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155 of 156 people found the following review helpful:
5.0 out of 5 stars
See the Forest Through the Trees, March 24, 2008
This review is from: A Student's Guide to Maxwell's Equations (Paperback)
This is the best overview of Maxwell's equations I have ever come across. I cannot praise it enough for it's brilliant clarity.
If you have taken or are taking an electromagnetism or vector calculus course, you may have run into the classic problem of not being able to see the forest through the trees. These courses can be very dense, and anything that can help give a sense of perspective can be very helpful. Daniel Fleisch's book is just such a tool. It provides a thorough overview of Maxwell's equations with stunning clarity. Each equation is broken down into it's component parts, and the physical significance of each part is thoroughly explained. In this way, not only are the core concepts of Maxwell's equations made clear, but many concepts from vector calculus are also brought out in crystal clarity, (I got much more out of this book than I did the often recommended "Div, Grad, Curl"). It will help you see the "forest through the trees".
Also of note are the problem sets at the end of each chapter. The problems work very well to reinforce the concepts from each chapter. They are not overly difficult or too simplistic. They are geared specifically at reinforcing concepts. The author has also posted on his web site a set of solutions for every problem, and each of the problems is thoroughly worked out with clear explanations. This is a HUGE plus for anyone picking up this book for self-study.
In my mind this book is a perfect compliment to an electromagnetism or a vector calculus class (or as a review after having taken such a class). Although the writing is clear enough that one could probably get a lot even without having had a vector calculus class, ideally one would have had at least some minimal exposure to vector calculus. It's not that you need to be an expert in vector calculus; all the concepts are explained very well in the book and the actual calculus you need for solving the problems is minimal, but in my mind the book will work best for those with some exposure to vector calculus.
My only suggestion to the author would be to include a table summarizing Maxwell's equations, (and perhaps a table of some basic constants). Other than that, this is a perfect book. It is THE standard by which other self-study books ought to be compared.
Update: When I wrote the above review I was half way through chapter 4 (of five chapters). Having completed the book, I do want to point out that the beginning of chapter 5 ('From Maxwell's Equations to the Wave Equation) does include a summary of Maxwell's equations. It would have been nice to have such a table at the front or back of the book for quick reference, but the summary is there, contrary to what I had originally thought. Chapter five also has a nice summary of the del operator and its use in finding the gradient, divergence, and curl. And finally, chapter five provides a very good physical description of the Divergence Theorem and Stokes' Theorem. So all in all, there is really little one can fault in this book. It's the book to get if you want to see the forest through the trees.
[Side note to author (written before the above update, and answered by the author in the comments): I believe the solution to problem 2.3 for surfaces 'A' and 'B' should include a factor of 1/2 since the area is a triangle; I did not see a feedback form on the website, or I would have posted there.]
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68 of 71 people found the following review helpful:
5.0 out of 5 stars
Epiphany of clarity!, March 2, 2008
This review is from: A Student's Guide to Maxwell's Equations (Paperback)
Maxwell's equations represent a comprehensive and descriptive condensation of (once believed to be disparate) electromagnetic phenomena, into a gloriously concise set of self-consistent (albeit arcane) mathematical statements. Daniel Fleisch has lucidly crafted explanations both of Maxwell's equations that describe EM phenomena, while simultaneously employing the latter to motivate, justify, and describe the vector calculus of the former with great clarity--the perfect synthesis. The author addresses chapters to each of the four equations in turn: (1) Gauss's law for electric fields, (2) Gauss's law for magnetic fields, (3) Faraday's law, and (4) the Ampere-Maxwell law; describing each first in its integral then differential forms, with brief expansion of the utilities for each form. The final chapter concludes elaborating the true nature of light as part of the greater EM spectrum, culminating in motivation of the wave equation and determination of c, the speed of light. I wish I had a shelf full of similar pithy, fun-reading, and revelatory books on other like topics!
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19 of 19 people found the following review helpful:
5.0 out of 5 stars
Everthing you wanted to know about Maxwell's equation but were afraid to ask!, June 28, 2008
Like most practicing engineers, my understanding of EM is based more on experience rather than rigorous mathematical theory.
I'm sure many of us can remember being exposed to vector calculus as applied to EM as undergraduates, but regarding it as an academic hurdle to be overcome, rather than something that might actually be useful later in a professional career.
The situation is worsened latterly by the evolution of EM modeling tools, which do all the donkey work for you - further reducing the requirement for a sound understanding of Maxwell.
But one day, you run into a problem that needs a bit more than the stock solutions - what now ? You rush to your text books, and you than discover that you have forgotten everything from your college days, and without your friendly old professor on hand, everything looks like gobbledegook !
I always been amazed that such an important subject is always presented so poorly, even in well regarded text books. In my opinion, a book should convey understanding - not just regurgitate facts.
Fleisch does an excellent job of conveying the concepts of div,grad and curl. The influence of the late Prof Kraus is clearly evident in his style (ref Electomagnetics, Kraus). Fleisch uses analogy to help the reader get an intuitive feel for the problem before diving into the maths. Personally, I fully endorse this approach - Fleisch is also diligent enough to highlight the limits of the analogous approach, which should keep the purists happy.
My only minor criticism of this book has already been stated by another reviewer, a tabular summary of equations covered in each chapter would be helpful. Also having the word 'student' in the title means I have to keep it stowed in my draw when not in use to avoid embarrassment ;)
So just own up - you're just like me - you never really understood Maxwell, and have been afraid to ask ! Get this book and sort your EM life out.
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