A Student's Guide to Maxwell's Equations

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. There are on-line hints to solve each of the problems or you can look up the fully solved answer. If you are a student you should obviously try to solve the problems first without help and then resort to the hints and fully worked out problems. For more casual readers it is wonderful just to see the worked out problems. Each of the chapters is succinct and the writing very clear. The book is written at a undergraduate level. A few errors in the text appear to have been worked out with each successive printing. Please see the Cambridge website errata list. You will need the basics of vector and multidimensional calculus to easily follow the text. Some basic understanding of electricity and magnetism would also be helpful. I have not looked at the lectures on You-Tube but look forward to watching them. The same author has another text on vectors and tensors which I have just ordered. I would encourage him to write a similar style books on basic quantum mechanics and particle physics. Addendum:According to Amazon I first ordered this work in 2011. I decided to read it once again after ten years. It remains one of the best examples texts that are written for self learners. I would only add that review of basic trigonometry, vector calculus, spherical and cylindrical coordinate systems will make your study easier. This should include familiarity with flux, gradient, divergence, and curl. Some degree of comfort with Stoke's theorem and the divergence theorem is also helpful. If you have that foundation, Fleisch's Maxwell's Equations is a fast and beautiful read. The question is what do you do if your foundation was never built or needs to be refreshed. There are many workbooks. I have enjoyed Stroud's Engineering Mathematics and Advanced Engineering Mathematics. Their approach of step by step programed learning works well. However, I do wish that they had worked out solutions for the additional problems. My 1st edition of Schey's Divergence, Grad, Curl and all that is extremely well worn. I have not seen the newer editions. Hopefully they have more examples with fully worked out solutions. Someone should write a version for self learners with fully worked out solutions would be great. For self learners the Schaum 3000 solved problems series has lot of worked out examples. My copies of Precalculus, Calculus, and Physics have been extensively used. There are many other alternatives. Mathematical Methods in the Physical Sciences by Boas is widely used in colleges prior to advanced physics and engineering classes. Unfortunately it does not have worked out solutions for the problems. For a quick review of the the math and physics problems please see Chris McMullen's 100 Instructive Calculus-based Physics Examples. Volume 2 :Electricity and Magnetism. I have just started it. It looks well done and will write a review of it in the future.

Maxwell's equations are some of the most important things that you will learn if you are taking physics and/or working on an electrical engineering degree. They basically describe the concepts of electricity and magnetism, which apply to things like the power to our homes to semiconductor chips that are in every single device we own. Unfortunately, a lot of the textbooks (both physics and EM engineering textbooks) give them a bit of short shrift, giving a basic explanation and maybe deriving one or two of them, but do not give a good explanation of why they are useful and, thus, what they represent can be lost on students. This is a small book (about 130 pages) that covers all four equations, one per chapter. That breaks down what each equation represents, what the variables in the equation mean, and provides both the integral form of the equations and the differential form. I think the best way to use this guide is to supplement your textbook material so that when you get to the point in the textbook where one of the equations is discussed, use this to flesh out the theory behind the equations that your textbook may not cover (or cover in as much detail). To be clear, this is not something like "Maxwell's Equations for Dummies" or something like that, which assumes you have little to no background going in. You do need to have some understanding of calculus (if you have taken multivariable calculus, that will definitely help because there is a lot of discussion of surface integrals and vectors), and know some of the physics concepts you will learn before getting to the electricity and magnetism topics (which is covered in the second semester of physics). So, if you are taking calculus-based physics and/or have to take an electricity and magnetism class (electric and magnetic fields) as a part of an engineering program, this will be very useful. It is probably overkill for those who just have to take algebra-based physics because it will go way beyond what you will be exposed to in class or expected to learn.

