Abstract
In order to evaluate the intractable integrals arising from Equation 4.53, we need to devote some space first to the theory of functions of a complex variable. We shall present with no proof, or very little, many results that deserve careful study and rigorous treatment. The reader is advised to read one of the good books on the subject,1 or to attend lectures on the subject by a mathematician.
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
Preview
Unable to display preview. Download preview PDF.
Notes
Among the well-known books on functions of a complex variable are: Churchill, R. V., J. W. Brown, and R F. Verhey. Complex Variables and Applications. New York; McGraw-Hill, 1974; Franklin, P. 3d ed. Functions of Complex Variables. Englewood Cliffs, NJ: Prentice-Hall, 1947.
The uniqueness of the derivative at a point must survive also the use of various complicated spirals along which h may approach zero. In fact, the C-R conditions and the continuity of the functions u and v are sufficient to guarantee uniqueness. See Churchill, R V., and J. W. Brown. Fourier Series and Boundary Value Problems 3d ed. New York: McGraw-Hill, 1978.
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bloch, I. (1997). Integration in the Complex Plane. In: The Physics of Oscillations and Waves. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0050-0_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0050-0_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0052-4
Online ISBN: 978-1-4899-0050-0
eBook Packages: Springer Book Archive