Fujiwara T. Complex Function Theory 2023 torrent

Textbook in PDF format

This book is an English version of “Complex Function Theory” in the University of Tokyo Engineering Course prepared in Japanese for undergraduate students. The goal of the book is to provide ease of use and applicability, not mathematical rigor. The explanations avoid abstract or too many general points as much as possible and are based on a few key examples to help university students understand and use the important properties of complex functions.
The complex function theory in this book is mainly classical mathematics, which was established in the 19th or early 20th century. We believe studying complex function theory is significant in two ways. One is that it prepares the way for applied mathematics that is used widely in specialist fields. A deeper study of differential equations and Fourier–Laplace analysis is not possible without the help of complex function theory. These are also points of entry to mathematics as a more broadly applicable tool. The other is that complex function theory is one of the classical forms of mathematics, so some aspects of it are good educational material for reconsidering the form of mathematics as an academic discipline, and from the perspective of slightly deeper immersion in specialist areas. Therefore, the complex function theory generally comes up in the second year, at the earliest, or in the third year after studying calculus and linear algebra right after entering university.
Preface.
Complex numbers and their functions.
Complex Functions and Holomorphy.
Elementary Functions.
Conformal Transformation.
Singularities.
Complex Integrals.
Cauchy’s Integral Formula and Power Series Expansion of Complex Functions.
Advanced Complex Integrals.
Analytic Continuation and Riemann Surface.
Meromorphic Functions.
Elliptic Integrals and Elliptic Functions.
Ordinary Differential Equations of Complex Variables.
Orthogonal Polynomials.
Functions Written With Hypergeometric Functions.
Functions Written With Confluent Hypergeometric Functions.
Bibliography.
Index