A First Course in Fourier Analysis 2nd Edition by David W. Kammler (PDF)

Description

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I don’t like this book’s treatment of Fourier analysis–it jumps right into applications, without developing the theory as logically as in a book directed to a mathematician audience–and that’s because it’s directed towards a “scientist”/engineer/physics audience. (I’m in physics, nonetheless, and I like mathematics.) It’s just a very idiosyncratic approach to the subject–it probably would work very well for a far more specific, specially offered course, but for a general course, not. I will be looking for another book.Example: T_p is not defined, as someone mentioned in a previous comment, which is bad math form–it is just that sort of book.It’s not really a terrible book–I hope someone else does actually find this book useful and like it–because it seems like it should be likable and enjoyable book, in another context (less formal/logically rigorous, more applications-focused setting, etc.).It was the required text for Univ. Maryland MATH 464–looks like they still use the text (looking at another UMD student’s comment from years back). Don’t know why…since the Norbert Wiener Center for Harmonic Analysis is here, one would think they’d use a better book on Fourier analysis!!

⭐I was very fortunate take Dr. Kammler’s class several year. This was toughest class I ever took and best. He covered entire book in a semester.

⭐Overblown and even absurd in places this is one to pass by.Try dover instead – loads of proven titles available at a fractionof the price.

⭐Great book. Have got a A+ with this in university.

⭐A better title for this book would be a Second Course in Fourier Analysis. It is an excellent book to use to widen your expertise in Fourier Analysis, but do not expect get much out of it as a first course. The book is a keeper and is worth a second or third read.I would give the book a 5 Star if answers are provided for the questions in each chapter, the book would then be a first class self-study reference, and help the student solidly expand his mathematical understanding.The book provides a more coherent treatment of Fourier Analysis than a first course, including good explanations to confusing topics in a first course, such as Fourier-Poisson Cube, Parseval and Plancherel Identites, Gibbs Phenomena, and Fourier Analysis with a rigid reference to the domain of interest (real and discrete, periodic and aperiodic).The book builds the topics very logically and sequentially, many statements given with lucid proofs, and there are numerous and consistent reference to earlier results and problems that serves to re-enforce learning.The author is more applications oriented and the book shows that, proving many interesting real life examples, and even the odd historical reference of the mathematical point of interest.The most important chapter in the book is Chapter 7 Generalized Functions. More than anything, expertise in this topic will expand your understanding of Fourier Analysis. The mathematical formalism using used to discuss generalized functions facilitates the understanding of partial differential equations. Excellent examples in pde chapter gives a concise and simple discussion in waves, diffusion and diffraction and reference to real world applications including quantum mechanics.As a bonus, the book gives excellent development of probability, music and wavelets.

⭐I used this book as part of a class at the University of Maryland. What I have discovered is that Kammler didn’t really write a very good book for a first course in Fourier analysis. I am a math/physics major and found the book to be very scattered for a FIRST course. For example, the first chapter just dumps a whole bunch of information without presenting much background or context. That being said, I do think the book contains a lot of valuable information and might be good for students already familiar with Fourier analysis (I should note that I was familiar with Fourier series and Fourier transforms prior to the class).

⭐I’m an electrical engineer, with a focus in signal processing. This is the book I learned Fourier analysis from, and once I did, the classes that EEs usually dread were relatively easy for me. This is the only textbook I actually read every chapter of (and we only covered the first half in the Fourier analysis course). Kammeler writes in a conversational style, which I like in a text, and goes through many practical examples in math, physics, and engineering. I appreciated the rigor devoted to generalized functions (Dirac deltas are almost always glossed over in engineering texts, and thus remain mysterious and sometimes non-sensical), yet Kammeler always keeps intuition close by so it’s relatively easy to follow if you’re not a mathematician. The parts I didn’t like were when Kammeler fell back on more elementary yet more complicated presentations to avoid introducing too many new concepts. For example, I think the FFT is most easily understood with Z-transforms and multirate systems, and that Fourier analysis in general is more easily understood in terms of Hilbert spaces. It’s hard to fault him for it though, because it’s primarily a math book and needs to be mostly self-contained. It’s also typeset in LaTeX, and looks beautiful.

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