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.
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Publish Date
2013
Publisher
Bookboon.com
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Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms
2013, Bookboon.com
8776819728 9788776819729
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Book Details
Table of Contents
Content
1. Power-series solution of ODEs
1.1. Series solution: essential ideas
1.2. ODEs with regular singular points
1.3. Exercises 1
2. The method of Frobenius
2.1. The basic method
2.2. The two special cases
2.3. Exercises
3. The Bessel equation and Bessel functions
3.1. First solution
3.2. The second solution
3.3. The modified Bessel equation
4. The Legendre polynomials
4.1. Exercises 4
5. The Hermite polynomials
5.1. Exercises 5
6. Generating functions
6.1. Legendre polynomials
6.2. Hermite polynomials
6.3. Bessel functions
6.4. Exercises 6
7. Answers
8. Part II: An introduction to Sturm-Liouville theory
9. Preface
10. List of Equations
11. Introduction and Background
11.1. The second-order equations
11.2. The boundary-value problem
11.3. Self-adjoint equations
11.4. Exercises 1
12. The Sturm-Liouville problem: the eigenvalues
12.1. Real eigenvalues
12.2. Simple eigenvalues
12.3. Ordered eigenvalues
12.4. Exercises 2
13. The Sturm-Liouville problem: the eigenfunctions
13.1. The fundamental oscillation theorem
13.2. Using the fundamental oscillation theorem
13.3. Orthogonality
13.4. Eigenfunction expansions
13.5. Exercises 3
14. Inhomogeneous equations
14.1. Exercise 4
15. Answers
16. Part III: Integral transforms
17. Preface
18. List of Problems
19. Introduction
19.1. The appearance of an integral transform from a PDE
19.2. The appearance of an integral transform from an ODE
19.3. Exercise 1
20. The Laplace Transform
20.1. LTs of some elementary functions
20.2. Some properties of the LT
20.3. Inversion of the Laplace Transform
20.4. Applications to the solution of differential and integral equations
20.5. Exercises 2
21. The Fourier Transform
21.1. FTs of some elementary functions
21.2. Some properties of the FT
21.3. Inversion of the Fourier Transform
21.4. Applications to the solution of differential and integral equations
21.5. Exercises 3
22. The Hankel Transform
22.1. HTs of some elementary functions
22.2. Some properties of the HT
22.3. Application to the solution of a PDE
22.4. Exercises 4
23. The Mellin Transform
23.1. MTs of some elementary functions
23.2. Some properties of the MT
23.3. Applications to the solution of a PDE
23.4. Exercises 5
24. Tables of a few standard Integral Transforms
25. Answers
26. Index
ID Numbers
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| February 4, 2018 | Edited by Tom Morris | merge authors |
| June 25, 2015 | Edited by Alice Kirk | Edited without comment. |
| June 25, 2015 | Created by Alice Kirk | Added new book. |