A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

11. Integral Transforms

• 11.1. General Form of Integral Transforms. Some Formulas
  • 11.1.1. Integral Transforms and Inversion Formulas
  • 11.1.2. Residues. Jordan Lemma
• 11.2. Laplace Transform
  • 11.2.1. Laplace Transform and the Inverse Laplace Transform
  • 11.2.2. Main Properties of the Laplace Transform. Inversion Formulas for Some Functions
  • 11.2.3. Limit Theorems. Representation of Inverse Transforms as Convergent Series and Asymptotic Expansions
• 11.3. Mellin Transform
  • 11.3.1. Mellin Transform and the Inversion Formula
  • 11.3.2. Main Properties of the Mellin Transform. Relation Among the Mellin, Laplace, and Fourier Transforms
• 11.4. Various Forms of the Fourier Transform
  • 11.4.1. Fourier Transform and the Inverse Fourier Transform
  • 11.4.2. Fourier Cosine and Sine Transforms
• 11.5. Other Integral Transforms
  • 11.5.1. Integral Transforms Whose Kernels Contain Bessel Functions and Modified Bessel Functions
  • 11.5.2. Summary Table of Integral Transforms. Areas of Application of Integral Transforms
• References for Chapter 11

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