A Student's Guide to Maxwell's Equations

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1. laiudmJan 2024
   Years ago I completed a post-graduate degree in physics, and although I had studied Maxwell's equations, I didn't have a good "feel" for them.

   I recently read "A Student's Guide to Maxwell's Equations", and it was perfect for me - it explained enough of the maths to understand the equations, without having to first learn differential geometry. https://www.cambridge.org/highereducation/books/a-students-g...

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2. photon_linesMay 2022
   Great introductory books along with videos:

     - Mathematics and Its History (John Stillwell)
     - Journey through Genius: The Great Theorems of Mathematics (William Dunham)
     - Proofs Without Words: Exercises in Visual Thinking (Roger B. Nelsen)
     - The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (William Dunham)
     - Odds & Ends: Introducing Probability & Decision with a Visual Emphasis (Jonathan Weisberg)
     - Introduction to Probability (Joseph K. Blitzstein, Jessica Hwang)
     - The Secret Life of Equations: The 50 Greatest Equations and How They Work (Richard Cochrane)
     - Euler's Gem: The Polyhedron Formula and the Birth of Topology (David S. Richeson)
     - 3Blue1Brown Essence of Linear Algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab 
     - 3Blue1Brown Differential Equations: https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6 
     - Dynamics: The Geometry of Behavior (Ralph Abraham, Christopher Shaw)
     - Geometry, Relativity and the Fourth Dimension (Rudolf Rucker)
     - 3Blue1Brown Essence of Calculus: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr 
     - Calculus for the Practical Man (J.E. Thompson)
     - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Harry M. Schey)
     - Who Is Fourier? a Mathematical Adventure
     - Physics, Topology, Logic and Computation: A Rosetta Stone (John C. Baez, Mike Stay)
     - An Illustrated Guide to Relativity (Tatsu Takeuchi)
     - The Mathematics Of Quantum Mechanics (Martin Laforest)
     - A Student's Guide to Maxwell's Equations (Daniel Fleisch) or if you're also interested in a visual guide, I wrote one as well: https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations 
     - Introduction to Elementary Particles (David J. Griffiths)
     - An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Brendan Fong, David I Spivak)
     - Solving Mathematical Problems: A Personal Perspective (Terence Tao)

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3. thothFeb 2016
   When I was an undergrad and graduate EE student, the "go to" book to help with electromagnetics was Div, Grad, Curl, and all that (http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161). Back in my era it was the 1st edition of the book, not the 4th.

   I see another book with good recommendations, A Student's Guide to Maxwell's Equations (http://www.amazon.com/Students-Guide-Maxwells-Equations/dp/0...) but I have not read that one.

   Div, Grad, Curl helped a bit, but what really made it click for me was an excellent professor some other EE math-class-in-disguise that explained those vector calc operations in terms of divergence (source density) and flux (change in time/space).

   As far as understanding the linked paper, I can't follow the proof either. Equations 1-4 I've never seen, 5-8 are Maxwell's Equations which are familiar but we wrote them with different notation, 9-18 are again equations I've never seen. The meat of the proof in 19-21 is built on 14 mystery equations and 4 that I recognize.

   As a former EE I guess we didn't prove equations as much as take their existence as given and then figured out what that implied for the real world. ;) Other posters aroberge and wraithm have mentioned also needing QM from physics to follow the proof, which must be where the other equations are from!

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4. markus2012Feb 2016
   I've always felt that if I had done all of my calculus with Mathematica I would have left college with an excellent grasp on how to use higher level functions provided by Mathematica that would have largely abstracted away all of this.

   Of course, the higher level functions might get covered in cobwebs - but I suspect not the same way; I would have kept these higher level skills up to date because:

   - I recently went though a couple of books on Bayes and computer vision. I would have used Mathematica - refreshing my memory. - I sometimes need to do some stats / analysis - Refresh... - I recently picked up a Student's guide to Maxwell's equations - Refresh... - I need to help my children with Calculus...

   If I had been using a high level tool my whole life I think I actually would make use of calculus and other mathematics.

   I'm curious if anyone else feels the same.

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