Complex Analysis
Elias M. Stein & Rami Shakarchi

Elias M. Stein, Winner of the 2005 Stefan Bergman Prize, American Mathematical Society

Cloth | 2003 | $85.00 / £59.00 | ISBN: 9780691113852
392 pp. | 6 x 9 | 64 line illus.

eBook | 2009 | $85.00 | ISBN: 9781400831159

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Introduction [PDF] | Chapter 2 [PDF] | Chapter 10 [PDF]

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.

Table of Contents

This book has been translated into:

• Japanese

Other Princeton books by Elias M. Stein:

• Beijing Lectures in Harmonic Analysis. (AM-112).
• Fourier Analysis: An Introduction.
• Functional Analysis: Introduction to Further Topics in Analysis.
• Hardy Spaces on Homogeneous Groups. (MN-28).
• Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43).
• Introduction to Fourier Analysis on Euclidean Spaces (PMS-32).
• Real Analysis: Measure Theory, Integration, and Hilbert Spaces.
• Singular Integrals and Differentiability Properties of Functions (PMS-30).
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63).

Other Princeton books by Rami Shakarchi:

• Fourier Analysis: An Introduction.
• Functional Analysis: Introduction to Further Topics in Analysis.
• Real Analysis: Measure Theory, Integration, and Hilbert Spaces.

Subject Area:

• Mathematics

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