Abstract
It is not within the scope of this book to discuss the transform theory in detail; many books have been written on integral transforms. The reader will find an excellent summary of this theory with practical examples of its use in the book by J. Irving and N. Mullineux, Mathematics in Physics and Engineering. The theory of integral transforms is very important, integral transforms are useful in reducing inhomogeneous differential equations and boundary conditions into algebraic equations. The kernel, then, is represented by a set of orthogonal functions.
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References
Aseltine, J. A.: Transform method in linear system analysis. New York, N. Y.: McGraw-Hill. 1958.
Boxer, R.: A note on numerical transform calculus. I.R. E. Proc. 45 (1957) 1401–1406.
Boxer, R., Thaler, S.: A simplified method of solving linear and nonlinear systems.I.R. E. Proc. 44 (1956) 89–101; Extensions of numerical transform theory. Rome Air Dev. Ctr. Tech. Rep., p. 56–115, November 1956.
Carslaw, H. S., Jaeger, J. C.: Operational methods in applied mathematics. New York, N. Y.: Dover Publication. 1963.
Doetscii, G.: Theorie und Anwendung der Laplace-Transformation. Berlin: Springer. 1937.
Funk, P., Sagan, H., Selig, F.: Die Laplace-Transformation und ihre Anwendung. Wien: Deuticke. 1953.
Gardner, E. U., Barnes, J. L.: Transients in linear systems. New York, N. Y.: Wiley. 1948.
Goldberg, R.: Fourier transforms. Cambridge University Press. 1962.
Irving, J., Mullineux, M.: Mathematics in physics and engineering. Academic Press, New York and London 1959.
Jaeger, J. C.: An introduction to the Laplace transformation. New Yorrk, N. Y.: Wiley. 1949.
Kuo, B. C.: Automatic control systems. Englewood Cliffs, N. J.: Prentice-Hall 1962.
Lepage, W. R.: Complex variables and the Laplace transform for engineers. New York, N. Y.: McGraw-Hill. 1961.
Pol, B. Van Der, Bremmer, H.:l. Operational calculus based on the two-sided Laplace integral. New York, N. Y.: Cambridge University Press. 1950.
Scott, E. J.: Transform calculus. New York, N. Y.: Harper and Brothers. 1955.
Thomson, W. T.: Laplace transformation theory and engineering applications. New York, N. Y.: Prentice-Hall. 1950.
Wagner, K. W.: Operatorenrechnung nebst Anwendungen in Physik und Technik. Leipzig: Barth. 1939.
Wasow, W.: Discrete approximation to the Laplace transformation. Z. angew. Math. u. Phys. 8 (1957) 401–407.
Watson, G. N.: A treatise on the theory of Bessel functions. Cambridge, Ma.: Cambridge University Press, 1952.
Writtaken, E. T., Watson, G. N.: Modern analysis. Cambridge University Press. 1952.
Widder, D. V.: The Laplace transform. Princeton University Press. 1941.
Wylie, C. R., Jr.: Advanced engineering mathematics. New York, N. Y.: McGraw-Hill. 1966.
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Skudrzyk, E. (1971). Integral Transforms and the Fourier Bessel Series. In: The Foundations of Acoustics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8255-0_8
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DOI: https://doi.org/10.1007/978-3-7091-8255-0_8
Publisher Name: Springer, Vienna
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