My high school doesn't have AP Calculus

[nickmo94]

To kick off my first post here I will begin with a desperate plea for help and guidance: My high school is unfortunately not one of the best by any means. It is gigantic and has over 3000 students in it, meaning that most of the focus is spent on teaching students who don't give a damn about education.

I fortunately, am not one of those students, as I absolutely love to learn. It is literally my hobby. Sadly, my high school does not provide the two AP classes that I desire most, AP Calculus BC, and AP Physics C. It does have AP Calculus AB, and AP Physics B, which is much better than nothing.

But, alas, I am the type of person who wants to maximize my education before college (I just finished sophomore year by the way, I will be a junior once school starts) and in order to do that I need to challenge myself.

So... (sorry for the long introduction, I am naturally a long-winded person) What would you recommend I do in order to study EFFECTIVELY for both AP Calculus BC and AP Physics C during the next two years.

Right now I plan on doing independent study in calculus until school starts (which is in about two months), and hopefully I will be able to do a semesters worth in that time. And then once school starts I will continue to study the second semester topics and then restudy the first semester topics as my class works through them.

Then, senior year I plan on doing independent study in Physics (both mechanics and electricity and magnetism) as then I will be proficient in calculus and able to actually DO Physics C.


Is there anything you would do different? (also know, that I will be taking AP statistics as wells next year, which will allow for slightly less time at home to study, and senior year is swamped with 6 other AP Classes)

And more importantly, here is the main reason of my post:

If you've skipped everything else in my post, at the least read this (please).

I need some recommendations on the BEST possible textbook/textbooks for independent Calculus and Physics study. Price is not an issue.

As for as my abilities go I am a generally quick learner, and am quite smart (but far from genius). I am not super great at math, I just am a very, very dedicated learner, and more importantly, I enjoy doing math (it entertains me more than television). Who I am as a student can be summed up with this example from my past: I attempted Algebra II in the third grade and stuck to it for a whole two years, even though I couldn't comprehend half of the topics, after that I entered hiatus, only to return as a teenager to tackle it again, and I successfully learned many of the topics in Algebra II before I even understood geometry or took an Algebra class. So, I may not be the best, but I sure as hell will try hard.

So, with the understanding that I might have difficulties with complexly worded textbooks, and that I'm a first time calculus (and physics) student, but also knowing that I will dedicate myself 100% to learning them both, which textbooks or books would you recommend to teach me all the way up to the levels required for Calc BC and Physics C?

I have 9-10 months before the AP tests. So give me your best shot

Thank you VERY much to whomever reads this. I truly will appreciate any feedback as I have had very little support from others in this aspect, and need guidance.
-Nicholas

 

[johnnyies]

You have a community college in your area that you can attend?

 

[nickmo94]

I do, but to say that its the cream of the crop would be a gross overstatement...

I'm already enrolled with it (the college by the way is Mount Hood Community College) for Spanish over this summer, but nothing else.

I should mention that I just finished precalculus over this summer as one of my teachers at school happens to actually be good, and started a summer program to allow students to skip precalculus next year and go straight into calculus. So because of that class, I didn't sign up for any math classes at my community college (although I did take the placement test at that college prior to learning trigonometry and got placed into calculus anyways... I just didn't take it because I wanted to make sure I did well in trig first. Which I did.)

 

[nickmo94]

Oh, I should say that http://freevideolectures.com/ has some great looking calculus classes that I could "take" instead of attending my local community college.

The bigger issue is what textbook would be best for self study.

Any other additional tips would be appreciated as well though ;D

 

[naele]

You should be able to take the calculus physics concurrently with calculus, so give that a try.

Also, if you're absolutely dead set on self-studying, Halliday/Resnick Fundamentals of Physics is probably the best freshman physics book, and Stewart Early Transcendentals is a good calculus book.

