Ready to Master Calculus at 15? Discover the Best Resources!

[Mins]

I really do.
All my friends know calculus.(or do they? I don't know for sure).
Can you suggest a book or a website?
I'm 15.

 

[ice109]

I really do.
All my friends know calculus.(or do they? I don't know for sure).
Can you suggest a book or a website?
I'm 15.

http://www.abebooks.com/servlet/Boo...bn=0534393578&n=200000237&pid=1651435&x=0&y=0

not a bad price but i found an international edition for 50$, you might want to wait around for that or get a previous edition

 

[rocomath]

I really do.
All my friends know calculus.(or do they? I don't know for sure).
Can you suggest a book or a website?
I'm 15.

"they think they know it"

HS calc is crap! i won't truly know it for a longgg time! so i doubt they do.

since you're young, i would suggest Algebra & Trigonometry by Judith Beecher along with Stewart's Calculus. I'm in love with Beecher's book, solely bc it's a Calculus-prep book.

 

[Johan de Vries]

The books on Calculus by Walter Rudin are also very good. He explains everything in a self contained way starting at the fundamentals.

 

[dtl42]

Teach yourself. or take a college course. I did, and I'm 15 also. I used Stewart's book, it was nice and easy. You just have to be disciplined about it. Make sure you have a great algebra foundation, and you are super confident with analytic trigonometry. It shouldn't be too hard, Go for it!

 

[rocomath]

geesh, i wish i was this motivated when i was younger

but girls > math!

 

[JasonRox]

geesh, i wish i was this motivated when i was younger

but girls > math!

True.

 

[d_leet]

The books on Calculus by Walter Rudin are also very good. He explains everything in a self contained way starting at the fundamentals.

Are you being serious? I don't believe Walter Rudin has written a calculus book(amazon does not have a calculus book by him listed). Walter Rudin, however, is the author of a well known undergraduate level book for Real Analysis as well as graduate level books on Real and Complex Analysis and Functional Analysis. If you were suggesting Rudin's Principles of Mathematics Analysis as a book to learn calculus from, then that is not a very good idea at all, this book requires a good deal of mathematical maturity and familiarity with proofs, two things that someone just wanting to learn calculus does not likely have. Not that Rudin's book is bad, just that it is in no way suited for a first course in calculus.

Now a book I would recommend for someone wanting to teach him or herself calculus, check out Calculus by Michael Spivak, it starts with axioms for the real numbers and then builds on top of that with single variable calculus. It is not the easiest book, but if you have the determination and want a more theoretical treatment of calculus then this is the perfect book. Now if one wanted to study from Rudin after Spivak's book then I think one would be well prepared, but I would not suggest trying to learn Calculus from Rudin.

 

[ice109]

i think honestly what anyone should do is go to a college library and thumb through a couple books and pick which one is best for you.

 

[mathwonk]

read my thread, who wants to be a math guy.

 

[rocomath]

True.

i didn't even know about Calculus till my Junior/Senior yr in HS... :)

 

[chroot]

Since you're teaching yourself, you might even want to start with something like "Calculus for Dummies." It won't be rigorous, and it might not be good at developing your problem-solving skills, but it will definitely give you the conceptual understanding that will help you understand bona fide textbooks.

- Warren

 

[wildman]

I would also suggest some books like "Journey through Genius: The Great Theorems of Mathematics" and "Who is Fourier: A Mathematical Adventure" and "The Shape of Space". These books have the motivation of what moves mathematicians. They will make you excited about math. They are also filled with real math. The Fourier book has a real good intro to calculus as well as complex analysis all written in a simple style (really!).

When you attack the Calculus, I agree with chroot. Buy yourself the easiest books you can find. At 15, you have lots of time for rigorous textbooks. If you get "Calculus for Dummies" don't forget the workbook. Good luck.

 

[Saladsamurai]

Install RealPlayer if you need. http://press.princeton.edu/video/banner/8351.html

Grab one of the books these guys avove me suggested and check out these vids

 

[Johan de Vries]

Yes, Rudin may a bit too advanced. This is a free online book suitable for lay person.

 

[sr6622]

I thought Larson and Hostetler was good. Actually, you know what, just use Spivak Calculus.

 

[mathwonk]

my favorite for years was, calculus made easy by sylvanus p thompson, motto: "what one fool can do, another can".

 

[Howers]

Enjoy life thread starter. Math has its place, but calculus at 15 is not it.

 

[Darkiekurdo]

Why not? I'm 14 and mathematics/calculus is a great part of my life. And I still enjoy life.

 

[mathwonk]

Here is your first calculus lesson: try to find the line tangent to the graph of y = x^2, at x=1.

this means finding the graph of the linear function closest to x^2, near x=1.

well consider how x^2 changes as x changes near 1. we have x = 1+h so x^2 =

(1+h)^2 = 1+ 2h + h^2, where h = x-1.

