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Basic Complex Analysis - A Comprehensive Course in Analysis, Part 2A (Hardcover)
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Basic Complex Analysis - A Comprehensive Course in Analysis, Part 2A (Hardcover)
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A Comprehensive Course in Analysis by Poincare Prize winner Barry
Simon is a five-volume set that can serve as a graduate-level
analysis textbook with a lot of additional bonus information,
including hundreds of problems and numerous notes that extend the
text and provide important historical background. Depth and breadth
of exposition make this set a valuable reference source for almost
all areas of classical analysis. Part 2A is devoted to basic
complex analysis. It interweaves three analytic threads associated
with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view
focuses on the differential and integral calculus of functions of a
complex variable, with the key topics being the Cauchy integral
formula and contour integration. For Riemann, the geometry of the
complex plane is central, with key topics being fractional linear
transformations and conformal mapping. For Weierstrass, the power
series is king, with key topics being spaces of analytic functions,
the product formulas of Weierstrass and Hadamard, and the
Weierstrass theory of elliptic functions. Subjects in this volume
that are often missing in other texts include the Cauchy integral
theorem when the contour is the boundary of a Jordan region,
continued fractions, two proofs of the big Picard theorem, the
uniformization theorem, Ahlfors's function, the sheaf of analytic
germs, and Jacobi, as well as Weierstrass, elliptic functions.
General
Imprint: |
American Mathematical Society
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Country of origin: |
United States |
Release date: |
December 2015 |
Authors: |
Barry Simon
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Dimensions: |
254 x 178 x 38mm (L x W x T) |
Format: |
Hardcover
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Pages: |
641 |
ISBN-13: |
978-1-4704-1100-8 |
Categories: |
Books
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LSN: |
1-4704-1100-8 |
Barcode: |
9781470411008 |
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