Boundary value problems : and partial differential equations /

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Boundary 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. Professo...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Powers, David L. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier Academic Press, ©2006.
Edición:5th ed.
Temas:
Boundary value problems > Textbooks.
Differential equations, Partial > Textbooks.
MATHEMATICS > Differential Equations > Partial.
Boundary value problems
Differential equations, Partial
Textbooks
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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