I purchased this book on Maxwell's Equations for a peculiar reason. I have a t-shirt that lists the four Maxwell Equations that God purportedly used to create light. I wanted to be able to answer any technical questions I might get while wearing it. Humor aside, this book is truly 5-star. Both the integral and differential forms of Gauss's Laws of electricity and magnetism, Faraday's Law, and the Ampere-Maxwell Law are provided. The book is organized into separate sections for each equation. Within each section are detailed explanations of each variable, constant and mathematical operation. There are representative problems with solutions for calculating electric and magnetic fields for practical scientific or engineering application. There are also problems for you to test your understanding. If you want to have a fundamental understanding of electromagnetism this book is a great resource. It goes well beyond what you will find in introductory physics textbooks. After reading this book, I believe I am fully prepared to answer any technical question about Maxwell's Equations I might get wearing my t-shirt, even if I have to refer back to the book for reference. Excellent book for both undergraduate and graduate students and professional scientists and engineers. Also for those who just what to understand what's in the air around them.

A Student's Guide to Maxwell's Equations by D. Fleisch- focuses attention on the four Maxwell's equations in 130 pages. This book consists of five chapters, and the first four chapters deal with four Maxwell's equations, respectively. The final chapter is about inducing electric and magnetic wave equations from Maxwell's equations. In my opinion, the most appropriate audience of the book is undergraduate students who are studying or studied the freshmen-level of physics and calculus. To understand the book, readers should know, in advance, the Coulomb's law, electric field, capacitor, what a current is, etc. (Although they are explained, if you have not encountered them before, you may have difficulty in understanding the book). The Maxwell's equations are expressed in the language of vector calculus such as the vector fields, the divergence of a vector field, the curl of a vector field, the line integral of a vector field on a curve, and the surface integral of a vector field on a surface. So, a firm understanding of vector calculus is very helpful to understand Maxwell's equations. The virtue of the book is that it puts all its efforts into understanding the language of vector calculus in detail. Although there had been a great need for such books, only few were available. In the way of doing it, the author shows the physical meaning of divergence, curl, integrals of vector fields, not just giving mathematical explanations. That was also very helpful to me. I titled my book review as "Learning vector calculus via Maxwell's equations" in the hope that people who learned vector calculus but failed to have a unified picture would benefit from the book. In mathematics curriculum, even in physics, some professors spend much time in giving detailed proofs of theorems of vector calculus, for example, the Green's theorem, the divergence theorem, and the Stokes' theorem. But I think that this is not a wise choice. Like the book, it would be better that professors explain vector calculus using physical meaning, show how to apply them to concrete examples, and leave their proof to students. For students, it is sufficient to know that there are mathematical proofs for them. In the book, the differential version of Maxwell's equations appear. The Maxwell's equations that we generally know are in fact the integral version. Freshmen-level physics textbooks don't deal with the differential version. In the final chapter, it is shown that the two versions are equivalent by using the divergence theorem and the Stokes' theorem. Here, the readers should not think that there are mathematical proofs for them in the book. Proofs are unavailable there. To show that the two versions of Maxwell's equations are equivalent, it uses two equivalent definitions of the divergence (and the curl) without proof. But that's the point that we have to prove mathematically, that is, we have to show that the different-looking definitions are actually equivalent. But as I said, I think that we don't need to know the detailed proof for that. Just have a glance at the proof in a mathematical textbook. In the case of vector calculus, having a whole picture and easy understanding is more important than following a detailed proof. I pointed that, since we must know for sure what the logical structure is in a book even though we don't need the proofs right away. Here are some detailed points. 1. Suppose that there are some electric charges in space. Consider an imaginary sphere that does not contain any of the charges. By Gauss's law for electric fields, the flux of the electric field of the charges through the sphere is zero. Some teachers say that Gauss's law holds "because" any field line coming in must come out. But as we see in the definition of the flux of a field through a surface, we must consider the angles at which the field lines and the surface meet. So such an argument is wrong. It is the Gauss's law that makes the argument hold, and Gauss's law is an experimental fact or a physical principle that we should accept. I realized this while reading the book. Such kind of inaccuracy can also happen when people say about Gauss's law for magnetic fields. Some teachers might say that Gauss's law for magnetic fields holds because the magnetic charge always occur in pairs and so any field line coming out a surface must come in. By the same reason, this argument is wrong and we should accept Gauss's law for magnetic fields as an experimental fact. 2. Most electromagnetic theory textbooks, including the book, say that the four Maxwell's equations explain all electromagnetic phenomena. In my opinion, some precaution is needed. To say that, we should know what electric and magnetic fields are. And to know them, we should know what electric and magnetic forces are, in other words, how to measure them in a laboratory. I think that this point should be explained in more detail when authors say that Maxwell's equations explains all. 3. The book is excellent as a supplement, not as a main textbook, I think. Considering the amount of 130 pages, this is not a bad point. 4. The book is sloppy in some places. For example, in explaining the meaning of the integral of a vector field on a curve, the book says that a finite sum of some quantities is equal to what we want. But the finite sum cannot be equal to it! Only the limit of a sequence of finite sums is what we want. 5. The Appendix seems to be just a summary rather than something from which we can learn. 6. In the book, two Faraday's laws are introduced. One is the generally known, and the other is an alternative form. They are equivalent to each other. But the difference of the two in the physical sense is not so clear in the book. At least, not explained in an easy way. I had to make my own effort to understand it. In my opinion, the key to understand it lies in the question of what is the source of a current in a circuit with a battery. Does a current flow because the battery forms an electric field in the circuit or because the battery does work for that by EMF (electromotive force)? This confuses me. If you actually consider the charge distribution in a circuit, you will find the electric field cannot be confined in the wire. Then is it by the EMF? But EMF is also ultimately due to an electric force (ultimately, there are only four forces in Nature, gravitational, electromagnetic, weak and strong nuclear forces), so in the case also, we have to say that the battery forms an electric field in the circuit, and the electric field is the source of a current. I hope it comes clear to me someday.

One thing about the book is the kindness that author shows towards the students and teaches them step by step knowing that we may have a very low knowledge in subject. Another issue that makes me very upset is lack of any example and also how to measure and with what device in even a mental scenario. That doesn't exists and if I don't have even one practical question then I have more questions than answers. For practical , I have bought a plasma globe and tried to see if the value on the globe is correct by the equation but neither I know the volt/ meter of the center of the globe nor my voltmeter shows a constant volt on the surface. It reads 41 volt in AC then -2 volt in DC?! Taking in consideration the E value, permittivity constant is available on google of Pyrex glass but I am not sure if what I get is correct. How do we know if this formula is correct when we can't even calculate it!? We just have to have " faith" that others have done so , so accept it! That is more like religion not science. Reminds me of a wise guy who was once asked by a king to count the number of stars and get gold if correct, wise guy said " it is equal to the number of the hair of my donkey! If you don't believe it please go count it for your self!".

fantastic book ever written on this subject for students

I recently got a job where having more than a passing familiarity with electromagnetic theory is in my best interest. I was a physics major many years ago but had forgotten everything I ever knew about the subject. I started out by watching the Walter Lewin videos from MIT and working every odd electromagnetics problem in the Freshman electromagnetism text book, Serway (something like 200 problems). At this point I thought I really knew my stuff. So I moved on to a more advanced undergraduate text book hoping to once again work through the entire book then maybe move on to a graduate level text. That hit me like a brick wall. The jump in difficulty between freshman physics and advanced undergraduate physics is huge. After working a couple problems which neither seemed practical nor well written I gave up. Now, a few months later I bought this book. It really is an amazing book to bridge that gap. It is just so much better written and is really made for someone to teach themselves the subject. Many books are assuming a professor to fill in the blanks. This is particularly bad when the books don't give answers to problems. It is absolutely impossible to learn a subject without feedback. Problems without solutions are worthless. Unfortunately the answers for this book are not in the book, but the website is good enough that it makes up for it. By the end of every chapter I have had a much better understanding of the subject. I haven't got back to the more advanced textbooks though, so it remains to be seen if I need more to bring me up to where I need to be. If nothing else I know a lot more than when I bought the book though.

This is an outstanding short little book on Maxwell's equations and what they mean, both qualitatively and quantitatively. It is a good book to go through if you have just finished a course on EM, or you can use it as a supplement as you go through such a course. The explanations are clear and to the point and the examples and problem sets are excellent. To me the definitive self-study textbook on the subject is Engineering Electromagnetics by Nathan Ida. It explains everything, including the math, from the beginning. If you have an incomprehensible text and an incomprehensible professor, both these books will see you through. Also, note the MIT lectures of Professor Walter Lewin on electricity and magnetism in his Physics 8.02 class as posted on youtube. This student guide is so clear and coincides so well with what Prof. Lewin is teaching it almost seems like it was written by him. At any rate I can't recommend these three resources: Dr. Lewin, this student guide, and the big text by Nathan Ida strongly enough. Even if you think you're an engineer who just wants to code or design FPGA's the rest of your professional life, do realize that electricity does come back to these basics and you should understand it.

I dont know how many ways I can say, I loved this book sooo much. When I was simply trying to understand the Maxwell's equations, this book saved me. Guess what, this book would refresh concept even from the very basic vector dot product, cross product etc, so there is no chance that, the reader will find some concepts inaccessible. It covers what is divergence, what is gradient, what is Curl etc (even though, I would recommend the reader to get the concept of Divergence, Curl, Gradient cleared before reading this book; the reader can get those concepts from Khan Academy online). This book explained well 'what is path integral', 'what is surface integral', 'why there is a circle sign in the middle of a integral operator' etc. Anyway, I wont believe that, someone who understands calculus, wont understand maxwell's equations even after reading this very thin book with very less effort. The reader does not even need to be a master of calculus. If a partial derivative and Integral operator makes sense to the reader, he/she will find this book accessible. In the last chapter, (chapter 5), the author derived the Electromagnetic wave equations from maxwell's equation. That part was the most exciting part for me as I was simply waiting for learning that. If the reader knows that, a Wave Equation can be expressed in second order partial derivative form, then, this chapter will makes sense. This book did not explain where and how we got the Wave equation using second order partial derivative. I think, the author could explain that in a paragraph by writing few lines. As I was already familiar with wave equation, I did not have any problem understanding that part. Anyway, I find my every penny worth and I feel myself fortunate that I bought this book.

Die Maxwell'schen Gleichungen, stellen den Beginn einer neuen Physik dar.In diesem Werk werden in knapper Form die wesentliche Erkenntnisse der Maxwell'schen Theorie auf den Punkt gebracht und anhand einfacher einleuchtender Beispiele gezeigt, wie man sie anwendet. Wenn man die Mathematik kann, das ist allerdings die Voraussetzung, ist man in der Lage innerhalb eines Nachmittags dieses Werk zu verinnerlichen, und sich die wichtigsten Resultate der Klassischen Elektrodynamik ins Gedächtnis zurückzurufen und was man damit machen kann.

Great value, the book offers a clear explanation to all aspects of the maxwell equations at an affordable price! The book also gives some exercises and detailed answers at the end of all (sub)chapters. It might be a good idea to have some knowledge about vectors, vector fields and matrices. Thats probably the reason amazon recommended also buying a students guide to vectors and tensors. I have not read that book, so I am not sure if its a good recommendation to read before reading this book.

One of the best book i ever studied. He author nicely explain something which is not written in standard text book.

* Introduction [update Feb 2014] Its amazing feature being that its author encourages better mathematical and physics comprehension of these phenomena. But yet the whole book is still explained with enough undergraduate student fair rigour to not get in the way of its own ideas and concepts. * Design feature of the book The truly beautiful key part of the book being each of the Maxwell equation's is selected in turn, and within its own chapter is each equation components disassembled. This allows deeper, friendlier explanations at its component level. The matematical method includes the well known theory of calculus, and discussions of analysis. If your fine with both its an easier ride. Some of the descriptive work still requires comprehension of applied math technique's,from other sources. But if you study say the well - known 'Further Engineering Mathematics' (Stroud), this will encourage you to comprehension of these areas. * Summary The author of this book at this level makes it magnificently understandable, and shows clarity. Its explanations uses at least undergraduate engineering level rigor. I have been rereading this magnificent book again and it just gets better and better in explaining these topics. This book IS the way to go to start grasping electromagnetic phenomena with strong and logical examinations. If your in final year engineering and need some help in this arena, this IS the best I have read so far. I am sure this will sharpen your comprehension from an engineering and physics perspective of electromagnetic phenomena in any further studies you may attempt.