The Princeton Lectures in Analysis is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M. Stein and Shakarchi wrote the books based on a sequence of intensive undergraduate courses Stein began teaching in the spring of at Princeton University. At the time Stein was a mathematics professor at Princeton and Shakarchi was a graduate student in mathematics. Though Shakarchi graduated in , the collaboration continued until the final volume was published in The series emphasizes the unity among the branches of analysis and the applicability of analysis to other areas of mathematics.
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Every once in a while, I am struck by how often mathematics textbooks sound just like each other. There are honorable exceptions of course, and I'm always glad to see one, because they indicate that at least some mathematicians are still actively thinking about what should be taught, in what order, and how. Stein and Rami Shakarchi. The series wants to serve as an integrated introduction to "the core areas in analysis.
The basic pre-requisite for the series seems to be a standard undergraduate introduction to analysis covering the basic theory of convergence, derivatives, and the Riemann integral. Some basic familiarity with the complex numbers and elementary functions e. So the book is aimed at graduate students and maybe advanced undergraduates. The new series begins with Fourier analysis because the authors feel that this subject plays a central role in modern analysis and because it has played an important historical role.
It is also much more concrete than abstract measure theory or functional analysis. Finally, the authors plan to use results from volume one in the following volumes, emphasizing that analysis is a coherent whole rather than a collection of disjointed topics. The first book covers the basic theory of Fourier series, Fourier transforms in one and more dimensions, and finite Fourier analysis.
The last topic allows the authors to present, as an application, the proof of Dirichlet's theorem on primes in arithmetic progressions. The result would make a great book for independent study courses with advanced undergraduates, and, I think, would also be useful for graduate courses.
It's definitely worth a look. Fernando Q. Skip to main content. Search form Search. Login Join Give Shops.
Halmos - Lester R. Ford Awards Merten M. Elias M. Publication Date:. Number of Pages:. Foreword vii Preface xi Chapter 1. The Genesis of Fourier Analysis 1 Chapter 2. Basic Properties of Fourier Series 29 Chapter 3.
Convergence of Fourier Series 69 Chapter 4. Some Applications of Fourier Series Chapter 5. The Fourier Transform on R Chapter 6. The Fourier Transform on R d Chapter 7. Finite Fourier Analysis Chapter 8. Real Analysis. Log in to post comments.
Fourier Analysis : An Introduction
Many of our ebooks are available through library electronic resources including these platforms:. This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties.
Fourier Analysis: An Introduction / Edition 1
Fourier Analysis: An Introduction