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A Student's Guide to Maxwell's Equations [Paperback]

Daniel Fleisch
4.8 out of 5 stars  See all reviews (111 customer reviews)

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Book Description

January 28, 2008 0521701473 978-0521701471 1
Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

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A Student's Guide to Maxwell's Equations + A Student's Guide to Vectors and Tensors + Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
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Editorial Reviews


'Professor Fleisch is a great scientific communicator.'

'... good examples and problems are given so the student can practice the skills being taught.' IEEE Microwave Magazine

'... its virtue ... is to address, through judicious selection of material and masterful repetition of important facts, the needs of a student who finds lectures and textbooks hard to understand, too complex, and besides the point of doing the assigned problems. ... Students who are struggling with the material will love the Guide. The Guide is a well-written, concise, honest tool that delivers just what it promises.' American Journal of Physics

Book Description

Maxwell's equations are four of the most influential equations in science. In this book, each equation is the subject of an entire chapter, making it a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. Audio podcasts and solutions to the problems are available at

Product Details

  • Paperback: 142 pages
  • Publisher: Cambridge University Press; 1 edition (January 28, 2008)
  • Language: English
  • ISBN-10: 0521701473
  • ISBN-13: 978-0521701471
  • Product Dimensions: 8.9 x 5.9 x 0.3 inches
  • Shipping Weight: 8.5 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (111 customer reviews)
  • Amazon Best Sellers Rank: #25,212 in Books (See Top 100 in Books)

More About the Author

Dan Fleisch is a Professor in the Department of Physics at Wittenberg University, where he specializes in electromagnetics and space physics. He is the author of A Student's Guide to Maxwell's Equations published by Cambridge University Press in 2008, and is co-author with the late Prof. John Kraus of The Ohio State University of the McGraw-Hill textbook Electromagnetics with Applications. His most recent book, A Student's Guide to Vectors and Tensors, was published by Cambridge University Press in 2011. Prof. Fleisch has published articles in the IEEE Transactions, the Journal of Atmospheric and Terrestrial Physics, and Microwave Journal. He has presented more than a dozen professional papers on topics related to high-speed microwave instrumentation and radar cross-section measurement. He has been a regular contributor of science commentary to PBS station WYSO of Yellow Springs and appears in the public-television documentary The Dayton Codebreakers. Prof. Fleisch was named Outstanding Faculty Member at the Wittenberg Greek scholarship awards in 2000, and in 2002 he won the Omicron Delta Kappa award for Excellence in Teaching. In 2003 and 2005 he was recognized for Faculty Excellence and Innovation by the Southwestern Ohio Council for Higher Education (SOCHE), and in 2004 he received Wittenberg's Distinguished Teaching Award, the university's highest faculty award. In November 2010, Fleisch was named the Ohio Professor of the Year by the Council for the Advancement and Support of Education and the Carnegie Foundation. Fleisch received his B.S. in Physics from Georgetown University and his M.S. and Ph.D. in Space Physics and Astronomy from Rice University.

Customer Reviews

Most Helpful Customer Reviews
196 of 198 people found the following review helpful
5.0 out of 5 stars See the Forest Through the Trees March 24, 2008
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.
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89 of 92 people found the following review helpful
5.0 out of 5 stars Epiphany of clarity! March 2, 2008
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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47 of 48 people found the following review helpful
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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25 of 25 people found the following review helpful
4.0 out of 5 stars Read this book before that first EM class August 18, 2008
Format:Paperback|Verified Purchase
The first class in Electricity and Magnetism is often difficult for undergraduates. The course material brings together diverse concepts in Physics and Mathematics in a way that can challenge some students. This book is a useful primer for undergraduates. The book focuses on the mechanics of applying the four equations attributed to Maxwell. There is little or no discussion of the engineering or physics involved in applying these equations. The author presents each equation in a separate chapter and shows the different forms, e.g. integral, differential, in which they are written. The step by step identification of each and every term and operation can get boring but it provides a good explanation for the new student. It is a quick read and can be a useful reference during a class. The problems at the end of each chapter are good ones and I particularly liked the approach of providing solutions to all problems on a website.
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Most Recent Customer Reviews
5.0 out of 5 stars Green's Flux oozing along the Gradient
This is a pretty good book. I managed pretty well in my calculus 3 class however sometimes I had difficulty visualizing what I was doing. Read more
Published 1 day ago by James R. Elliott
5.0 out of 5 stars Five Stars
Excellent, concise, and good practice exercises.
Published 8 days ago by Craig Chamberlin
4.0 out of 5 stars Good book but...
Good book but it's like tiny, i'd like it to be a little bigger, with more information about everything (personal opinion), but in the other hand it's just what is supposed to be... Read more
Published 17 days ago by Gerardo
5.0 out of 5 stars Perfect format for self learners. As a pedagogue he has it absolutely...
The author Daniel Fleisch is to be congratulated for this wonderful book. It is perfect for both students and self learners. There are nice exercises at the end of each chapter. Read more
Published 17 days ago by Leeber Cohen
5.0 out of 5 stars Maxwell's equations plus
line integrals, curls, divergence, gradients, etc. You will need at least a BS Physics degree to fully understand and apprreciate this book.
Published 1 month ago by Gary
5.0 out of 5 stars Great Book.
I read it, and made the problema in two weeks, because I need it to review the basis before the Electrodynamics Theory, I found the book, very well organized, the use of the... Read more
Published 1 month ago by Christian Jimenez
5.0 out of 5 stars Nice breakdown
A well thought out text and worth the price.
Get your geek on and buy this book.

Probably should be in the library of any maker or tinkerer.
Published 1 month ago by Mooki
5.0 out of 5 stars Excellent summary
This book is an extremely well done summary of Maxwell's equations. I would highly recommend it as a supplement to a physics or engineering course in electromagnetics or simply... Read more
Published 3 months ago by D. Knapp
5.0 out of 5 stars Electricty and Magnetism Science, Maxwell's Equations by Daniel...
This book is only for someone looking for a thourgh grounding in Maxwell's Equations and an understanding of electric and magnetic force fields. Read more
Published 3 months ago by Joseph B. Ennis
5.0 out of 5 stars The Smallest Book with the Highest Concepts !!!
This book it is an excellent refresher course for the seasoned engineers that need a fast refresher course in advanced calculus and how it applies to everyday design challenges. Read more
Published 4 months ago by Ricardo Rabinovich
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