Here, We provided Complex Analysis Hand Written Note By S K Rathore. The complex analysis may be a cornerstone of mathematics, making it an important element of any area of study in graduate mathematics. The first two chapters constitute a reasonably rapid, but comprehensive course in complex analysis. The third chapter is dedicated to the study of harmonic functions on the disk and therefore the half-plane, with a stress on the Dirichlet problem.
Starting with the fourth chapter, the idea of Riemann surfaces is developed in some detail and with complete rigor. From the start, the geometric aspects are emphasized and classical topics like elliptic functions and elliptic integrals are presented as illustrations of the abstract theory.
The special role of compact Riemann surfaces is explained, and their reference to algebraic equations is established. The book concludes with three chapters dedicated to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and therefore the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. Complex Analysis Hand Written Note By S K Rathore.
This text is meant as a reasonably detailed, yet fast-paced intermediate introduction to those parts of the idea of 1 complex variable that appear most useful in other areas of mathematics, including geometric pure mathematics, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve for instance concepts and concepts, and therefore the many problems at the top of every chapter give the reader ample opportunity for practice and independent study.
We enter the intriguing world of complex analysis. From the primary theorems on, the elegance and sweep of the results are clear. The start line is that the simple idea of extending a function initially given for real values of the argument to at least one that’s defined when the argument is complex. From there, one proceeds to the most properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
BOOK INFO
BOOK NAME – COMPLEX ANALYSIS HAND WRITTEN NOTE
AUTHOR – S K RATHORE
SIZE – 6.3MB
PAGES – 250
With this background, the reader is prepared to find out a wealth of additional material connecting the topic with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and therefore the prime theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a topic with many ramifications, while striking a careful balance between conceptual insights and therefore the technical underpinnings of rigorous analysis, Complex Analysis is going to be
Some of the essential ideas from functional analysis also are included. This is the sole book to require this unique approach. The third edition includes a replacement chapter on differentiation. Proofs of theorems presented within the book are concise and complete and lots of challenging exercises appear at the top of every chapter. The book is arranged in order that each chapter builds upon the opposite, giving students a gradual understanding of the topic.
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