Funktionentheorie 1

The first four chapters of this presentation of classical function theory convey central results and methods of complex analysis of a variable with minimal conceptual effort and building on little prior knowledge. They culminate in a proof of the small Riemann mapping theorem and a characterization of simply connected domains. Further topics are: elliptic functions (Weierstrassian, Jacobian approach), the elementary theory of modular forms of a variable, applications of functions to number theory (including a proof of the prime number theorem). Plus: over 400 exercises with solutions.