Advertisement

Integral Transforms and the Fourier Bessel Series

  • Eugen Skudrzyk

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.

Keywords

Bessel Function Integral Transform Integral Theorem Excellent Summary Fourier Cosine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aseltine, J. A.: Transform method in linear system analysis. New York, N. Y.: McGraw-Hill. 1958.Google Scholar
  2. Boxer, R.: A note on numerical transform calculus. I.R. E. Proc. 45 (1957) 1401–1406.MathSciNetGoogle Scholar
  3. 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.Google Scholar
  4. Carslaw, H. S., Jaeger, J. C.: Operational methods in applied mathematics. New York, N. Y.: Dover Publication. 1963.Google Scholar
  5. Doetscii, G.: Theorie und Anwendung der Laplace-Transformation. Berlin: Springer. 1937.Google Scholar
  6. Funk, P., Sagan, H., Selig, F.: Die Laplace-Transformation und ihre Anwendung. Wien: Deuticke. 1953.Google Scholar
  7. Gardner, E. U., Barnes, J. L.: Transients in linear systems. New York, N. Y.: Wiley. 1948.Google Scholar
  8. Goldberg, R.: Fourier transforms. Cambridge University Press. 1962.Google Scholar
  9. Irving, J., Mullineux, M.: Mathematics in physics and engineering. Academic Press, New York and London 1959.MATHGoogle Scholar
  10. Jaeger, J. C.: An introduction to the Laplace transformation. New Yorrk, N. Y.: Wiley. 1949.Google Scholar
  11. Kuo, B. C.: Automatic control systems. Englewood Cliffs, N. J.: Prentice-Hall 1962.Google Scholar
  12. Lepage, W. R.: Complex variables and the Laplace transform for engineers. New York, N. Y.: McGraw-Hill. 1961.Google Scholar
  13. Pol, B. Van Der, Bremmer, H.:l. Operational calculus based on the two-sided Laplace integral. New York, N. Y.: Cambridge University Press. 1950.Google Scholar
  14. Scott, E. J.: Transform calculus. New York, N. Y.: Harper and Brothers. 1955.Google Scholar
  15. Thomson, W. T.: Laplace transformation theory and engineering applications. New York, N. Y.: Prentice-Hall. 1950.Google Scholar
  16. Wagner, K. W.: Operatorenrechnung nebst Anwendungen in Physik und Technik. Leipzig: Barth. 1939.Google Scholar
  17. Wasow, W.: Discrete approximation to the Laplace transformation. Z. angew. Math. u. Phys. 8 (1957) 401–407.MathSciNetMATHCrossRefGoogle Scholar
  18. Watson, G. N.: A treatise on the theory of Bessel functions. Cambridge, Ma.: Cambridge University Press, 1952.Google Scholar
  19. Writtaken, E. T., Watson, G. N.: Modern analysis. Cambridge University Press. 1952.Google Scholar
  20. Widder, D. V.: The Laplace transform. Princeton University Press. 1941.Google Scholar
  21. Wylie, C. R., Jr.: Advanced engineering mathematics. New York, N. Y.: McGraw-Hill. 1966.Google Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations