Beginning Partial Differential Equations.

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: O'Neil, Peter V.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Wiley, 2014.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Half Title page
  • Title page
  • Copyright page
  • Preface
  • Chapter 1: First Ideas
  • 1.1 Two Partial Differential Equations
  • 1.2 Fourier Series
  • 1.3 Two Eigenvalue Problems
  • 1.4 A Proof of the Convergence Theorem
  • Chapter 2: Solutions of the Heat Equation
  • 2.1 Solutions on an Interval [0, L]
  • 2.2 A Nonhomogeneous Problem
  • 2.3 The Heat Equation in Two Space Variables
  • 2.4 The Weak Maximum Principle
  • Chapter 3: Solutions of the Wave Equation
  • 3.1 Solutions on Bounded Intervals
  • 3.2 The Cauchy Problem
  • 3.3 The Wave Equation in Higher Dimensions
  • Chapter 4: Dirichlet and Neumann Problems
  • 4.1 Laplace's Equation and Harmonic Functions
  • 4.2 The Dirichlet Problem for a Rectangle
  • 4.3 The Dirichlet Problem for a Disk
  • 4.4 Properties of Harmonic Functions
  • 4.5 The Neumann Problem
  • 4.6 Poisson's Equation
  • 4.7 Existence Theorem for a Dirichlet Problem
  • Chapter 5: Fourier Integral Methods of Solution
  • 5.1 The Fourier Integral of a Function
  • 5.2 The Heat Equation on the Real Line
  • 5.3 The Debate over the Age of the Earth
  • 5.4 Burgers' Equation
  • 5.5 The Cauchy Problem for the Wave Equation
  • 5.6 Laplace's Equation on Unbounded Domains
  • Chapter 6: Solutions Using Eigenfunction Expansions
  • 6.1 A Theory of Eigenfunction Expansions
  • 6.2 Bessel Functions
  • 6.3 Applications of Bessel Functions
  • 6.4 Legendre Polynomials and Applications
  • Chapter 7: Integral Transform Methods of Solution
  • 7.1 The Fourier Transform
  • 7.2 Heat and Wave Equations
  • 7.3 The Telegraph Equation
  • 7.4 The Laplace Transform
  • Chapter 8: First-Order Equations
  • 8.1 Linear First-Order Equations
  • 8.2 The Significance of Characteristics
  • 8.3 The Quasi-Linear Equation
  • Chapter 9: End Materials
  • 9.1 Notation
  • 9.2 Use of MAPLE
  • 9.3 Answers to Selected Problems
  • Index

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