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delyra j complex calculus physics eng vol 1 sol man 2019

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Textbook in PDF format 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. Number, the Language of Science The Simplicity of Complex Numbers Elementary Functions, but Not Quite Even Less Elementary Functions Geometrical Aspects of the Functions Border Effects in Capacitors Complex Calculus I: Differentiation Complex Calculus II: Integration Complex Derivatives and Integrals Complex Inequalities and Series Series, Limits and Convergence Representation of Functions by Series Convergence Criteria and Proofs Laurent Series and Residues Calculation of Integrals by Residues Residues on Riemann Surfaces

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DeLyra J. Solutions for Complex Calculus...Vol 1. 2019.pdf 3.4 MB
DeLyra J. Complex Calculus...for Physics and Engineering Vol 1. 2019.pdf 3.8 MB

Details for: DeLyra J. Complex Calculus...Physics and Eng.Vol 1.+Sol.Man 2019

delyra j complex calculus physics eng vol 1 sol man 2019

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