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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!