 

[Mattowander]

I can't make any recommendations about textbooks for either Physics or Calculus but I can recommend some great online resources to use to help teach yourself calculus and physics. First, I would recommend that you check out MIT opencourseware. They have free lectures for both physics at the AP Physics C level and the Calculus BC level and the 8.01 physics levels are terrific. I have listed a few other links that might be beneficial to you. The first one deals mainly with problem solving but it is still very useful. The second one is a series of online notes for Calculus 1 to get yourself started with calculus. Notes for later calculus courses are also included at the same website. The last link is hard for me to explain but it has a lot of helpful resources for AP Physics C and AP Calculus BC and so I'd suggest that you check it out! I hope that these help!


http://ocw.mit.edu/courses/most-visited-courses/
http://press.princeton.edu/video/banner/
http://tutorial.math.lamar.edu/pdf/CalcI/CalcI_Complete.pdf
http://www.montereyinstitute.org/nroc/nrocdemos.html

 

[murmillo]

If you've taken AP Calculus AB, you should find that there's actually not that much new stuff to learn in BC Calculus--mainly just infinite sequences and series, power series, convergence tests, and Taylor series. If you're using a good standard calculus textbook, there should be enough in it to cover BC topics. I've heard that the Calculus textbook by Larson and Hostetler is really good (though I haven't read it). At my high school BC Calculus students used Foerster. In AB Calculus, my high school used Calculus: Graphical, Numerical, and Analytic by Demana et al.

I didn't actually take BC Calculus, but I self-studied it after high school so I could start college with linear algebra. I used the Demana text with some online help and placed out of the equivalent calculus class at my college.

I think a really good and concise calculus book is Short Calculus by Serge Lang. If you've taken AB, then you only need to read the last two chapters of the book. But you might find the book too difficult.

Also, on physics: Yes, Halliday and Resnick is good, but the material in BC Physics might be difficult to understand mathematically if you haven't had exposure to multivariable calculus. And by self-studying, you're missing out on an essential part of physics, which is lab. At my college it's very difficult to skip first-year physics even if you've gotten a 5 on AP Physics and do well on the placement test. So you should consider just taking it in college, unless you're sure you can get credit for it. You may do better learning some basic multivariable calculus involving line integrals, for instance, before trying to learn about conservative forces.

 

[nickmo94]

@naele: Thanks for the physics book recommendation and study tip. I will attempt both at the same time and see how it goes.

@Mattowander: Those links look great. Thank you very much. The more resources the better :) And the college lecture notes are wonderful. Perfectly lucid and concise; it should prove to be a useful reference if I become stuck in a textbook.

@murmillo: I will definitely check out that textbook. Since there are several books published by Larson, the one you're referring to specifically is "Calculus (With Analytic Geometry)(8th edition)" correct?

I'll take a look at that book regardless of difficulty. If it proves to be too much to handle, no worries.

Hmmm, yeah, I forgot about the lab-work aspect of physics. I am taking AP Physics B next year, so I should be getting some decent labs. Although I'll be missing out on the Physics C stuff.

By the way, I'm not necessarily taking AP classes because I'm looking to skipping them in college. Rather, I just want to challenge myself in high school to avoid monotony and easy classes. Challenging=Fun for me. So I will probably take Physics and Calculus in college anyways; at the very least, to just review.

Edit: I just found out that my school just so happens to have the seventh edition of "Calculus" by Larson and Hostetler, so I will just go and check one out for the summer. Awesome!

But, after browsing around for a while, I've seen LOTS of people advocate for the Michael Spivak Calculus book; does anyone here have an opinion on it? To me it seems like its top notch, but should be approached after having a basic to an intermediate understanding of calculus.

 

[gigabyte3000]

Hmmm, yeah, I forgot about the lab-work aspect of physics. I am taking AP Physics B next year, so I should be getting some decent labs. Although I'll be missing out on the Physics C stuff.

Don't worry about the labs, they aren't too important, in my opinion. If you're fairly good at visualizing word problems you should be fine in that aspect. You could always also look online for Physics C labs and ask your teacher if you could use some equipment after school or something.

 

[murmillo]

Spivak is a great book, but I'm not sure it's the best for self-studying calculus. Since it's a book that tries to get the reader used to thinking up proofs for himself, it may be better to use that book if you have a teacher to correct your proofs and give hints. I think a good book for self-study should have tons of examples and exercises with solutions and should do most of the explaining and proving. Or at least that's the book I wanted when I wanted to learn math on my own in high school. Now I can pick up a college textbook and work my way through it, but in high school I wasn't prepared for a theorem-proof-example type book (which is not to say that Spivak is completely like that). I think it might be better to stick to a standard textbook, but I suppose that if it's not rigorous enough you can leaf through Spivak and guess whether it's for you.

