Need help preparing for Courant's Calculus

[superdupernoob]

Hello,

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!

 

[Dr.D]

How familiar are you with Shigley's Mech Engr Design? Somehow, it does not seem consistent with the level of mathematical rigor you seem to want. It is a good book; I've taught from it and I use it myself. But it is not mathematically very sophisticated at all.

If you are fairly proficient in trig and analytic geometry, I'm not sure you need to be worrying about preparations before tackling Courant.

 

[superdupernoob]

How familiar are you with Shigley's Mech Engr Design? Somehow, it does not seem consistent with the level of mathematical rigor you seem to want. It is a good book; I've taught from it and I use it myself. But it is not mathematically very sophisticated at all.

If you are fairly proficient in trig and analytic geometry, I'm not sure you need to be worrying about preparations before tackling Courant.

Hello Dr.D, I really have no idea what I'm doing and only have a vague one of what I want to be doing to be completely honest. I want to have a solid grasp of physics but I would also in the end want to become an Applied Physicist or Engineering Physicist, or even a Mechanical Engineer with a strong design focus. My background is in software design but I've always wanted to get more into developing physical products.

For example, I've been learning about FPGA chips and I want to build a drone and use an FPGA chip to enhance it . I'm more interested in the mechanical parts though. I wouldn't and couldn't do it from scratch but I'd like to at least design (and fabricate) parts of it myself and approach it like an engineer would. A friend told me that the difference between a maker and an engineer is that an engineer will create either a really detailed free body diagram, or plan it out and model it on CAD software for weeks before doing anything. And to do that I assume I will need a strong grasp of physics and some crash course in Mechanical Engineering design.

So I'm actually not sure if the path I've laid out is the right one but I do know I'll at least come out of it with a good understanding of university physics. My Precalculus course looks more like this now: Algebra by Jacobs, Geometry by Jacobs, Algebra / Methods of Coordinates by Gelfand, Basic Mathematics by Gilbert Lang, Functions and Graphys by Gelfand, Trigonometry by Nobbs, Elementary Vector Algebra by Macbeath.

Then it's Courant chapters 1-6 (First year Calculus), and then I dive into the Mechanics section of Alonso/Finn and Shifley's Mech Engineer Design.

 

[Dr.D]

Let me speak specifically to your desire to work through Shigley's book. The necessary background for this book is primarily the undergraduate course in mechanics of materials (also known as strength of materials), and undergraduate engineering statics and dynamics. You have not mentioned any of these prerequisites, but your focus seems to be much more on mathematics. The math will certainly not hurt (indeed, it will help), but that is not at all the thrust of Shigley.

 

[superdupernoob]

Let me speak specifically to your desire to work through Shigley's book. The necessary background for this book is primarily the undergraduate course in mechanics of materials (also known as strength of materials), and undergraduate engineering statics and dynamics. You have not mentioned any of these prerequisites, but your focus seems to be much more on mathematics. The math will certainly not hurt (indeed, it will help), but that is not at all the thrust of Shigley.

I have been looking through MIT OCW's suggested tracks for their mechanical engineering program but I simply don't know what I need to know in order to work through Shigley's book in a fruitful way. I was hoping that it would lay the foundation that I could build my "mechanical" knowledge on (the same way Courant's book would lay the foundation I could build my math knowledge on) . I know it's pretty much impossible to "teach yourself" mechanical engineering but based on your experience what would you do if you were in my position and university was not an option in the foreseeable future?

 

[Dr.D]

I think if I was starting from scratch, I'd begin by reading (and working all the problems therein) the books by Stephen Timoshenko - Statics, Dynamics, Strength of Materials, Advanced Strength of Materials, Vibrations. I'd caution you to get the original books by Timoshenko, not the modern revisions by Timoshenko and XXXX. The revisers have lost most of the value in the original books. If you have mastered all Timoshenko's books, then Shigley will make sense and be very useful for the capstone. Before that, you could probably get through Shigley, but you would miss much of the value hidden in the details.

 

[mathwonk]

i suggest just starting with courant, accepting the fact that the going will be slow. i suspect you already know enough to do that. it is a hard book though, even for people with poenty of preparation, so don't give up too soon. the upside is you will get a lot of benefit from a small number of pages or even lines in that book.

 

[MidgetDwarf]

For pre-calculus, I prefer Serge Lang: Basic Mathematics.
A better geometry book would be Moise/Downs: Geometry. Make sure the title of the book is not: Elementary Geometry From An Advance Standpoint. The latter is a nice book, but kind of advance, and not for a first exposure.