Complex Calculus Mathematical Methods For Physics And Engineering
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Complex Calculus: Mathematical Methods for Physics and Engineering -
There is a longstanding conflict between extension and depth in the teaching of mathematics to physics students. This text intends to present an approach that tries to track what could be called the ``middle way'' in this conflict. It is the result of several years of experience of the author teaching the mathematical physics courses at the Physics Institute of the University of São Paulo. The text is organized in the form of relatively short chapters, each appropriate for exposition in one lecture. Each chapter includes a list of proposed problems, which have varied levels of difficulty, including practice problems, problems that complete and extend the material presented in the text, and some longer and more difficult problems, which are presented as challenges to the students. There are complete solutions available, detailed and commented, to all the problems proposed, which are presented in separate volumes. This volume is dedicated to the complex calculus. This is a more practical and less abstract version of complex analysis and of the study of analytic functions. This does not mean that there are no proofs in the text, since all the fundamental theorems are proved with a good level of rigor. The text starts from the very beginning, with the definition of complex numbers, and proceeds up to the study of integrals on the complex plane and on Riemann surfaces. The facts and theorems established here will be used routinely in all the subsequent volumes of this series of books. The development is based on an analogy with vector fields and with electrostatics, emphasizing interpretations and proofs that have a geometrical character. The approach is algorithmic and emphasizes the representation of functions by series, with detailed discussion of the convergence issues.
Mathematical Methods in Physics and Engineering
Author: John W. Dettman
language: en
Publisher: Courier Corporation
Release Date: 2013-01-23
Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For this second revised edition, Professor Dettman included a new section on generalized functions to help explain the use of the Dirac delta function in connection with Green's functions. In addition, a new approach to series solutions of ordinary differential equations has made the treatment independent of complex variable theory. This means that the first six chapters can be grasped without prior knowledge of complex variables. However, since Chapter 8 depends heavily on analytic functions of a complex variable, a new Chapter 7 on analytic function theory has been written.
Mathematical Methods for Optical Physics and Engineering
Author: Gregory J. Gbur
language: en
Publisher: Cambridge University Press
Release Date: 2011-01-06
The first textbook on mathematical methods focusing on techniques for optical science and engineering, this text is ideal for upper division undergraduate and graduate students in optical physics. Containing detailed sections on the basic theory, the textbook places strong emphasis on connecting the abstract mathematical concepts to the optical systems to which they are applied. It covers many topics which usually only appear in more specialized books, such as Zernike polynomials, wavelet and fractional Fourier transforms, vector spherical harmonics, the z-transform, and the angular spectrum representation. Most chapters end by showing how the techniques covered can be used to solve an optical problem. Essay problems based on research publications and numerous exercises help to further strengthen the connection between the theory and its applications.