Precalculus Mathematics in a Nutshell + Spivak's Calculus ?

[Nunchi]

"Precalculus Mathematics in a Nutshell" + "Spivak's Calculus"?

Hey, I'm currently a senior in HS attending Elementary Calculus with a decent grade (B+).
I recently had an epiphany that I haven't actually learned anything, I've just temporarily memorized how to derive the answer from the set of information given. That fact disturbs me for whatever reason, seeing as how whatever future career path I choose will be heavily mathematics-based (like engineering + physics).

Though I skipped Pre-Calc and all that it entails yet somehow am passing Calc easily, I'm wondering if "Precalculus Mathematics in a Nutshell" will suffice in nailing down and/or covering all of the high school math I've learned and will completely prepare me for Calculus? It has amazing reviews. If so, I'd like to move onto Spivak's Calculus right after.

Is this a solid attack plan? Or do you not recommend one of these books?
If you don't recommend one, please provide alternatives. I just like the simplicity of this plan.

 

[WannabeFeynman]

I'll post a review of the books later, but you should check AoPS books and the NCERT books (available for free online). Spivak's great, but you need good preparation, for which those books I mentioned will suffice. "Basic mathematics" by Lang is good too. You should not skip precalculus by the way. I don't suggest precalculus in a nutshell

 

[Nunchi]

I'll post a review of the books later, but you should check AoPS books and the NCERT books (available for free online). Spivak's great, but you need good preparation, for which those books I mentioned will suffice. "Basic mathematics" by Lang is good too. You should not skip precalculus by the way. I don't suggest precalculus in a nutshell

Basic Mathematics would be sufficient by itself to get started in Calculus?
Any specific reason on why you wouldn't recommend precalc in a nutshell?

Also, apparently Spivak's Calculus is more for math majors and not for something engineering/physics oriented?

 

[WannabeFeynman]

Basic Mathematics should be sufficient, but I would suggest going through the free NCERT books (grade 11-12 which include calculus) at least. You can go through AoPS as well, as it will give you a very good understanding, but it may be too expensive.

 

[micromass]

Basic Mathematics would be sufficient by itself to get started in Calculus?

Yes, if you understand everything in Lang's "Basic Mathematics", then you are perfectly ready to start calculus. That's the beauty of the book, it contains everything you need to know and no extra fluff.

Also, apparently Spivak's Calculus is more for math majors and not for something engineering/physics oriented?

Yes, Spivak's Calculus is meant for math majors and people interested in pure math. A lot of the book is concerned with dealing with limits in a rigorous way.

If you are interested in math, mathematical physics or even theoretical physics, I think Spivak is worth it. But even then, it might not be the best "first book" on the subject. I think Lang's "first course in calculus" is better, even though his treatment of limits is a bit "weird".

If you just want to know calculus to do calculus computations, if you're not really interested in getting bogged down in mathematical details and just want to get to the physics as fast as possible, I think Spivak would be a bad book for you. Books like Stewart treat computational calculus, so they should work fine for you.

 

[Nunchi]

Basic Mathematics should be sufficient, but I would suggest going through the free NCERT books (grade 11-12 which include calculus) at least. You can go through AoPS as well, as it will give you a very good understanding, but it may be too expensive.

Yes, if you understand everything in Lang's "Basic Mathematics", then you are perfectly ready to start calculus. That's the beauty of the book, it contains everything you need to know and no extra fluff.



Yes, Spivak's Calculus is meant for math majors and people interested in pure math. A lot of the book is concerned with dealing with limits in a rigorous way.

If you are interested in math, mathematical physics or even theoretical physics, I think Spivak is worth it. But even then, it might not be the best "first book" on the subject. I think Lang's "first course in calculus" is better, even though his treatment of limits is a bit "weird".

If you just want to know calculus to do calculus computations, if you're not really interested in getting bogged down in mathematical details and just want to get to the physics as fast as possible, I think Spivak would be a bad book for you. Books like Stewart treat computational calculus, so they should work fine for you.

Thank you both, these are exactly the answers I was looking for!
I don't mind the math side of things, so I'll get those two books from Lang.
(using physicsforum's amazon link if that still works, of course :D)

Along with that, I was thinking about doing this http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/ online course thing and getting the "Sears and Zemansky's University Physics: with Modern Physics. 12th edition" book that they use with it.
Anyone have any experience with this or better suggestions? There's like ten 'physics I' courses, but this seemed to be the newest one.


On a side-note, it's raining right now for like the first time in a long time, and the sound is really relaxing.

 

[micromass]

On a side-note, it's raining right now for like the first time in a long time, and the sound is really relaxing.

https://www.youtube.com/watch?v=37G7aOPkEis

 

[Nunchi]

Oh jeez, now the background noise to my room will be pouring rain instead of the droning hum of a dehumidifier ^^

 

[micromass]

To answer your other questions: MIT's opencourseware is extremely good! But don't make the mistake that many other students make. Many students just watch the videos, see that they understand them and think that they know all about it.
You should see OCW as a secondary resource only, it will help your understanding, but it's not good enough by itself. You need to get a decent textbook too and do a lot of problems. I am not familiar with the textbook you name, but there are so many textbooks out there which cover intro physics, I don't think you can go wrong with it.

 

[Nunchi]

To answer your other questions: MIT's opencourseware is extremely good! But don't make the mistake that many other students make. Many students just watch the videos, see that they understand them and think that they know all about it.
You should see OCW as a secondary resource only, it will help your understanding, but it's not good enough by itself. You need to get a decent textbook too and do a lot of problems. I am not familiar with the textbook you name, but there are so many textbooks out there which cover intro physics, I don't think you can go wrong with it.

Thanks for the advice, you've been tons of help! And yeah, I'm definitely going through the book cover-to-cover once it gets here.

 

[dumplump]

I would not suggest Spivak for you. I would recommend a modern text, meaning an older edition calculus text geared towards the standard calculus class. After you feel like you understand some of calculus, then I would try out Spivak. Jumping head first into Spivak is usually a bad idea.