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Just to give you some background info, I'm a software developer looking to make a career switch to Mechanical Engineering (At least I think so). My interests lie in design, complex systems, maglev, rockets and new forms of space propulsion. Before I really commit myself to University, I would like to get my feet wet in Physics/Engineering. Most likely I'd major in Applied Physics or Engineering Physics.

Ultimately, my goal is to get through "Fundamental University Physics" by Alonso / Finn and then to get through Shigley's Mechanical Engineering Design. Alonso's text seems to require some heavy duty Calculus and Courant's Calculus book seems to have a lot of practical application problems so I think the two would compliment one another.

The only problem is, I'm not exactly sure what kind of Precalclus prep I would need for that. Mathwonk's favorite Precalculus book seems to be "The Principles of Mathematics" by Carl Barnett Allendoerfer, which looks to be a rigorous and proof focused trek through Precalculus. I'm not sure that this would be the best book for me if my preferences lean toward the more practical.

Generally to prep myself for Calculus I've been following a rough outline of what many here have already suggested:

Algebra:

-Elementary Algebra by Jacobs

-Algebra by Gelfand

-Functions and Graphs Gelfand

Geometry:

-Geometry 2nd Edition by Jacobs

-Geometry Revisited by Coxeter

Trigonometry:

-Trigonometry by Gelfand

General:

-What is Mathematics by Courant

Now, how should I handle this whole Precalculus thing? I skimmed through Addison-Wesley's Algebra and Trigonometry and I love that it's replete with practical-looking problems and novel facts about the given subtopic but it feels like a plug and chug type book. And as cool as calculating the parabolic cross sections of a car's headlights seems, it feels cheap and trivial.

So what's a good Precalculus book for the aspiring Applied Physicist / Engineer? Should I just stick with "The Principles of Mathematics?". Or should I replace that with "Precalculus in a Nutshell" or Serge Lang's "Basic Mathematics?" What would beset prepare me for Courant's book and beyond, given my goals?

Thanks!