 

[nickmo94]

Spivak is a great book, but I'm not sure it's the best for self-studying calculus. Since it's a book that tries to get the reader used to thinking up proofs for himself, it may be better to use that book if you have a teacher to correct your proofs and give hints. I think a good book for self-study should have tons of examples and exercises with solutions and should do most of the explaining and proving. Or at least that's the book I wanted when I wanted to learn math on my own in high school. Now I can pick up a college textbook and work my way through it, but in high school I wasn't prepared for a theorem-proof-example type book (which is not to say that Spivak is completely like that). I think it might be better to stick to a standard textbook, but I suppose that if it's not rigorous enough you can leaf through Spivak and guess whether it's for you.

Thank you for the info, I didn't know that stuff about the Spivak book. Nevertheless, I will still take a look at it, though, only after I've mastered the basics of Calculus.

And you're right, a textbook should have tons of examples and exercises; hopefully I will find the perfect one for me after some trial and error.

 

[hadsed]

As far as calculus based textbooks go, you should get this:

https://www.amazon.com/dp/0321513339/?tag=pfamazon01-20

This is absolutely the best textbook I've ever seen for physics. It covers mechanics, optics, thermodynamics, electromagnetism, and modern physics. Maybe not all those subjects to its entirety, but its meant for first/second year students. I highly recommend it, and so does every university in my state (Georgia, although that's not saying much, we do have GaTech here which is a top engineering school in the country).

 

[nickmo94]

Thank you hadsed, I will definitely look for that once I set out for my Physics books.

Okay, so I have a minor update. I went to my school yesterday and checked out our Calculus textbook "Calculus: Seventh Edition" by Larson and Hostetler, and have been reading it for about 10 or so hours (and doing the problems of course.)

However, some of the definitions and explanations seem to be POORLY done. Its formal definition of a limit for example, made no sense; I still do not understand what Epsilon is used for. Making no sense in the definition is fine, if it can actually give a lucid demonstration of what it entails (step-by-step preferably); it however, does not.

I use simpler textbooks for reference when it gets confusing, so I'm still able to continue. And most of the basic and non-formal concepts are easy to grasp and preform, but, I just don't want to spend 15 minutes looking over the formal definition and its "example" trying to understand what the hell it means.So anyways, I came across another book which seems to have rave reviews, "Engineering Mathematics" by K. A. Stroud, which is supposed to teach someone basically everything a normal Calculus textbook would, but in a more applied and less abstract manner, with less formal procedures.

What is the general opinion on learning calculus from an engineering textbook? Would I be missing out on anything? Should I study both at once? Are there any Calculus textbooks out there that cover the topic with as much depth as my Larson textbook, but with definitions that don't make your brain explode when trying to figure them out.

Thank you for the feedback so far, I REALLY appreciate it; and thank you in advance for any future feedback.EDIT: I forgot to mention, Mattowander, you're links have proved to be very useful so far as references and to help with understanding while I trudge through my poorly written textbook. I thank you so very much for them.

 

[naele]

The Stroud book is a math methods book, I would advise against learning calculus from that kind of book.

What's wrong with Larson's definition of a limit? As far as I know he uses the correct epsilon-delta definition, which is what you'll find in every calculus book and then again in real analysis. I think it has more to do with the fact that the definition isn't very intuitive since it's expressed through inequalities, than with how Larson presents it. Here's a great explanation that helped me understand it http://bobobobo.wordpress.com/2008/01/20/how-to-do-epsilon-delta-proofs-1st-year-calculus/

By the way, I might suggest buying a Schaum's Outline of Calculus and 3000 Solved Problems in Physics.

 

[nickmo94]

The Stroud book is a math methods book, I would advise against learning calculus from that kind of book.

What's wrong with Larson's definition of a limit? As far as I know he uses the correct epsilon-delta definition, which is what you'll find in every calculus book and then again in real analysis. I think it has more to do with the fact that the definition isn't very intuitive since it's expressed through inequalities, than with how Larson presents it. Here's a great explanation that helped me understand it http://bobobobo.wordpress.com/2008/01/20/how-to-do-epsilon-delta-proofs-1st-year-calculus/

By the way, I might suggest buying a Schaum's Outline of Calculus and 3000 Solved Problems in Physics.

