LEADER 05346nam 2200673Ia 450 001 9910877699103321 005 20170809161008.0 010 $a1-283-30616-6 010 $a9786613306166 010 $a1-118-03235-7 010 $a1-118-03060-5 035 $a(CKB)2550000000055769 035 $a(EBL)708228 035 $a(OCoLC)815646950 035 $a(SSID)ssj0000554402 035 $a(PQKBManifestationID)11308388 035 $a(PQKBTitleCode)TC0000554402 035 $a(PQKBWorkID)10512661 035 $a(PQKB)10409091 035 $a(MiAaPQ)EBC708228 035 $a(PPN)170223469 035 $a(EXLCZ)992550000000055769 100 $a20070921d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBeginning partial differential equations$b[electronic resource] /$fPeter V. O'Neil 205 $a2nd ed. 210 $aHoboken, N.J. $cWiley-Interscience$dc2008 215 $a1 online resource (493 p.) 225 1 $aPure and applied mathematics 300 $aIncludes index. 311 $a0-470-13390-2 327 $aBeginning Partial Differential Equations; Contents; 1 First-Order Equations; 1.1 Notation and Terminology; 1.2 The Linear First-Order Equation; 1.3 The Significance of Characteristics; 1.4 The Quasi-Linear Equation; 2 Linear Second-Order Equations; 2.1 Classification; 2.2 The Hyperbolic Canonical Form; 2.3 The Parabolic Canonical Form; 2.4 The Elliptic Canonical Form; 2.5 Some Equations of Mathematical Physics; 2.6 The Second-Order Cauchy Problem; 2.7 Characteristics and the Cauchy Problem; 2.8 Characteristics as Carriers of Discontinuities; 3 Elements of Fourier Analysis 327 $a3.1 Why Fourier Series?3.2 The Fourier Series of a Function; 3.3 Convergence of Fourier Series; 3.4 Sine and Cosine Expansions; 3.5 The Fourier Integral; 3.6 The Fourier Transform; 3.7 Convolution; 3.8 Fourier Sine and Cosine Transforms; 4 The Wave Equation; 4.1 d'PAlembert Solution of the Cauchy Problem; 4.2 d'TAlembert's Solution as a Sum of Waves; 4.3 The Characteristic Triangle; 4.4 The Wave Equation on a Half-Line; 4.5 A Half-Line with Moving End; 4.6 A Nonhomogeneous Problem on the Real Line; 4.7 A General Problem on a Closed Interval; 4.8 Fourier Series Solutions on a Closed Interval 327 $a4.9 A Nonhomogeneous Problem on a Closed Interval4.10 The Cauchy Problem by Fourier Integral; 4.11 A Wave Equation in Two Space Dimensions; 4.12 The Kirchhoff-Poisson Solution; 4.13 Hadamard's Method of Descent; 5 The Heat Equation; 5.1 The Cauchy Problem and Initial Conditions; 5.2 The Weak Maximum Principle; 5.3 Solutions on Bounded Intervals; 5.4 The Heat Equation on the Real Line; 5.5 The Heat Equation on the Half-Line; 5.6 The Debate Over the Age of the Earth; 5.7 The Nonhomogeneous Heat Equation; 5.8 The Heat Equation in Two Space Variables; 6 Dirichlet and Neumann Problems 327 $a6.1 The Setting of the Problems6.2 Some Harmonic Functions; 6.3 Representation Theorems; 6.4 Two Properties of Harmonic Functions; 6.5 Is the Dirichlet Problem Well Posed?; 6.6 Dirichlet Problem for a Rectangle; 6.7 Dirichlet Problem for a Disk; 6.8 Poisson's Integral Representation for a Disk; 6.9 Dirichlet Problem for the Upper Half-Plane; 6.10 Dirichlet Problem for the Right Quarter-Plane; 6.11 Dirichlet Problem for a Rectangular Box; 6.12 The Neumann Problem; 6.13 Neumann Problem for a Rectangle; 6.14 Neumann Problem for a Disk; 6.15 Neumann Problem for the Upper Half-Plane 327 $a6.16 Green's Function for a Dirichlet Problem6.17 Conformal Mapping Techniques; 6.17.1 Conformal Mappings; 6.17.2 Bilinear Transformations; 6.17.3 Construction of Conformal Mappings between Domains; 6.17.4 An Integral Solution of the Dirichlet Problem for a Disk; 6.17.5 Solution of Dirichlet Problems by Conformal Mapping; 7 Existence Theorems; 7.1 A Classical Existence Theorem; 7.2 A Hilbert Space Approach; 7.3 Distributions and an Existence Theorem; 8 Additional Topics; 8.1 Solutions by Eigenfunction Expansions; 8.2 Numerical Approximations of Solutions; 8.3 Burger's Equation 327 $a8.4 The Telegraph Equation 330 $aA rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addre 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aDifferential equations, Partial 606 $aEquations 615 0$aDifferential equations, Partial. 615 0$aEquations. 676 $a515.353 676 $a515/.353 686 $a31.44$2bcl 686 $aSK 540$2rvk 700 $aO'Neil$b Peter V$0511885 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877699103321 996 $aBeginning partial differential equations$93925134 997 $aUNINA