Book Review: A Student's Guide to Waves

Recently, I read the 'A Student's Guide to Waves' by Danel Fleisch (he has different student's guides, all very good, check it out), it is such a pleasant reading that I wish I have read it when I first studied waves. I recommend anyone wants to learn waves, or have already learned to go through this book (you will find it you go through it very fast). It is truly a student's guide and if in the future I will teach this subject, I am sure, this will be my class text ^)^

The very nice part of this book is that it explains everything in plain English. All the concepts and equations are explained like reading a story that you just want to follow with the author to understand deeper. Besides, the book is only ~200 pages, and each section is short, makes it a book that you can read anywhere (I actually read this book mostly on the flight or on Bart). The author has very deep understanding of the subject that he gives a lot of the nice explanation that I never read from other books (I am a student in Seismology, I read many books talking about the mechanical waves, but most of the time, I finish the book with more confused view about waves, it took me long time to understand it).

This book starts with the fundamentals of waves, concepts like the wavenumber, complex numbers, Euler relations, wavefunctions, etc. are introduced here. These are basics for learning more of the waves. The author did very nice job showing how did these concepts come up, and accompany with the figures, these concepts become very clear.

Afterwards, the book talks about the wave equation. How the wave equation derived in a simple way, and why it is the 2nd partial derivative are all nicely explained it here. Also, there are many details in the equations that we often ignore but pointed out by the author which help us to understand better of the subject.

Later, the book gives the general solutions to the wave equation and the importance of the boundary conditions. After all these, the Fourier synthesis and Fourier analysis are discussed with the aids of many figures that you will find that the important Fourier synthesis and analysis are really simple and will store into your mind forever. It even talks about the 'uncertainty principle' between the time/frequency domain and the distance/wavenumber domain that dominant many analysis in practice.

The last part of the book deals with specific types of waves, i.e. mechanical wave equation, electromagnetic wave equation and the quantum wave equation. Armed with the concepts and equations you learned before, you will find how to apply them to specific types of waves in the real world to address some of the interesting problems. Even though I am a seismologist, and mostly interested in the mechanical waves, but I found the electromagnetic and quantum wave equations are also very interesting. I was so impressed by the way all the nature phenomenon links to wave equation in various forms.

Overal, it is a great short book that suitable for beginners or more advanced researchers.