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Fourier Analysis : An Introduction(2003)  무료배송

 
지은이 : Elias M. Stein, Rami Shakarchi
출판사 : Princeton
판수 : 1 edition
페이지수 : 320 pages
ISBN : 069111384x
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 50,000원 ( 무료배송 )
적립금 : 1,500 Point
     

 
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. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. 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. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. 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 Fourier Analysis is the first, 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.
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 100
Chapter 5. The Fourier Transform on R 129
Chapter 6. The Fourier Transform on R d 175
Chapter 7. Finite Fourier Analysis 218
Chapter 8. Dirichlet's Theorem 241
Appendix: Integration 281
Notes and References 299
Bibliography 301
Symbol Glossary 305



"I have just finished a class with the book as its main textbook. The book is well written, but you honestly have to work through each page with pen and paper in hand filling in the omitted steps. Nothing is spoon-fed to you. The exercises are very challenging while the problems develop small theories. If you work through the pain and sweat through the exercises, you will at the end of the book greatly improve your skills and intuition.

The author Stein is a leader in his field and has provided plenty of depth and breadth. This also means that he is on a different level and an argument that he calls "simple" has quite often taken me two pages to justify. However, if you put in the effort it will pay off tenfold."


"I used this book for an undergraduate-level course in Fourier analysis. It is an excellent text, although I would recommend the prospective learner to take a basic course in real analysis first (or perhaps concurrently, if the learner dares!). With my experience in analysis, it proved very readable. In fact, it strengthened my understanding of (and even interest in!) analysis, as it provides a fruitful application of the subject--one gets to see various important analysis ideas and techniques used in context. One could almost say that the text is an excellent complement to real analysis to help the ideas jell. On the other hand, perhaps it is theoretically possible to use this book as a springboard into learning analysis. The proofs do gloss over some details, which as the previous reviewer noted, can make things tough going at times... I actually found this useful (again, perhaps because of analysis experience), as it omits just enough detail to stay focused on the subject at hand (being too pedantic is likely to make those of shorter attention spans, such as myself, want to wander away), and yet supplies enough detail to remind the reader of the underlying theory, and that all this stuff is mathematically rigorously justified.

The course I took was actually a brand-new course created at the undergraduate level, and was structured around the book, which had also just come out at the time. I can say with confidence that the course was a success, which is pretty unusual for something hot off the press (true, the book itself was based on lectures, but every university has its quirks...)."

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