Partial differential equations with Mathematica / Dimitri Vvedensky.
Series Physics series (Wokingham, England): Editor: Wokingham, England ; Reading, Mass. : Addison-Wesley Pub. Co., c1993Descripción: xi, 465 p. : ill. ; 25 cmISBN: 0201544091Tema(s): Mathematica (Computer file) | Differential equations, Partial -- Data processingOtra clasificación: 35-01 (33-01 34-01 34-04 81U40)Preface V -- 1. Introduction [1] -- 1.1 Introduction to Partial Differential Equations [2] -- 1.2 Outline of Book [6] -- 1.3 Introduction to Mathematica [8] -- 1.4 Mathematical Preliminaries [10] -- Further Reading [26] -- References [26] -- Problems [28] -- 2. First-Order Partial Differential Equations [35] -- 2.1 The Method of Characteristics [36] -- 2.2 Boundary Conditions of First-Order Equations [45] -- 2.3 Nonlinear First-Order Equations [52] -- 2.4 The Complete Integral [60] -- Further Reading [63] -- References [64] -- Problems [65] -- 3. Second-Order Partial Differential Equations [77] -- 3.1 Equations with Constant Coefficients [79] -- 3.2 Boundary Conditions of Second-Order Equations [84] -- 3.3 Geometry of Cauchy Boundary Conditions [89] -- 3.4 Hyperbolic Equations [91] -- 3.5 Parabolic Equations [97] -- 3.6 Elliptic Equations [101] -- Further Reading [107] -- References [107] -- Problems [108] -- 4. Separation of Variables and the Sturm—Lionville Problem -- 4.1 The Method of Separation of Variables [120] -- 4.2 Orthogonality of Functions [124] -- 4.3 Fourier Series [126] -- 4.4 Fourier Series Solutions of Differential Equations [133] -- 4.5 The Sturm-Liouville Problem I43 -- Further Reading [146] -- References [147] -- Problems [148] -- 5. Series Solutions of Ordinary Differential Equations [167] -- 5.1 Singular Points of Differential Equations [168] -- 5.2 The Method of Frobenius [171] -- 5.3 Constructing Complementary Solutions [180] -- 5.4 Standard Forms of Equations with Singular Points [191] -- Further Reading [194] -- References [195] -- Problems [196] -- 6. Special Functions and Orthogonal Polynomials [207] -- 6.1 Hermite Polynomials [208] -- 6.2 Legendre Polynomials [215] -- 6.3 Legendre Functions and Spherical Harmonics [222] -- 6.4 Bessel Functions [226] -- 6.5 Generating Functions [235] -- Further Reading [240] -- References [241] -- Problems [242] -- 7. Transform Methods and Green’s Functions [261] -- 7.1 The Fourier Transform [262] -- 7.2 The Laplace Transform and the Bromwich Integral [269] -- 7.3 Fundamental Solution of the Diffusion Equation [274] -- 7.4 Fundamental Solution of Poisson’s Equation [279] -- 7.5 Fundamental Solution of the Wave Equation [283] -- 7.6 Green’s Functions in the Presence of Boundaries: -- The Method of Images [286] -- Further Reading [293] -- References [293] -- Problems [294] -- 8. Integral Representations [317] -- 8.1 The Laplace Transform [318] -- 8.2 The Euler Transform [322] -- 8.3 Hypergeometric Functions [328] -- 8.4 Bessel Functions [331] -- 8.5 Hankel Functions [338] -- Further Reading [343] -- References [343] -- Problems [344] -- 9. Introduction to Nonlinear Partial Differential -- Equations [355] -- 9.1 Nonlinearity in Partial Differential Equations [356] -- 9.2 The Burgers Equation—An Exact Solution [361] -- 9.3 Elementary Soliton Solutions [366] -- 9.4 Backlund Transformations [371] -- 9.5 Nonlinear Superposition Principles [377] -- Further Reading [385] -- References [386] -- Problems [388] -- 10. The Method of Inverse Scattering [403] -- 10.1 Evolution of Eigenfunctions and Eigenvalues [405] -- 10.2 The Inverse Scattering Transform [412] -- 10.3 Solution of the Scattering Problem [422] -- 10.4 Lax’s Method [434] -- Further Reading [437] -- References [438] -- Problems [439] -- Index [453] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 35 V995 (Browse shelf) | Available | A-9402 |
Incluye referencias bibliográficas e índice.
