Complex Variables with Applications

• Main Authors: Ponnusamy, S. (Author), Silverman, Herb (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2006.
• Subjects: Mathematics.; Functions of complex variables.; Applied mathematics.; Engineering mathematics.; Geometry.; Number theory.; Functions of a Complex Variable.; Applications of Mathematics.; Several Complex Variables and Analytic Spaces.; Number Theory.; Appl.Mathematics/Computational Methods of Engineering.

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The author...

Table of Contents:

• Algebraic and Geometric Preliminaries
• Topological and Analytic Preliminaries
• Bilinear Transformations and Mappings
• Elementary Functions
• Analytic Functions
• Power Series
• Complex Integration and Cauchy’s Theorem
• Applications of Cauchy’s Theorem
• Laurent Series and the Residue Theorem
• Harmonic Functions
• Conformal Mapping and the Riemann Mapping Theorem
• Entire and Meromorphic Functions
• Analytic Continuation.