Items related to Integral Transforms and their Applications
Synopsis
I: The Laplace Transform.- 1. Definition and Elementary Properties.- 2. The Inversion Theorem.- 3. Ordinary Differential Equations.- 4. Partial Differential Equations.- 5. Integral Equations.- 6. The Inversion Integral.- II: The Fourier Transform.- 7. Definitions and Elementary Properties.- 8. Application to Partial Differential Equations.- 9. Generalized Functions.- 10. Greek's Functions.- 11. Fourier Transforms in Two or More Variables.- III: Other Important Transforms.- 12. Mellin Transforms.- 13. Mellin Transforms in Summation.- 14. Integrals Involving a Parameter.- 15. Hankel Transforms.- 16. Dual Integral Equations.- 17. Integral Transforms Generated by Green's Functions.- IV: Special Techniques.- 18. The Wiener-Hopf Technique.- 19. Methods Based on Cauchy Integrals.- 20. Laplace's Method for Ordinary Differential Equations.- 21. Numerical Inversion of Laplace Transforms.- Appendices.- A: The Factorial Function.- B: Riemann's Zeta Function.- C: The Exponential Integral.
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