Title: Complex Variables Demystified Author(s): David McMahon Pages: 275 Publisher: McGraw-Hill Professional; 1 edition Publication date: 2008 Language: English Format: PDF ISBN-10: 007154920X ISBN-13: Description: Take the complication out of COMPLEX VARIABLES
Ready to learn the fundamentals of complex variables but can't seem to get your brain to function on the right level? No problem! Add Complex Variables Demystified to the equation and you'll exponentially increase your chances of understanding this fascinating subject.
Written in an easy-to-follow format, this book begins by covering complex numbers, functions, limits, and continuity, and the Cauchy-Riemann equations. You'll delve into sequences, Laurent series, complex integration, and residue theory. Then it's on to conformal mapping, transformations, and boundary value problems. Hundreds of examples and worked equations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
This fast and easy guide offers:
* Numerous figures to illustrate key concepts
* Sample problems with worked solutions
* Coverage of Cauchy-Riemann equations and the Laplace transform
* Chapters on the Schwarz-Christoffel transformation and the gamma and zeta functions
* A time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for an advanced student, Complex Variables Demystified is your integral tool for understanding this essential mathematics topic.
Complex variables, and its more advanced version, complex analysis, is one of the most fascinating areas in pure and applied mathematics. It all started when mathematicians were mystified by equations that could only be solved if you could take the square roots of negative numbers. This seemed bizarre, and back then nobody could imagine that something as strange as this could have any application in the real world. Thus the term imaginary number was born and the area seemed so odd it became known as complex.
These terms have stuck around even though the theory of complex variables has found a home as a fundamental part of mathematics and has a wide range of physical applications. In mathematics, it turns out that complex variables are actually an extension of the real variables.
A student planning on becoming a professional pure or applied mathematician should definitely have a thorough grasp of complex analysis.
Perhaps the most surprising thing about complex variables is the wide range of applications it touches in physics and engineering. In many of these applications, complex variables proves to be a useful tool. For example, because of Euler's identity, a formula we use over and over again in this book, electromagnetic fields are easier to deal with using complex variables.
Other areas where complex variables plays a role include fluid dynamics, the study of temperature, electrostatics, and in the evaluation of many real integrals of functions of a real variable.
In quantum theory, we meet the most surprising revelation about complex variables. It turns out they are not so imaginary at all. Instead, they appear to be as "real" as real numbers and even play a fundamental role in the working of physical systems at the microscopic level.
About the Author
David McMahon has worked for several years asa physicist and researcher at Sandia National Laboratories. He is the author of Linear Algebra Demystified, Quantum Mechanics Demystified, Relativity Demystified, and MATLAB Demystified, among other successful titles.
Title: Complex Variables Demystified