrations in a Membrane with Fixed Frame 46\u003c\/p\u003e \u003cp\u003e3.3.2 The Poisson Integral Solution 47\u003c\/p\u003e \u003cp\u003e3.3.3 Hadamard’s Method of Descent 47\u003c\/p\u003e \u003cp\u003e4 Dirichlet and Neumann Problems 49\u003c\/p\u003e \u003cp\u003e4.1 Laplace’s Equation and Harmonic Functions 49\u003c\/p\u003e \u003cp\u003e4.2 The Dirichlet Problem for a Rectangle 50\u003c\/p\u003e \u003cp\u003e4.3 The Dirichlet Problem for a Disk 52\u003c\/p\u003e \u003cp\u003e4.4 Properties of Harmonic Functions 57\u003c\/p\u003e \u003cp\u003e4.4.1 Topology of Rn 57\u003c\/p\u003e \u003cp\u003e4.4.2 Representation Theorems 58\u003c\/p\u003e \u003cp\u003e4.4.3 The Mean Value Theorem and the Maximum Principle 60\u003c\/p\u003e \u003cp\u003e4.5 The Neumann Problem 61\u003c\/p\u003e \u003cp\u003e4.5.1 Uniqueness and Existence 61\u003c\/p\u003e \u003cp\u003e4.5.2 Neumann Problem for a Rectangle 62\u003c\/p\u003e \u003cp\u003e4.5.3 Neumann Problem for a Disk 63\u003c\/p\u003e \u003cp\u003e4.6 Poisson’s Equation 64\u003c\/p\u003e \u003cp\u003e4.7 An Existence Theorem for the Dirichlet Problem 65\u003c\/p\u003e \u003cp\u003e5 Fourier Integral Methods of Solution 67\u003c\/p\u003e \u003cp\u003e5.1 The Fourier Integral of a Function 67\u003c\/p\u003e \u003cp\u003e5.2 The Heat Equation on the Real Line 70\u003c\/p\u003e \u003cp\u003e5.3 The Debate Over the Age of the Earth 73\u003c\/p\u003e \u003cp\u003e5.4 Burgers’ Equation 73\u003c\/p\u003e \u003cp\u003e5.5 The Cauchy Problem for the Wave Equation 74\u003c\/p\u003e \u003cp\u003e5.6 Laplace’s Equation on Unbounded Domains 76\u003c\/p\u003e \u003cp\u003e6 Solutions Using Eigenfunction Expansions 79\u003c\/p\u003e \u003cp\u003e6.1 A Theory of Eigenfunction Expansions 79\u003c\/p\u003e \u003cp\u003e6.2 Bessel Functions 83\u003c\/p\u003e \u003cp\u003e6.3 Applications of Bessel Functions 87\u003c\/p\u003e \u003cp\u003e6.3.1 Temperature Distribution in a Solid Cylinder 87\u003c\/p\u003e \u003cp\u003e6.3.2 Vibrations of a Circular Drum 87\u003c\/p\u003e \u003cp\u003e6.4 Legendre Polynomials and Applications 90\u003c\/p\u003e \u003cp\u003e7 Integral Transform Methods of Solution 97\u003c\/p\u003e \u003cp\u003e7.1 The Fourier Transform 97\u003c\/p\u003e \u003cp\u003e7.2 Heat and Wave Equations 101\u003c\/p\u003e \u003cp\u003e7.3 The Telegraph Equation 104\u003c\/p\u003e \u003cp\u003e7.4 The Laplace Transform 106\u003c\/p\u003e \u003cp\u003e8 First-Order Equations 109\u003c\/p\u003e \u003cp\u003e8.1 Linear First-Order Equations 109\u003c\/p\u003e \u003cp\u003e8.2 The Significance of Characteristics 111\u003c\/p\u003e \u003cp\u003e8.3 The Quasi-Linear Equation 114\u003c\/p\u003e \u003cp\u003eSeries List 117\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406897094999,"sku":"9781118630099","price":26.55,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118630099.jpg?v=1730497481","url":"https:\/\/bookcurl.com\/products\/solutions-manual-to-accompany-beginning-partial-differential-equations-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9781118630099","provider":"Book Curl","version":"1.0","type":"link"}