Synopses & Reviews
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Synopsis
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
About the Author
Tristan Needham is Associate Professor of Mathematics at the University of San Francisco. For part of the work in this book, he was presented with the
Carl B. Allendoerfer Award by the Mathematical Association of America.
Table of Contents
1. Geometry and Complex Arithmetic
2. Complex Functions as Transformations
3. Möbius Transformations and Inversion
4. Differentiation: The Amplitwist Concept
5. Further Geometry of Differentiation
6. Non-Euclidean Geometry*
7. Winding Numbers and Topology
8. Complex Integration: Cauchy's Theorem
9. Cauchy's Formula and Its Applications
10. Vector Fields: Physics and Topology
11. Vector Fields and Complex Integration
12. Flows and Harmonic Functions