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.
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
Visual Complex Analysis 4.3 out of 5based on
More than 1 year ago
While my headline might make sense based on the title of this book, this book is amazing at providing lots of detailed images getting at the nuts and bolts of what is going on with the spaces when you preform certain complex operations. I purchased this book to accompany the Complex analysis textbook used in my Graduate School course, which while not a bad book focused very heavily on the analysis and often beautiful visual results where skipped over and ignored completely.
More than 1 year ago
More than 1 year ago
A superb book which clearly explain the simple but profound geometrical ideas which are at the base of complex analysis.
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