Complex Analysis
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€104.99
A01=Elias M. Stein
A01=Rami Shakarchi
Absolute value
Addition
Airy function
Analytic continuation
Analytic function
Arithmetic progression
Asymptote
Asymptotic formula
Author_Elias M. Stein
Author_Rami Shakarchi
Automorphism
Bessel function
Big O notation
Category=PBKD
Cauchy's integral formula
Cauchy's theorem (geometry)
Cauchy's theorem (group theory)
Change of variables
Compact space
Complex analysis
Complex number
Complex plane
Conformal map
Continuous function (set theory)
Coprime integers
Corollary
Curve
Derivative
Differentiable function
Eisenstein series
Elliptic function
Entire function
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Euler's formula
Existential quantification
Factorization
Fourier series
Fourier transform
Function (mathematics)
Functional equation
Gamma function
Harmonic function
Holomorphic function
Integer
Jordan curve theorem
Laplace's method
Lecture
Logarithm
Mathematics
Maximum modulus principle
Mean value theorem
Meromorphic function
Methods of contour integration
Natural number
Parametrization
Poisson kernel
Poisson summation formula
Polynomial
Power series
Prime number
Prime number theorem
Principal branch
Real number
Rectangle
Riemann zeta function
Series (mathematics)
Sign (mathematics)
Simply connected space
Special case
Summation
Theorem
Uniform convergence
Upper half-plane
Product details
- ISBN 9780691113852
- Weight: 709g
- Dimensions: 152 x 235mm
- Publication Date: 27 Apr 2003
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.
