<< 1 >>
Rating: 
Summary: Not application oriented
Review: I am working on my research which involves applications of Fourier transforms. I spent the whole weekend reading the first five chapters of the book and briefly looking at the exercises, hoping to get a general picture of Fourier analysis and its applications. While theories are actually well presented, I didn't find interesting applications. The book does talk about "applications", like the area enclosed by a simple curve is maximized when the curve is a circle, or that you can find a continuous but nowhere differentiable function using fourier analysis, and other examples in NUMBER THEORY. This kind of applications may be interesting to mathematics students (I was), but obviously not to engineers (I am now). Plus, a lot of nice results are actually placed in the exerciese. I would have missed those if I didn't look at the exercises. So this might be a good text book for mathematics students (if they really do all exercises), it is obviously not for those who are interested in computations and applications.
Rating: 
Summary: Challenging
Review: 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.
Rating:
Summary: Challenging
Review: 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.
Rating: 
Summary: Excellent, if you've got some experience in analysis
Review: 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...).
<< 1 >>
| 
