LEADER 05494nam 2200709 a 450 001 9910956133503321 005 20200520144314.0 010 $a9786610961450 010 $a9781280961458 010 $a1280961457 010 $a9780080470795 010 $a0080470793 035 $a(CKB)1000000000363687 035 $a(EBL)286658 035 $a(OCoLC)437176588 035 $a(SSID)ssj0000114140 035 $a(PQKBManifestationID)11130089 035 $a(PQKBTitleCode)TC0000114140 035 $a(PQKBWorkID)10102565 035 $a(PQKB)10499017 035 $a(MiAaPQ)EBC286658 035 $a(Au-PeEL)EBL286658 035 $a(CaPaEBR)ebr10167083 035 $a(CaONFJC)MIL96145 035 $a(PPN)170271404 035 $a(FR-PaCSA)41001494 035 $a(FRCYB41001494)41001494 035 $a(EXLCZ)991000000000363687 100 $a20060117d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBoundary value problems $eand partial differential equations /$fDavid L. Powers 205 $a5th ed. 210 $aAmsterdam ;$aBoston $cElsevier Academic Press$dc2006 215 $a1 online resource (515 p.) 300 $aDescription based upon print version of record. 311 08$a9780125637381 311 08$a0125637381 320 $aIncludes bibliographical references (p. 433-434) and index. 327 $aCover; Contents; Preface; Chapter 0. Ordinary Differential Equations; 0.1 Homogeneous Linear Equations; 0.2 Nonhomogeneous Linear Equations; 0.3 Boundary Value Problems; 0.4 Singular Boundary Value Problems; 0.5 Green's Functions; Chapter Review; Miscellaneous Exercises; Chapter 1. Fourier Series and Integrals; 1.1 Periodic Functions and Fourier Series; 1.2 Arbitrary Period and Half-Range Expansions; 1.3 Convergence of Fourier Series; 1.4 Uniform Convergence; 1.5 Operations on Fourier Series; 1.6 Mean Error and Convergence in Mean; 1.7 Proof of Convergence 327 $a1.8 Numerical Determination of Fourier Coefficients1.9 Fourier Integral; 1.10 Complex Methods; 1.11 Applications of Fourier Series and Integrals; 1.12 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 2. The Heat Equation; 2.1 Derivation and Boundary Conditions; 2.2 Steady-State Temperatures; 2.3 Example: Fixed End Temperatures; 2.4 Example: Insulated Bar; 2.5 Example: Different Boundary Conditions; 2.6 Example: Convection; 2.7 Sturm-Liouville Problems; 2.8 Expansion in Series of Eigenfunctions; 2.9 Generalities on the Heat Conduction Problem; 2.10 Semi-Infinite Rod 327 $a2.11 Infinite Rod2.12 The Error Function; 2.13 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 3. The Wave Equation; 3.1 The Vibrating String; 3.2 Solution of the Vibrating String Problem; 3.3 d'Alembert's Solution; 3.4 One-Dimensional Wave Equation: Generalities; 3.5 Estimation of Eigenvalues; 3.6 Wave Equation in Unbounded Regions; 3.7 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 4. The Potential Equation; 4.1 Potential Equation; 4.2 Potential in a Rectangle; 4.3 Further Examples for a Rectangle; 4.4 Potential in Unbounded Regions 327 $a4.5 Potential in a Disk4.6 Classification and Limitations; 4.7 Comments and References; Chapter Review; Miscellaneous Exercises; Chapter 5. Higher Dimensions and Other Coordinates; 5.1 Two-Dimensional Wave Equation: Derivation; 5.2 Three-Dimensional Heat Equation; 5.3 Two-Dimensional Heat Equation: Solution; 5.4 Problems in Polar Coordinates; 5.5 Bessel's Equation; 5.6 Temperature in a Cylinder; 5.7 Vibrations of a Circular Membrane; 5.8 Some Applications of Bessel Functions; 5.9 Spherical Coordinates; Legendre Polynomials; 5.10 Some Applications of Legendre Polynomials 327 $a5.11 Comments and ReferencesChapter Review; Miscellaneous Exercises; Chapter 6. Laplace Transform; 6.1 Definition and Elementary Properties; 6.2 Partial Fractions and Convolutions; 6.3 Partial Differential Equations; 6.4 More Difficult Examples; 6.5 Comments and References; Miscellaneous Exercises; Chapter 7. Numerical Methods; 7.1 Boundary Value Problems; 7.2 Heat Problems; 7.3 Wave Equation; 7.4 Potential Equation; 7.5 Two-Dimensional Problems; 7.6 Comments and References; Miscellaneous Exercises; Bibliography; Mathematical References; Answers to Odd-Numbered Exercises; Chapter 0; Chapter 1 327 $aChapter 2 330 $aBoundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions 606 $aBoundary value problems$vTextbooks 606 $aDifferential equations, Partial$vTextbooks 615 0$aBoundary value problems 615 0$aDifferential equations, Partial 676 $a515/.353 700 $aPowers$b David L$030383 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910956133503321 996 $aBoundary value problems$9319411 997 $aUNINA