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The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy–Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions. Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. 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. Errata(s) Errata (72 KB)
This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study. A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics. Request Inspection Copy
Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.
A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu
An Introduction to Complex Analysis and Geometry provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The book developed from courses given in the Campus Honors Program at the University of Illinois Urbana-Champaign. These courses aimed to share with students the way many mathematics and physics problems magically simplify when viewed from the perspective of complex analysis. The book begins at an elementary level but also contains advanced material. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 through 7 develop the Cauchy theory and include some striking applications to calculus. 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. A reader of the first four chapters will be able to apply complex numbers in many elementary contexts. A reader of the full book will know basic one complex variable theory and will have seen it integrated into mathematics as a whole. Research mathematicians will discover several novel perspectives.
This book concisely addresses the classical results of the field, emphasizes the beauty, power, and counterintuitive nature of the subject, and moves the notion of power series front and center, giving readers a primary tool to deal with problems from modern function theory. Uniquely defines analyticity in terms of power series (as opposed to differentiability), making power series a central concept and tool to solve problems Features many “counterintuitive” concepts as a learning tool, such as addressing Liouville's Theorem, the factorization of analytic function, the Open Mapping Theorem, and the Maximum Principle in quick succession early on in the book in an attempt to prepare readers for the development of the Cauchy integral theory Classroom tested for 10+ years by the author at the University of Scranton as well as colleagues at Rose-Hulman Institute of Technology and Adams State College Presents sequences and series early on, distinguishes complex analysis from real analysis and calculus, and emphasizes geometry when analyzing complex functions Contains appendices for basic notation of sets and functions as well as necessary topics from advanced calculus, such as Leibnitz's Rule and Fubini's Theorem An Instructor's Manual containing all solutions is available via request to the Publisher. Written with a reader-friendly approach and provides a wide range of exercises and numerous figures throughout, allowing readers to gain intuition for solving problems.

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