Now the linear part of this expression is 2h, and for x near 1, i.e. small h, h^2 is extremely small. e.g. h=.1 implies h^2 = .01.

So the linear approximation to x^2 near x=1 seems to be 1^2 +2h, or 1+2(x-1).
Thus near x=1, the linear function closest to x^2 seems to be y = 2x-1.

This says the tangent line to y=x^2, at x= 1, should be the graph of y = 2x-1.

more generally, this method shows the linear approximation to y = x^2 near x = a,

is y = a^2 + 2a(x-a).

 

[Johan de Vries]

C'mon, finding the equation of tangent lines are exactly the kind of excercises that put students off from learning math. The first few calculus lessons should contain spectacular material, most of which is too difficult to be treated rigorously, it's purpose is only to serve as an illustration of the power of calculus.

So, instead of finding equations of a tangent line, one could illustrate Newton's method for finding zeroes. Of course, this also involves the equation of a tangent line. However, as a first lesson it is better, as makes clear that calculus has applications outside of calculus itself.

In the first lessons one could also illustrate the idea of aTaylor expansion and show how Euler used it to argue (nonrigorously) that:

1 + 1/2^2 + 1/3^2 + 1/4^2 + ... = pi^2/6

and that this implies that that the probability that two large numbers have a gcd of 1 equals 6/pi^2.

After showing a lot of these spectacular things, the studens have a better idea of why it's worth to spend some effort to study calculus.

 

[mathwonk]

this is a good suggestion. however it is somewhat inconsistent with your earlier advice, as the book of rudin you originally recommended starts with the question of the rigorous construction of the real numbers by means of dedekind cuts,

and your second suggestion seems a standard looking limit based approach, beginning also with the problem of slopes. [oops, this appears to be not a book at all, but a set of comments and problems to accompany the book of stewart.]

but i also enjoy the beauty of being able to calculate even values of the zeta function.

my simple example following fermat's approach to linearization (which is used by thompson), is on a much lower level, but does consider the basic problem of differential calculus, finding tangents.

this problem motivated many people such as fermat, descartes,...

perhaps the pupil will benefit from some of these suggestions.

 

[mathwonk]

the point at the beginning, as you say, is to motivate the student. there may be more than one way to do this, i.e. displaying big applications is one method.

however we seem to be dealing here with an already motivated student. and presentation of an example the student can actually understand is another method of building confidence.

my goal is not so much to dazzle with displays of what others have done, but to reveal what the student himself can do, and hence to suggest that the other level is not so far off as it may seem.

 

[mathwonk]

the solution by euler of the basel problem mentioned above, is at:

http://en.wikipedia.org/wiki/Basel_problem
note moreover that the solution i.e. the spectacular application, was obtained purely formally, by manipulating infinite series.

euler semed to consider such methods as precalculus, since they are taught in his book on "analyse infinitesimale", essentially a precalculus book, according to his own summary of it.

Johan is quite right that such spectacular results did motivate the creators of the calculus to justify the results.

of course at an earlier time, the problem of finding the tangent to a parabola was equally celebrated, and the solution i gave by fermat, was one that later theories of calculus also justify.

so the problem of finding tangents existed for some 1500+ years before descartes and fermat, and the basel problem for some 100 years before euler's solution. but the younger one may appear more spectacular to younger persons.

 

[silver-rose]

In terms of textbook,

I would suggest

Calculus by Howard Anton (not too hard, not too easy). Then, if you go back to restudy it, Calculus with Linear Algebra by Apostol (this is a very rigorous book that will give you the proper proof-based understanding of calculus).

 

[mathwonk]

the more i think about it the more i like johans idea.

so here is a copy of euler's own book on amazon, (get book I):
https://www.amazon.com/dp/0387968245/?tag=pfamazon01-20i have just ordered a copy for myself and also a copy of the wokrs of archimedes. not everyone need agree, but to me finding the volume and area of a sphere is a spectacular mental feat, and apparently the one of which archimedes, perhaps the most prescient scientist in history so far, was proudest.

 

[mathwonk]

by the way, calculus, or the relation between derivatives and integrals, is not needed for most of these applications, merely the idea of arbitrarily close approximations, i.e. limits.

 

[Johan de Vries]

Mathwonk, yes, the thread starter probably doesn't need such motivation. But then most students in school would need to be motivatated more if we want them to become interested in the topic.

Euler's book looks very intersting to read

 

[mathwonk]

take a look. i believe he calculates in it the values of the zeta function at all even integers up to 20 or 40 or so. i.e. the sums of various even powers of (1/n). in particular of 1/n^2.

 

[Evo]

Anyone receiving a solicitation via PM needs to report it to a mentor.

 

[Mins]

Thanks for replies to my thread, I really appreciated it, although the books were a bit 'over my head' for me at that age :)

I'm now in university and getting along well.
I got help from the book Calculus The Easy Way to get a grip of what it's like.
For serious studying, I studied calculus at high school, and also by studying for physics olympiad.
Thanks for your concern!