Boundary value problems: and partial differential equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier Academic Press
c2006
|
| Ausgabe: | 5th ed |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 433-434) and index Cover -- 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 -- 1.8 Numerical Determination of Fourier Coefficients -- 1.9 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 -- 2.11 Infinite Rod -- 2.12 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 -- 4.5 Potential in a Disk -- 4.6 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 -- 5.11 Comments and References -- Chapter 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 |
| Beschreibung: | 1 Online-Ressource (xi, 501 p.) |
| ISBN: | 0080470793 0125637381 9780080470795 |
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| 245 | 1 | 0 | |a Boundary value problems |b and partial differential equations |c David L. Powers |
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| 500 | |a Cover -- 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 -- 1.8 Numerical Determination of Fourier Coefficients -- 1.9 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 -- | ||
| 500 | |a - 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 -- 2.11 Infinite Rod -- 2.12 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 -- 4.5 Potential in a Disk -- 4.6 Classification and Limitations -- 4.7 Comments and References -- | ||
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Datensatz im Suchindex
| _version_ | 1804175500646547456 |
|---|---|
| any_adam_object | |
| author | Powers, David L. |
| author_facet | Powers, David L. |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV043095676 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| edition | 5th ed |
| format | Electronic eBook |
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| id | DE-604.BV043095676 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:17Z |
| institution | BVB |
| isbn | 0080470793 0125637381 9780080470795 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028519868 |
| oclc_num | 127115041 |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xi, 501 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Elsevier Academic Press |
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| spelling | Powers, David L. Verfasser aut Boundary value problems and partial differential equations David L. Powers 5th ed Amsterdam Elsevier Academic Press c2006 1 Online-Ressource (xi, 501 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 433-434) and index Cover -- 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 -- 1.8 Numerical Determination of Fourier Coefficients -- 1.9 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 -- 2.11 Infinite Rod -- 2.12 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 -- 4.5 Potential in a Disk -- 4.6 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 -- 5.11 Comments and References -- Chapter 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 MATHEMATICS / Differential Equations / Partial bisacsh Boundary value problems fast Differential equations, Partial fast Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=187200 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Powers, David L. Boundary value problems and partial differential equations MATHEMATICS / Differential Equations / Partial bisacsh Boundary value problems fast Differential equations, Partial fast Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Boundary value problems and partial differential equations |
| title_auth | Boundary value problems and partial differential equations |
| title_exact_search | Boundary value problems and partial differential equations |
| title_full | Boundary value problems and partial differential equations David L. Powers |
| title_fullStr | Boundary value problems and partial differential equations David L. Powers |
| title_full_unstemmed | Boundary value problems and partial differential equations David L. Powers |
| title_short | Boundary value problems |
| title_sort | boundary value problems and partial differential equations |
| title_sub | and partial differential equations |
| topic | MATHEMATICS / Differential Equations / Partial bisacsh Boundary value problems fast Differential equations, Partial fast Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | MATHEMATICS / Differential Equations / Partial Boundary value problems Differential equations, Partial Boundary value problems Textbooks Differential equations, Partial Textbooks Randwertproblem |
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