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**headhurts****Member**- Registered: 2014-05-04
- Posts: 8

Quick intro: I was getting my math kicked by calculus. Everything past in a tangent after the first few weeks. Tried many websites, youtube tutorials, library books. Still confused. Was right on the verge of going for a private tutor. Decided to try the mighty intrawebs one last time. Ended up on math is fun.

Suddenly calculus makes sense. Almost easy even. Everyone understands differently and the way it's explained on this website just... worked for me! I can narrow it down to few things:

a. Good explanation of basic concepts - very thorough. One of many examples: I had no idea derivatives and f' and d/dx are all the same darn thing. I kept getting confused when the lecturer kept interchanging the terms in class.

b. Good examples to apply theory into practice.

c. GREAT selection of practice problems at the end of lessons. Really helps to hammer in the knowledge.

So really: A BIG THANK YOU to the people who put in such a great effort.

Secondly, now that the basics are out of the way, I need to move on to other course topics like implicit differentiation, related rates, newton's method etc. And I am really hoping that someone can point me in the direction of any other good website like mathisfun where I can PROPERLY learn those topics. Not just learn to solve individual problems using rules (which the youtube videos are great for) but actually understand why and what am I doing. I seem to learn a lot better that way since I have a math memory so if I don't understand it, I forget it by next week.

Cheers

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,700

Hi;

Welcome to the forum.

I think that you are really thanking MIF, he is the creator of the material that has helped you so much.

And I am really hoping that someone can point me in the direction of any other good website like mathisfun where I can PROPERLY learn those topics.

One of the best ways to learn is by doing. But whenever you can not do a problem bring it in here and someone will help you.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Hi headhurts,

Welcome to the forum!

What is your favorite color?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,482

Hi headhurts,

That was a neat introduction!

**Welcome to the forum!**

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,659

hi headhurts

**Welcome to the forum.**

I, too, have to understand rather than just learn rules.

If you cannot find what you want on the teaching pages of MIF, post here.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Welcome to the forum, headhurts.

It's very good that you are leaning towards actually understanding the mathematics rather than just "plug and chug" methods which is the general pedagogy at most high schools. Memorization is not the key to understanding mathematics or physics (or any other science). Math and physics students have a tiny closet of first principle memorized concepts, and maybe another tiny closet or two of more specific memorized concepts pertaining to the class at hand. Vast warehouses of memorized concepts? Doing that hinders rather than helps understanding of math and physics. In math and physics, the ability to solve a problem from first principles is much more important than is memorized trivia.

The unfortunate thing is that there are few websites online which provide that as most are just suited towards the high school curriculum.

Here are a few excellent online resources for a rigorous treatment of calculus:

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/

Both of them have full lecture notes, video lectures and numerous problem sets and exams.

These are another set of lecture notes for MIT's 2014 course:

http://math.mit.edu/suppnotes/suppnotes01-01a/index-01.html

And these are the problem sets for MIT's 2014 course:

http://math.mit.edu/classes/18.01/2014SP/problemsets.html

And here are the exams for MIT's 2014 course:

http://math.mit.edu/classes/18.01/2014SP/exams.html

The whole course site for the course containing the syllabus and other things is at:

http://math.mit.edu/classes/18.01

I would also recommend supplementing some of that with some textbooks (in order of recommendation level):

Spivak's "Calculus", Apostol's "Calculus", Courant's "Introduction to Calculus and Analysis" or "Differential and Integral Calculus"

I think for you, the best route will be buying Spivak's "Calculus", watching the 2010 MIT course video lectures and reading notes and doing problem sets/exams from all of those courses (and Spivak's book).

*Last edited by ShivamS (2014-05-05 08:36:18)*

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**headhurts****Member**- Registered: 2014-05-04
- Posts: 8

ShivamS wrote:

Welcome to the forum, headhurts.

Thanks for all the links.

On a somewhat related note: is Spivak the best calculus book? My uni, just like most others, insist on using Stewart.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Spivak, by most mathematicians (all that I have talked to - this may be a generalisation of course) is the best calculus book available. An even better part about the book is that it introduces analysis to you as well.

By the way, Spivak, Apostol and Courant are not too different in terms of quality and all three are regarded as the best calculus books available. Spivak is more friendly for an introduction to calculus which is why I recommend it.

Most universities use Stewart and the likes because their students have not had the mathematical background to cover a rigorous book like Spivak. However, you, with enough motivation can definitely cover it. If you find Spivak a bit too hard, ask questions here or search up some online resources (the notes and videos I linked are enough) or you can get a copy of "Basic Mathematics" by Serge Lang, which is ideal preparation for Spivak.

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