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

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
Authors / Creators: Agarwal, Ravi P. (Author, http://id.loc.gov/vocabulary/relators/aut), O'Regan, Donal. (http://id.loc.gov/vocabulary/relators/aut)
Other Authors / Creators:O'Regan, Donal. author.
Other Corporate Authors / Creators:SpringerLink (Online service)
Format: Electronic eBook
Language:English
Edition:1st ed. 2009.
Imprint: New York, NY : Springer New York : Imprint: Springer, 2009.
Series:Universitext,
Subjects:
Differential equations.
Numerical analysis.
Mathematical physics.
Engineering mathematics.
Engineering—Data processing.
Differential Equations.
Numerical Analysis.
Mathematical Methods in Physics.
Mathematical and Computational Engineering Applications.
Online Access:Available in Springer Mathematics and Statistics eBooks 2009 English/International.
Table of Contents:
  • 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 (Cont’d.)
  • 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 (Cont’d.)
  • Boundary Value Problems
  • Boundary Value Problems (Cont’d.)
  • Green’s Functions
  • Regular Perturbations
  • Singular Perturbations
  • Sturm–Liouville Problems
  • Eigenfunction Expansions
  • Eigenfunction Expansions (Cont’d.)
  • Convergence of the Fourier Series
  • Convergence of the Fourier Series (Cont’d.)
  • 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 (Cont’d.)
  • The One-Dimensional Wave Equation
  • The One-Dimensional Wave Equation (Cont’d.)
  • 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 (Cont’d.)
  • Nonhomogeneous Equations
  • Fourier Integral and Transforms
  • Fourier Integral and Transforms (Cont’d.)
  • Fourier Transform Method for Partial DEs
  • Fourier Transform Method for Partial DEs (Cont’d.)
  • Laplace Transforms
  • Laplace Transforms (Cont’d.)
  • Laplace Transform Method for Ordinary DEs
  • Laplace Transform Method for Partial DEs
  • Well-Posed Problems
  • Verification of Solutions.

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