Math sequence for advanced optics

[Scrumhalf]

I am an electrical engineer 20 years from my last formal course in grad school. I wish to teach myself advanced optics, particularly diffraction theory, analysis of polarization using Jones calculus, aberrations, etc. I realize that my mathematics chops are sadly rusty through years of disuse, hence I am seeking advice on the best way to regain my facility in this crucial area before venturing into the physics.

I had the following in mind:

1. Thorough review of calculus (working on Strang cover to cover and have Apostol has well).

2. Multi-variable and vector calculus (need good reference book here).

3. Linear algebra/ODE/PDE (haven't decided on the books)

I am hoping that this should enable me to tackle something like Introduction to Fourier Optics by Joseph Goodman, as well as other more rigorous optics texts.

I would greatly appreciate any advice on this. I would also like to tackle some grad level quantum mechanics, say Cohen-Tannoudji and I would like to know if I am missing something.

Thanks!

 

[unhorizon]

"Div, Grad, Curl and all that" by H.M. Schey is an awesome informal text on vector calculus. I'm using it right now for self study, and it's really good.

Also, you may want to look into "Optics" by Eugene Hecht. I think this book may be at a lower level then what you are interested in, but it still covers the topics you are interested in. I'm still an undergrad, so I don't know much advanced optics, and I am curious why you need to know so much linear algebra, ODE's, and PDE's. I didn't know a book like Intro to Fourier Optics required those topics.

Also, you may want to browse the internet for some math help. I've found some good University sites that are extremely helpful.

-Matt

 

[Scrumhalf]

Matt, thanks for your reply!

I have no trouble with the concepts depsite being out of school for 20 years. It is the mechanics of solving a line integral, or doing an inverse Fourier transform analytically and so on that have been rusty because frankly I have not had to do these kinds of math problems in my line of work for the entire time I have been out of grad school.

When I pick up Goodman, it starts with 2-dimensional Fourier analysis, the Helmholtz equation and Green's theorem. Immediately I realized that unless I went back and brushed up on those topics I will not be able to proceed. In order to deal with Green's theorem, one must of course know vector calculus. Moreover, any study of optics by necessity requires one to be well versed in E&M, which would require at least a working knowledge of differential equations.

So, I decided to start with calculus, make sure I can get back to my grad schoo level facility of integrating functions analytically and then proceed to regain my familiarity with matrix methods and solving DEs. I have given myself until next summer to regain my math chops so that I can get down to business!