Accedi Prova Gratuita

Follow us

Benvenuto su Bookboon

Per fornire i nostri servizi contiamo su una serie di cookie essenziali per accedere alle nostre funzionalità.

Vedere i dettagli dei cookies
Categories Corporate
Libro di testo gratuito

Second-order ordinary differential equations

Special functions, Sturm-Liouville theory and transforms

di R.S. Johnson
(26 valutazioni )
181
Lingua :  English
This text provides an introduction to all the relevant material normally encountered at university level. Numerous worked examples are provided throughout.
Scarica libri di testo in PDF gratuiti o leggi online. Meno del 15% di pubblicità.
Abbonamento Business gratuito per i primi 30 giorni, poi $5.99/mese
Descrizione
Contenuto

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.). Numerous worked examples are provided throughout.

  1. Power-series solution of ODEs
    1. Series solution: essential ideas
    2. ODEs with regular singular points
    3. Exercises 1
  2. The method of Frobenius
    1. The basic method
    2. The two special cases
    3. Exercises
  3. The Bessel equation and Bessel functions
    1. First solution
    2. The second solution
    3. The modified Bessel equation
  4. The Legendre polynomials
    1. Exercises 4
  5. The Hermite polynomials
    1. Exercises 5
  6. Generating functions
    1. Legendre polynomials
    2. Hermite polynomials
    3. Bessel functions
    4. Exercises 6
  7. Answers
  8. Part II: An introduction to Sturm-Liouville theory
  9. Preface
  10. List of Equations
  11. Introduction and Background
    1. The second-order equations
    2. The boundary-value problem
    3. Self-adjoint equations
    4. Exercises 1
  12. The Sturm-Liouville problem: the eigenvalues
    1. Real eigenvalues
    2. Simple eigenvalues
    3. Ordered eigenvalues
    4. Exercises 2
  13. The Sturm-Liouville problem: the eigenfunctions
    1. The fundamental oscillation theorem
    2. Using the fundamental oscillation theorem
    3. Orthogonality
    4. Eigenfunction expansions
    5. Exercises 3
  14. Inhomogeneous equations
    1. Exercise 4
  15. Answers
  16. Part III: Integral transforms
  17. Preface
  18. List of Problems
  19. Introduction
    1. The appearance of an integral transform from a PDE
    2. The appearance of an integral transform from an ODE
    3. Exercise 1
  20. The Laplace Transform
    1. LTs of some elementary functions
    2. Some properties of the LT
    3. Inversion of the Laplace Transform
    4. Applications to the solution of differential and integral equations
    5. Exercises 2
  21. The Fourier Transform
    1. FTs of some elementary functions
    2. Some properties of the FT
    3. Inversion of the Fourier Transform
    4. Applications to the solution of differential and integral equations
    5. Exercises 3
  22. The Hankel Transform
    1. HTs of some elementary functions
    2. Some properties of the HT
    3. Application to the solution of a PDE
    4. Exercises 4
  23. The Mellin Transform
    1. MTs of some elementary functions
    2. Some properties of the MT
    3. Applications to the solution of a PDE
    4. Exercises 5
  24. Tables of a few standard Integral Transforms
  25. Answers
  26. Index
Scrivi una recensione
home.libro.su_autore

R.S. Johnson

home.libro.scoprire_autore
home.libro.relativo_contenuto