Classical Prerequisites for Jackson's Classical Electrodynamics

[askalot]

Hello,
I have already studied Griffith's book, Intro to Electrodynamics.
However when I try Jackson's book, I find it a bit hard for me.
My question is, what Maths and Physics texts (or specifically, chapters of texts) do you recommend, so that I would be best prepared for a graduate course in electrodynamics?
What should I know?
Thank you in advance,
askalot.

 

[Khashishi]

Purcell - Electricity and Magnetism is at a lower level and might help.
I don't have a recommendation for a multivariable calculus text or complex analysis text, but these are needed.

 

[ZapperZ]

Hello,
I have already studied Griffith's book, Intro to Electrodynamics.

What exactly do you mean by "studied"? Did you use it as the text in your E&M class? Or did you simply read through it like a novel?

This is because a lot of the mathematics that is needed to do Jackson's book, you would have used it in some form in the exercises from Griffith. You may not have to use the math as extensively in Griffith as you would in Jackson, but you would at least have seen the type of math needed (as in the solutions to many partial differential equations).

As always, as I've advised many students on here, if you haven't looked at Mary Boas's text "Mathematical Methods in the Physical Sciences", you should!

Zz.

 

[deskswirl]

First I'm going to assume you actually understood most of what you read in Griffiths and therefore have a basic understanding of ordinary differential equations, partial differential equations, linear vector spaces, and vector calculus over real fields.

However, unless you are really comfortable with solving partial differential equations and boundary value problems in Cartesian, cylindrical, spherical and ellipsoidal coordinates (at minimum) I would encourage reading An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics with applications to problems in mathematical physics by Byerly. It is an old book (1893 publishing) but has one of the most inductive approaches to PDEs and special functions making everything seem natural. I found it cited by Jackson in several chapters. Don't try to solve every problem just learn enough so that you accept what special functions show up in the respective geometries and why.

Review and strengthen your vector calculus by reading Chapter 1 on "Mathematical Preliminaries" in Modern Electrodynamics by Zangwill. There are other books on vector calculus specifically (some better some worse) but this has all you need and covers some other necessary topics.

Learn complex contour integration. If you are still in school take a course in complex variables (the applied course not complex analysis) before you graduate. If you can't fit it in your schedule pick up a copy of Schuam's Outline of Theory and Problems with an introduction to conformal mapping by Spiegel (I prefer the 1964 edition). The chapters you want to focus on are 4 through 9. An alternative to chapter 8,9 of Spiegel is to read Section 7.4-7.8 "Method of Conformal Transformation" in Fields and Waves in Communication Electronics by Ramo, Whinnery and Van Duzar. But it is much much shorter.

If you are already familiar with one-dimensional Fourier series/transforms, complex variables, basic special functions and vector calculus then I would suggest the following:

Section 9.3-9.4 on "Two -dimensional Fourier Transforms" and "Hankel Transforms" in Linear Systems, Fourier Transforms, and Optics by Gaskill
Chapter 2 on "Green's Functions" in Field Theory of Guided Waves by R.E. Collin
Section 4.1-4.2 on "Vector Spherical Harmonics" in Absorption and Scattering of Light by Small Particles by Bohren and Huffman
Chapter 4 on "Asymptotic Evaluation of Integrals" in Radiation and Scattering of Waves by L.B. Felsen and N. Marcuvitz
Section 2.2-2.7 on "Steinmetz representation of time-harmonic vectors" in Electromagnetic Waves by C. Someda

That should get you through Chapter 10 of the 3rd edition baring any variational or pertubative approach.

 

[adamf14]

What exactly do you mean by "studied"? Did you use it as the text in your E&M class? Or did you simply read through it like a novel?

This is because a lot of the mathematics that is needed to do Jackson's book, you would have used it in some form in the exercises from Griffith. You may not have to use the math as extensively in Griffith as you would in Jackson, but you would at least have seen the type of math needed (as in the solutions to many partial differential equations).

As always, as I've advised many students on here, if you haven't looked at Mary Boas's text "Mathematical Methods in the Physical Sciences", you should!

Zz.

While Boas' text is quite comprehensive in its own right, her treatment of partial differential equations, differential series solutions, and special functions is lacking in the mathematical rigor required for a proper understanding of Jackson's book. What do you think?

 

[Dr Transport]

@adamf14 really, the post is over three years old...I think they already completed Jackson...

 

[adamf14]

Touche! My fault for not checking the date! Although, knowing Jackson... :)