Abstract
This first chapter describes a brief definition of integral transforms, such as the Laplace and Fourier transforms, and a rough definition of delta and step functions which are frequently used as the source function. The multiple integral transforms and their notations are also explained. The last short comment lists some important formula books which are crucial for the inverse transform, i.e. the evaluation of the inversion integral.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Erdélyi A (ed) (1954) Tables of integral transforms, vol I and II. McGraw-Hill, New York
Gradshteyn IS, Ryzhik IM (1980) In: Jefferey A (ed) Table of integrals, series, and products, 5th edn. Academic Press, San Diego
Magnus W, Oberhettinger F, Soni RP (1966) Formulas and theorems for the special functions of mathematical physics. Springer, New York
Moriguchi S, Udagawa K, Ichimatsu S (1972) Mathematical formulas, vol I, II, III. Iwanami, Tokyo (in Japanese)
Sneddon IN (1951) Fourier transforms. McGraw-Hill, New York
Titchmarsh EC (1948) Introduction to the theory of Fourier integrals, 2nd edn. Clarendon Press, Oxford
Watson GN (1966) A treatise on the theory of bessel functions. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Watanabe, K. (2014). Definition of Integral Transforms and Distributions. In: Integral Transform Techniques for Green's Function. Lecture Notes in Applied and Computational Mechanics, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-319-00879-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-00879-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00878-3
Online ISBN: 978-3-319-00879-0
eBook Packages: EngineeringEngineering (R0)