A First Course in Complex Analysis was developed from lecture notes for a one-semester undergraduate course taught by the authors. Found insideAs a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources. Found insideThis book contains a rigorous coverage of those topics (and only those topics) that, in the author's judgement, are suitable for inclusion in a first course on Complex Functions. This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Found insideAdvanced textbook on central topic of pure mathematics. Found insideThis book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. This radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. Using several hundred diagrams this is a new visual approach to the topic. Found insideThis text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. This text is part of the International Series in Pure and Applied Mathematics. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus. The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text. This is a concise textbook of complex analysis for undergraduate and graduate students. Found insideHints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: ... The objective of this book is to: • introduce students to the complex number system • equip students with necessary knowledge and skills to enable them handle problems involving complex numbers • help students apply techniques of ... Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study. The 280 exercises range from simple computations to difficult problems. Their variety makes the book especially attractive. Found insideThis Briefs volume develops the theory of entire slice regular functions. Introduction to Complex AnalysisBy Michael Taylor In this textbook, a concise approach to complex analysis of one and several variables is presented. With this second volume, we enter the intriguing world of complex analysis. Found insideThis book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics. Found insideA concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on ... Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space. Contents: Algebra of Complex Number, Functions of Complex Number, Limit and Continuity, Analytic Functions, Complex Integration, Cauchy Integral Theorem, Contour Integration, Series in Complex Number, Taylor and Laurent Series. Found insideAn authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course ... Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory. Found insideOriginally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals. Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. The guide that helps students study faster, learn better, and get top grades More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike. Complex Number System 1 7 2. Found insideThis text on complex variables is geared toward graduate students and undergraduates who have taken an introductory course in real analysis. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. Found insideYet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. Found insideThis book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Found insideThis book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. 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