LEADER 05423nam 2200649Ia 450 001 9910458660803321 005 20200520144314.0 010 $a1-281-03822-9 010 $a9786611038229 010 $a0-08-053193-8 035 $a(CKB)1000000000364336 035 $a(EBL)312736 035 $a(OCoLC)476100605 035 $a(SSID)ssj0000157673 035 $a(PQKBManifestationID)11147410 035 $a(PQKBTitleCode)TC0000157673 035 $a(PQKBWorkID)10139654 035 $a(PQKB)10279912 035 $a(MiAaPQ)EBC312736 035 $a(Au-PeEL)EBL312736 035 $a(CaPaEBR)ebr10190334 035 $a(CaONFJC)MIL103822 035 $a(OCoLC)437189361 035 $a(EXLCZ)991000000000364336 100 $a19950425d1995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFourier analysis and boundary value problems$b[electronic resource] /$fby Enrique A. Gonza?lez-Velasco 210 $aSan Diego $cAcademic Pres$dc1995 215 $a1 online resource (565 p.) 300 $aDescription based upon print version of record. 311 $a0-12-289640-8 320 $aIncludes bibliographical references (p. 539-542) and index. 327 $aFront Cover; Fourier Analysis and Boundary Value Problems; Copyright Page; Table of Contents; Preface; CHAPTER 1. A HEATED DISCUSSION; 1.1 Historical Prologue; 1.2 The Heat Equation; 1.3 Boundary Value Problems; 1.4 The Method of Separation of Variables; 1.5 Linearity and Superposition of Solutions; 1.6 Historical Epilogue; Exercises; CHAPTER 2. FOURIER SERIES; 2.1 Introduction; 2.2 Fourier Series; 2.3 The Riemann-Lebesgue Theorem; 2.4 The Convergence of Fourier Series; 2.5 Fourier Series on Arbitrary Intervals; 2.6 The Gibbs Phenomenon; 2.7 Feje?r Sums; 2.8 Integration of Fourier Series 327 $a2.9 Historical EpilogueExercises; CHAPTER 3. RETURN TO THE HEATED BAR; 3.1 Existence of a Solution; 3.2 Uniqueness and Stability of the Solution; 3.3 Nonzero Temperature at the Endpoints; 3.4 Bar Insulated at the Endpoints; 3.5 Mixed Endpoint Conditions; 3.6 Heat Convection at One Endpoint; 3.7 Time-Independent Problems; 3.8 The Steady-State Solution; 3.9 The Transient Solution; 3.10 The Complete Solution; 3.11 Time-Dependent Problems; Exercises; CHAPTER 4. GENERALIZED FOURIER SERIES; 4.1 Sturm-Liouville Problems; 4.2 The Eigenvalues and Eigenfunctions; 4.3 The Existence of the Eigenvalues 327 $a4.4 Generalized Fourier Series4.5 Approximations; 4.6 Historical Epilogue; Exercises; CHAPTER 5. THE WAVE EQUATION; 5.1 Introduction; 5.2 The Vibrating String; 5.3 D'Alembert's Solution; 5.4 A Struck String; 5.5 Bernoulli's Solution; 5.6 Time-Independent Problems; 5.7 Time-Dependent Problems; 5.8 Historical Epilogue; Exercises; CHAPTER 6. ORTHOGONAL SYSTEMS; 6.1 Fourier Series and Parseval's Identity; 6.2 An Approximation Problem; 6.3 The Uniform Convergence of Fourier Series; 6.4 Convergence in the Mean; 6.5 Applications to the Vibrating String; 6.6 The Riesz-Fischer Theorem; Exercises 327 $aCHAPTER 7. FOURIER TRANSFORMS7.1 The Laplace Equation; 7.2 Fourier Transforms; 7.3 Properties of the Fourier Transform; 7.4 Convolution; 7.5 Solution of the Dirichlet Problem for the Half-Plane; 7.6 The Fourier Transform Method; Exercises; CHAPTER 8. LAPLACE TRANSFORMS; 8.1 The Laplace Transform and the Inversion Theorem; 8.2 Properties of the Laplace Transform; 8.3 Convolution; 8.4 The Telegraph Equation; 8.5 The Method of Residues; 8.6 Historical Epilogue; Exercises; CHAPTER 9. BOUNDARY VALUE PROBLEMS IN HIGHER DIMENSIONS; 9.1 Electrostatic Potential in a Charged Box 327 $a9.2 Double Fourier Series9.3 The Dirichlet Problem in a Box; 9.4 Return to the Charged Box; 9.5 The Multiple Fourier Transform Method; 9.6 The Double Laplace Transform Method; Exercises; CHAPTER 10. BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY; 10.1 Vibrations of a Circular Membrane; 10.2 The Gamma Function; 10.3 Bessel Functions of the First Kind; 10.4 Recursion Formulas for Bessel Functions; 10.5 Bessel Functions of the Second Kind; 10.6 The Zeros of Bessel Functions; 10.7 Orthogonal Systems of Bessel Functions; 10.8 Fourier-Bessel Series and Dini-Bessel Series 327 $a10.9 Return to the Vibrating Membrane 330 $aFourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems hav 606 $aFourier analysis 606 $aBoundary value problems$xNumerical solutions 608 $aElectronic books. 615 0$aFourier analysis. 615 0$aBoundary value problems$xNumerical solutions. 676 $a515/.353 700 $aGonza?lez-Velasco$b Enrique A$0627633 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458660803321 996 $aFourier analysis and boundary value problems$91213847 997 $aUNINA