Ordinary and Partial Differential Equations [electronic resource] With Special Functions, Fourier Series, and Boundary Value Problems / by Ravi P. Agarwal, Donal O'Regan.
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...
Uniform Title: | Universitext,
2191-6675 |
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Main Authors: | |
Corporate Author: | |
Language: | English |
Published: |
New York, NY :
Springer New York : Imprint: Springer,
2009.
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Edition: | 1st ed. 2009. |
Series: | Universitext,
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Subjects: | |
Online Access: | |
Format: | Electronic eBook |
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.