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Complex Numbers and Analytic Functions: Limits, Differentiation and Integration of Complex Variable Functions

Mathematics for Scientists & Engineers

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Description

This book is an expanded and improved version of lecture notes that became the basis for a didactic notebook entitled Introduction to Functions of Complex Variables, written for the Distance Mathematics Teaching Degree Program at the Federal Rural University of the Semi-Arid (UFERSA). The text is designed to provide an initial familiarization for mathematics and engineering students with the theory of complex functions and to serve as a textbook for an introductory semester course on the subject. All the presented theory possesses an elegant logical structure that, besides being prominent in pure mathematics, represents an indispensable tool for ap plied mathematicians, engineers, and physicists. A calculus course covering derivatives and integrals is a prerequisite for a smooth progression through the course. This book is divided into three parts. The first part deals with the theory of complex numbers, emphasizing the algebraic and geometric aspects of complex numbers, their representation in polar form, the use of De Moivre’s formula for calculating complex roots, and Euler’s relation. The second part presents functions of complex variables, including topics such as limits, continuity, and derivatives of these functions. Special empha sis is also given to the Cauchy–Riemann equations and elementary functions: exponential, trigonometric, hyperbolic, and logarithmic functions. The third part first presents the basic theory of complex function integration, highlighting the renowned Cauchy integral formula and the Cauchy-Goursat theorem and their implications, and a study of primitives of a complex function. Finally, important applications of the theory are presented. The book also contains a wide range of application examples and sections with solved exercises, which provide a collection of models for solving the proposed problems in each unit, for which we present complete answers at the end of each unit. Finally, after eachanswersection, wepresentappendicesthatbringcuriosities about complex numbers, conjectures involving prime and perfect numbers, and Fermat’s theorem.

Product Specifications

Format: paperback
ASIN: B0DXLD2QB7
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Applied Mathematics > Mathematics for Scientists & Engineers
Domain: Amazon UK
Release Date: 18 February 2025
Listed Since: 18 February 2025

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Complex Numbers and Analytic Functions: Limits, Differentiation and Integration of Complex Variable Functions

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