An edition of Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms
(2013)
Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms
by R. S. Johnson
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Last edited by Tom Morris
February 4, 2018 | History
Ordinary differential equations, and second-order equations in particular, are at the heart of many mathematical descriptions of physical systems, as used by engineers, physicists and applied mathematicians. This text provides an introduction to all the relevant material normally encountered at university level: series solution, special functions (Bessel, etc.), Sturm-Liouville theory (involving the appearance of eigenvalues and eigenfunctions) and the definition, properties and use of various integral transforms (Fourier, Laplace, etc.).
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Publish Date
2013
Publisher
Bookboon
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Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms
2013, Bookboon
8776819728 9788776819729
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Book Details
Table of Contents
Power-series solution of ODEs
Series solution: essential ideas
ODEs with regular singular points
Exercises 1
The method of Frobenius
The basic method
The two special cases
Exercises
The Bessel equation and Bessel functions
First solution
The second solution
The modified Bessel equation
The Legendre polynomials
Exercises 4
The Hermite polynomials
Exercises 5
Generating functions
Legendre polynomials
Hermite polynomials
Bessel functions
Exercises 6
Answers
Part II: An introduction to Sturm-Liouville theory
Preface
List of Equations
Introduction and Background
The second-order equations
The boundary-value problem
Self-adjoint equations
Exercises 1
The Sturm-Liouville problem: the eigenvalues
Real eigenvalues
Simple eigenvalues
Ordered eigenvalues
Exercises 2
The Sturm-Liouville problem: the eigenfunctions
The fundamental oscillation theorem
Using the fundamental oscillation theorem
Orthogonality
Eigenfunction expansions
Exercises 3
Inhomogeneous equations
Exercise 4
Answers
Part III: Integral transforms
Preface
List of Problems
Introduction
The appearance of an integral transform from a PDE
The appearance of an integral transform from an ODE
Exercise 1
The Laplace Transform
LTs of some elementary functions
Some properties of the LT
Inversion of the Laplace Transform
Applications to the solution of differential and integral equations
Exercises 2
The Fourier Transform
FTs of some elementary functions
Some properties of the FT
Inversion of the Fourier Transform
Applications to the solution of differential and integral equations
Exercises 3
The Hankel Transform
HTs of some elementary functions
Some properties of the HT
Application to the solution of a PDE
Exercises 4
The Mellin Transform
MTs of some elementary functions
Some properties of the MT
Applications to the solution of a PDE
Exercises 5
Tables of a few standard Integral Transforms
Answers
Index
ID Numbers
Links outside Open Library
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| February 4, 2018 | Edited by Tom Morris | merge authors |
| April 11, 2016 | Edited by Alice Kirk | Edited without comment. |
| April 11, 2016 | Created by Alice Kirk | Added new book. |