Forgive my lack of knowledge, but what exactly do you mean by math methods? And (not to say that you're wrong) why is it not good to learn calculus from that book?

Oh, its not that the definition is wrong, I understand that it is right, its just he didn't explain it at all, or, barely. And the examples where it is explained are terrible (at least to me, as someone who is just starting calculus).

I will take a look at both those books; and thank you for the epsilon-delta explanation! :]

 

[Mattowander]

Math methods focus more on using math specifically for problem solving and so learning from a math methods book would probably skip over a lot of the more theoretical information that would be useful to you. The way I see it, math methods books are more useful when you have already been introduced to the topics inside because those books focus more on applying math rather than teaching the basics.

Just my two cents though. I hope that made sense...I'm really tired as I'm writing this.

 

[Bourbaki1123]

For problem solving at your level, I've heard that Serge Lang's Basic Mathematics has difficult problems from subjects you would probably be familiar with. It covers high school algebra, trig, analytic geometry (pre cal) etc. Though you have presumably finished classes in those areas, his book may give you some challenging problems to work on.

Shoot, if you're really ambitious, try learning linear algebra (make sure you understand the proofs) and then pick up Michael Artin's book entitled "Algebra" (and maybe Dummit and Foote's Abstract Algebra? I found it to be a relatively easy read). The subject matter is of the upper level undergraduate level; I learned it alongside linear algebra and multivariate calculus. It'll give you a strong taste of abstract mathematics, at least on the discrete end of the spectrum.

 

[nickmo94]

Math methods focus more on using math specifically for problem solving and so learning from a math methods book would probably skip over a lot of the more theoretical information that would be useful to you. The way I see it, math methods books are more useful when you have already been introduced to the topics inside because those books focus more on applying math rather than teaching the basics.

Just my two cents though. I hope that made sense...I'm really tired as I'm writing this.

For problem solving at your level, I've heard that Serge Lang's Basic Mathematics has difficult problems from subjects you would probably be familiar with. It covers high school algebra, trig, analytic geometry (pre cal) etc. Though you have presumably finished classes in those areas, his book may give you some challenging problems to work on.

Shoot, if you're really ambitious, try learning linear algebra (make sure you understand the proofs) and then pick up Michael Artin's book entitled "Algebra" (and maybe Dummit and Foote's Abstract Algebra? I found it to be a relatively easy read). The subject matter is of the upper level undergraduate level; I learned it alongside linear algebra and multivariate calculus. It'll give you a strong taste of abstract mathematics, at least on the discrete end of the spectrum.

@Mattowander: Okay, that makes sense to me, thank you. I will use both types of books then, one to learn it, and the engineering math methods to practice it.


@Bourbaki: I really appreciate that info, you've opened up a completely new area to study. Now, I'm not really all that familiar with linear algebra, so can you enlighten me? Does it involve calculus? And how hard are the proofs to understand?

I'll be honest, throughout my precalculus class, I basically ignored every proof. It bored me and seemed redundant. Maybe it was because of the fact that my precalculus text sucked, but still...

Is there anything that I can do to help my understanding of proofs? Or make me care about them more? And, are they really that important to learn? I mean, I don't really see myself becoming a mathematician or engineer, I simply just enjoy studying math; so would it be necessary to learn proofs?

 

[nickmo94]

Okay, I finally found the textbook that was right for me. Stewart's "Calculus: Early Trancendentals" 6th Edition has all the rigor (if not more) than a standard textbook, but it explains everything in a manner that is very clear, while providing around 10 or so examples per section helping you to grasp the concept even if the definition confuses you slightly.

That, in addition to the fact that it is probably the most complete calculus textbook that I've ever seen (it has 17 chapters that cover Calculus I, II, and III) make it easily the best.

Serway's "Physics for Scientists and Engineers" is also fantastic, but I'm waiting until I get through more calculus before I continue with it.

Anyways, those two books are amazing, and thank you to everyone that helped me out here, I really really appreciate it.

 

[hadsed]

I also highly recommend Stewart's Calculus, but I have the regular edition. It is just as good, mine is the 4th edition, and there's really no difference between that and the 6th edition except that it costs about $130 dollars more (4th edition I got it for about $10). It has pretty difficult problems and it builds on your knowledge so if you can do those you will master calculus.