Physics is all about applying existing knowledge (including mathematics) to explore and gain new knowledge. Appreciating and understanding interrelationships and the cause and effects are important.

My research field imploded but I got a good job sidelining in quality assurance auditing. Applying methodologies learned in Physics enabled me to do a measurable better job than my other colleagues.

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>Would you say there's "something to be gotten out of" doing science and math on a personal level, even if one has no desire to apply it to their career?

You get to know how the Universe works, and it works in incredibly beautiful and strange ways, from the elementary particle physics up to living organisms. It's so much better than art or literature - remember that works of humans, like art, are constrained by our mind and creativity. Nature isn't constrained in this way, and the results are unimaginably better than anything created by a human.

>>7808643
I study math because it's fun. No other real reason.

I don't really buy into all that pretentious crap about how math is beautiful or how you get to see into the true framework of the universe.

It's just fun to learn how things work, to build theories and to solve hard problems.

That's probably a good book. Shankar is a great writer.
Assuming you know high school algebra and trigonometry all you should need to get most of introductory physics down is one-variable calculus.

Take a look at volume 1 of Courant if you want it for physics. People always talk about how he has stronger applications to physics than most calculus texts.