A Student's Guide to Waves

'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.

Another great book by Daniel Fleisch!This short book Introducing waves consists of 6 chapters:Chapter 1 Wave Fundamentals- A nice presentation of the basic fundamentals you might expect from a high school physics/first year college course. Also includes complex numbers, Euler's relation, and basic periodic wave functions for forward and backward moving waves. The chapter ends with a description of phasors which do not appear again anywhere later in the book.Chapter 2 The Classical Wave Equation- This famous linear, 2nd order partial differential equation relating the wave function to its direction of propagation and time is shown nicely derived in a couple different ways. Its properties are nicely explained also. A couple other equations somewhat similar to the wave equation but less interesting (to me anyway) are also discussed, the exception being a nice comparison with the world famous Schrodinger Equation.Chapter 3 Wave Components- General solutions to the wave equation are nicely derived. Boundary conditions are discussed with examples. Fourier Synthesis theory is also discussed in quite a lot of detail which caused me to get lost at some points.The last 3 chapters each deal with specific types of waves. Each is a "stand alone" chapter where one does not depend on another so they can be done in any order. I omitted Chapter 4 which dealt with Mechanical Waves since it didn't appeal to me (Sorry if I offend any Mechanical Engineers!).I loved Chapter 5 which dealt with Electromagnetic Waves. Maxwell's Equations are the main topic, of course. Dr. Fleisch deals with them very clearly but in their differential form only. The electromagnetic wave is highlighted along with solutions to the electromagnetic form of the Wave Equation. Diagrams are very very nice! The chapter ends with a very nice section dealing with electric and magnetic field energy densities, power formulas, and the Poynting Vector.Chapter 6 deals with the Quantum Wave Equation. Matter waves are discussed and the time independent and time dependent Schrodinger equations are introduced. Probability density and the method for normalizing wave functions is briefly explained along with quantum wave packets.As in Fleish's other books, solutions to all the problems at the end of the chapters can be found on-line if you get stuck... a very nice feature if you're doing self-study!All in all, a nice book to add to Fleisch's other Student Guides.

This short book is an excellent course supplement for undergraduate students of engineering and physics. This guide includes some of the elementary material that is often left out of textbooks. The first part of the book covers basic mathematical concepts up through partial differential equations. The remainder of the book provides examples of the wave equation in different fields such as electromagnetics and quantum physics. This is not a detailed treatment of waves and the wave equation but it is a good summary of the subject. I particularly liked the general approach to the subject that illustrates how mathematics can be applied to different topics in physics and engineering.

Very good coverage and descriptions of the mathematics of the wave equation. If you are a student trying to understand or a teacher trying to remember what was so troubling, this is well worth the price. Excellent descriptions of and comparison with various PDE'S related to the wave equation give you the intuition to see what's so special and what the different features that matter really are. Comparisons are carefully selected to illustrate important features one by one, from PDE order to linearity vs. Nonlinear equations. Very good coverage of Euler relation in multiple ways to drive home the importance of this to analysis of waves makes Fourier theory and concepts like negative frequency pop with that ..."duh, what was so confusing?"...clarity. Must read for anyone learning waves and wave equations.