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Ordinary and Partial Differential Equations With Special Functions, Fourier Series, and Boundary Value Problems /

This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures. Key Features: Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illustrations. Develops ODEs in conjuction with...

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Bibliographic Details
Main Authors: Agarwal, Ravi P. (Author), ORegan, Donal. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: New York, NY : Springer New York, 2009.
Series:Universitext
Subjects:
Mathematics.
Differential Equations.
Differential equations, partial.
Numerical analysis.
Mathematical physics.
Engineering mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Numerical Analysis.
Mathematical Methods in Physics.
Appl.Mathematics/Computational Methods of Engineering.
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-79146-3
Table of Contents:
  • Preface
  • Solvable Differential Equations
  • Second Order Differential Equations
  • Preliminaries to Series Solutions
  • Solution at an Ordinary Point
  • Solution at a Singular Point
  • Solution at a Singular Point (Continued)
  • Legendre Polynomials and Functions
  • Chebyshev, Hermite and Laguerre Polynomials
  • Bessel Functions
  • Hypergeometric Functions
  • Piecewise Continuous and Periodic Functions
  • Orthogonal Functions and Polynomials
  • Orthogonal Functions and Polynomials (Continued)
  • Boundary Value Problems
  • Boundary Value Problems (Continued)
  • Greens Functions
  • Regular Perturbations
  • Singular Perturbations
  • Sturm-Liouville Problems
  • Eigenfunction Expansions
  • Eigenfunction Expansions (Continued)
  • Convergence of the Fourier Series
  • Convergence of the Fourier Series (Continued)
  • Fourier Series Solutions of Ordinary Differential Equations
  • Partial Differential Equations
  • First-Order Partial Differential Equations
  • Solvable Partial Differential Equations
  • The Canonical Forms
  • The Method of Separation of Variables
  • The One-Dimensional Heat Equation
  • The One-Dimensional Heat Equation (Continued)
  • The One-Dimensional Wave Equation
  • The One-Dimensional Wave Equation (Continued)
  • Laplace Equation in Two Dimensions
  • Laplace Equation in Polar Coordinates
  • Two-Dimensional Heat Equation
  • Two-Dimensional Wave Equation
  • Laplace Equation in Three Dimensions
  • Laplace Equation in Three Dimensions (Continued)
  • Nonhomogeneous Equations
  • Fourier Integral and Transforms
  • Fourier Integral and Transforms (Continued)
  • Fourier Transform Method for PDEs
  • Fourier Transform Method for PDEs (Continued)
  • Laplace Transforms
  • Laplace Transforms (Continued)
  • Laplace Transform Method for ODEs
  • Laplace Transform Method for PDEs
  • Well-Posed Problems
  • Verification of Solutions
  • References for Further Reading
  • Index.

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