Visual Complex AnalysisThis 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. |
Contents
Geometry and Complex Arithmetic | 1 |
Similarities and Complex Arithmetic | 27 |
5 | 39 |
Copyright | |
51 other sections not shown
Other editions - View all
Common terms and phrases
algebraic amplification amplitwist analytic function analytic mapping angle arbitrary Argument Principle arrow branch point C₁ centred Chapter complex function complex inversion complex number complex plane conformal mapping consider constant convergence corresponding critical point curvature curve deduce defined derivative differential direct motion distance elliptic equal equation Euclidean example exercise fact Figure fixed points flow flux formula h-lines hyperbolic geometry hyperbolic plane illustrated image points infinitesimal infinity inside integral intersection line-segment linear log(z loop matrix Möbius transformation multiplication non-Euclidean geometry obtain orbit origin orthogonal Poincaré disc polynomial power series preimages pseudosphere radius real axis real numbers reflection region result Riemann sphere rotation round simple singularity square stereographic projection streamlines surface symmetric tangent Theorem tractrix triangle twist unit circle unit disc upper half-plane vanish vector field vertical winding number