Analysis III

Focusing on classical Cauchy theory, this volume emphasizes its diverse applications rather than solely the theory of analytic functions. It explores the generalization of Cauchy-type curvilinear integrals to multiple real variables and introduces the fundamentals of manifold theory, equipping readers with essential terminology and key theorems. The concluding chapter demonstrates the practical use of these theorems in constructing the compact Riemann surface of an algebraic function, a topic often overlooked in standard literature yet approachable with basic techniques.