LEADER 05824nam 2200709 450 001 9910791029003321 005 20200520144314.0 010 $a1-118-83210-8 035 $a(CKB)2550000001317608 035 $a(EBL)1687538 035 $a(SSID)ssj0001226121 035 $a(PQKBManifestationID)11742601 035 $a(PQKBTitleCode)TC0001226121 035 $a(PQKBWorkID)11269888 035 $a(PQKB)10701027 035 $a(MiAaPQ)EBC1687538 035 $a(DLC) 2013035005 035 $a(JP-MeL)3000065409 035 $a(Au-PeEL)EBL1687538 035 $a(CaPaEBR)ebr10882755 035 $a(CaONFJC)MIL618883 035 $a(OCoLC)857234464 035 $a(MiAaPQ)EBC7103899 035 $a(PPN)195533631 035 $a(EXLCZ)992550000001317608 100 $a20140625h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBeginning partial differential equations /$fPeter V. O'Neil 205 $aThird edition. 210 1$aHoboken, New Jersey :$cWiley,$d2014. 210 4$d2014 215 $a1 online resource (453 p.) 225 0 $aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 300 $aIncludes index. 311 $a1-118-62994-9 311 $a1-306-87632-X 320 $aIncludes bibliographical references and index. 327 $aBeginning Partial Differential Equations; Copyright; Contents; Preface; 1 First Ideas; 1.1 Two Partial Differential Equations; 1.1.1 The Heat, or Diffusion, Equati; 1.1.2 The Wave Equation; 1.2 Fourier Series; 1.2.1 The Fourier Series of a Function; 1.2.2 Fourier Sine and Cosine Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Fourier Convergence Theorem; 1.4.1 The Role of Periodicity; 1.4.2 Dirichlet's Formula; 1.4.3 The Riemann-Lebesgue Lemma; 1.4.4 Proof of the Convergence Theorem; 2 Solutions of the Heat Equation; 2.1 Solutions on an Interval [0, L] 327 $a2.1.1 Ends Kept at Temperature Zero2.1.2 Insulated Ends; 2.1.3 Ends at Different Temperatures; 2.1.4 A Diffusion Equation with Additional Terms; 2.1.5 One Radiating End; 2.2 A Nonhomogeneous Problem; 2.3 The Heat Equation in Two Space Variables; 2.4 The Weak Maximum Principle; 3 Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.1.1 Fixed Ends; 3.1.2 Fixed Ends with a Forcing Term; 3.1.3 Damped Wave Motion; 3.2 The Cauchy Problem; 3.2.1 d'Alembert's Solution; 3.2.1.1 Forward and Backward Waves; 3.2.2 The Cauchy Problem on a Half Line 327 $a3.2.3 Characteristic Triangles and Quadrilaterals3.2.4 A Cauchy Problem with a Forcing Term; 3.2.5 String with Moving Ends; 3.3 The Wave Equation in Higher Dimensions; 3.3.1 Vibrations in a Membrane with Fixed Frame; 3.3.2 The Poisson Integral Solution; 3.3.3 Hadamard's Method of Descent; 4 Dirichlet and Neumann Problems; 4.1 Laplace's Equation and Harmonic Functions; 4.1.1 Laplace's Equation in Polar Coordinates; 4.1.2 Laplace's Equation in Three Dimensions; 4.2 The Dirichlet Problem for a Rectangle; 4.3 The Dirichlet Problem for a Disk; 4.3.1 Poisson's Integral Solution 327 $a4.4 Properties of Harmonic Functions4.4.1 Topology of Rn; 4.4.2 Representation Theorems; 4.4.2.1 A Representation Theorem in R3; 4.4.2.2 A Representation Theorem in the Plane; 4.4.3 The Mean Value Property and the Maximum Principle; 4.5 The Neumann Problem; 4.5.1 Existence and Uniqueness; 4.5.2 Neumann Problem for a Rectangle; 4.5.3 Neumann Problem for a Disk; 4.6 Poisson's Equation; 4. 7 Existence Theorem for a Dirichlet Problem; 5 Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.1.1 Fourier Cosine and Sine Integrals; 5.2 The Heat Equation on the Real Line 327 $a5.2.1 A Reformulation of the Integral Solution5.2.2 The Heat Equation on a Half Line; 5.3 The Debate over the Age of the Earth; 5.4 Burger's Equation; 5.4.1 Traveling Wave Solutions of Burger's Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace's Equation on Unbounded Domains; 5.6.1 Dirichlet Problem for the Upper Half Plane; 5.6.2 Dirichlet Problem for the Right Quarter Plane; 5.6.3 A Neumann Problem for the Upper Half Plane; 6 Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.1.1 A Closer Look at Expansion Coefficients 327 $a6.2 Bessel Functions 330 $a"Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy"--$cProvided by publisher. 330 $a"This Third Edition provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms"--$cProvided by publisher. 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aDifferential equations, Partial 615 0$aDifferential equations, Partial. 676 $a515/.353 686 $aMAT007000$2bisacsh 700 $aO'Neil$b Peter V.$0511885 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910791029003321 996 $aBeginning partial differential equations$91974468 997 $aUNINA