Best way to tackle modern physics with engineering background

[oneleaf]

Hello!
I have occasionally lurked this forum and have found some really interesting discussions. I finally decided to join the forum and also wanted to start off with a question.

I have a bachelors degree in mechanical engineering so I have the mathematics and physics foundation typically achieved with that degree. I have also worked in a variety of industries for about 15 years, and have continued to apply statics and fluid mechanics in a variety of design and analysis projects. Unfortunately, this leads me to being quite rusty in electromagnetism and optics, as well as having had very little reinforcement of math skills beyond some basic calculus over the past decade.

Also, when I was in undergraduate, we spent very little time with modern physics areas. I am in the situation now where I have some time that I want to dedicate to catching up with all the physics that I forgot, as well as start tackling modern physics areas that I have always found extremely fascinating but never had a chance to study in depth.

At the moment, I am just going through the Young and Freedman University Physics book, one chapter at a time and doing problems. But I was wondering if any of you recommend that I also review calculus, differential equations, and linear algebra and other areas of math? Or should I just study physics and refer to math books only if and when I get stuck?

My hope is that once I get through the textbook, I can explore other areas like condensed matter, quantum mechanics, particle physics, etc.

The main reason I want to study all of this is because as much as I have enjoyed the projects I have worked on, there are a lot of areas of physics I absolutely loved in college and I want to have a chance to explore some other areas. Also, my career has been pretty good to me over the years and I am in a situation where I want to pursue new things and less concerned about salary. So my goal is that my self-study can inspire me to get into an area of physics that I might want to research and maybe lead me to grad school opportunities.

Any recommendations on areas of mathematics to consider, and/or math or physics textbooks would be appreciated! Thank you!

 

[jedishrfu]

I've been reviewing Vector / Tensor Analysis which is used in Classical Mechanics, ElectoMagnetic theory, and General Relativity. However, it seems that Differential Forms has taken over for much of the advanced stuff.

For QM beside partial differential equations and boundary value problems you might also consider group theory.

 

[atyy]

Young and Freedman is perfectly good background for quantum mechanics. It's usually helpful to have linear algebra also for quantum mechanics. But since you are learning for fun, you can just take a look at some standard QM texts and refer to other material when you get stuck.

 

[oneleaf]

Thanks guys! So a lot of my calculus is probably adequate to refresh as I go, but I need a good refresher on vector calc, group theory, and linear algebra. Do you think the Riley Mathematical Methods is an adequate book for self study and gaining more familiarity with these methods? I have read some of the Boas book on a previous project and the book style did not jive well with me in terms of gaining an understanding of the method.

 

[jedishrfu]

Thanks guys! So a lot of my calculus is probably adequate to refresh as I go, but I need a good refresher on vector calc, group theory, and linear algebra. Do you think the Riley Mathematical Methods is an adequate book for self study and gaining more familiarity with these methods? I have read some of the Boas book on a previous project and the book style did not jive well with me in terms of gaining an understanding of the method.

There's also Arfken and Weber:

https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20

and Nearing's free ebook book (or paid Dover softcopy):

http://www.physics.miami.edu/~nearing/mathmethods/

for Vector Calculus there's this accessible book by Schey:

https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20

 

[jtbell]

As an intermediate step between Young/Freedman and an upper-level undergraduate QM book like Griffiths, you might consider an intro modern physics book for courses that often follow right after the first-year introductory course:

Taylor / Zafiratos / Dubson (I taught a course from this book for several years)

Tipler / Llewellyn

Krane

(and others)

These books include basic relativity and QM, and introductions to various application areas: atomic, nuclear, solid-state, particle physics, etc.

 

[Arsenic&Lace]

The Feynman lectures concentrate on being interesting rather than pragmatic pedagogically, so they are a good supplementary set of books.

 

[oneleaf]

Thanks for the suggestions, everyone! Those info to modern physics books looks like a great step after Young and Freedman.

Regarding the Feynman Lectures, I have heard a lot about them. I wonder if I might get more out of them compared to Young/Freedman. For instance, I have mechanics and dynamics textbooks that have more calculus heavy problems, that I feel I would get more out of reviewing. Perhaps those coupled with Feynman would be a more interesting reentry into Physics?

 

[jedishrfu]

dont forget to use the thanks button on posts that were most helpful.