Preface V --
1. Introduction [1] --
1.1 Introduction to Partial Differential Equations [2] --
1.2 Outline of Book [6] --
1.3 Introduction to Mathematica [8] --
1.4 Mathematical Preliminaries [10] --
Further Reading [26] --
References [26] --
Problems [28] --
2. First-Order Partial Differential Equations [35] --
2.1 The Method of Characteristics [36] --
2.2 Boundary Conditions of First-Order Equations [45] --
2.3 Nonlinear First-Order Equations [52] --
2.4 The Complete Integral [60] --
Further Reading [63] --
References [64] --
Problems [65] --
3. Second-Order Partial Differential Equations [77] --
3.1 Equations with Constant Coefficients [79] --
3.2 Boundary Conditions of Second-Order Equations [84] --
3.3 Geometry of Cauchy Boundary Conditions [89] --
3.4 Hyperbolic Equations [91] --
3.5 Parabolic Equations [97] --
3.6 Elliptic Equations [101] --
Further Reading [107] --
References [107] --
Problems [108] --
4. Separation of Variables and the Sturm—Lionville Problem --
4.1 The Method of Separation of Variables [120] --
4.2 Orthogonality of Functions [124] --
4.3 Fourier Series [126] --
4.4 Fourier Series Solutions of Differential Equations [133] --
4.5 The Sturm-Liouville Problem I43 --
Further Reading [146] --
References [147] --
Problems [148] --
5. Series Solutions of Ordinary Differential Equations [167] --
5.1 Singular Points of Differential Equations [168] --
5.2 The Method of Frobenius [171] --
5.3 Constructing Complementary Solutions [180] --
5.4 Standard Forms of Equations with Singular Points [191] --
Further Reading [194] --
References [195] --
Problems [196] --
6. Special Functions and Orthogonal Polynomials [207] --
6.1 Hermite Polynomials [208] --
6.2 Legendre Polynomials [215] --
6.3 Legendre Functions and Spherical Harmonics [222] --
6.4 Bessel Functions [226] --
6.5 Generating Functions [235] --
Further Reading [240] --
References [241] --
Problems [242] --
7. Transform Methods and Green’s Functions [261] --
7.1 The Fourier Transform [262] --
7.2 The Laplace Transform and the Bromwich Integral [269] --
7.3 Fundamental Solution of the Diffusion Equation [274] --
7.4 Fundamental Solution of Poisson’s Equation [279] --
7.5 Fundamental Solution of the Wave Equation [283] --
7.6 Green’s Functions in the Presence of Boundaries: --
The Method of Images [286] --
Further Reading [293] --
References [293] --
Problems [294] --
8. Integral Representations [317] --
8.1 The Laplace Transform [318] --
8.2 The Euler Transform [322] --
8.3 Hypergeometric Functions [328] --
8.4 Bessel Functions [331] --
8.5 Hankel Functions [338] --
Further Reading [343] --
References [343] --
Problems [344] --
9. Introduction to Nonlinear Partial Differential --
Equations [355] --
9.1 Nonlinearity in Partial Differential Equations [356] --
9.2 The Burgers Equation—An Exact Solution [361] --
9.3 Elementary Soliton Solutions [366] --
9.4 Backlund Transformations [371] --
9.5 Nonlinear Superposition Principles [377] --
Further Reading [385] --
References [386] --
Problems [388] --
10. The Method of Inverse Scattering [403] --
10.1 Evolution of Eigenfunctions and Eigenvalues [405] --
10.2 The Inverse Scattering Transform [412] --
10.3 Solution of the Scattering Problem [422] --
10.4 Lax’s Method [434] --
Further Reading [437] --
References [438] --
Problems [439] --
Index [453] --
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