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I sort of dislike this kind of "philosophical" introduction to calculus. Maybe I don't have the spirit of an artist. The best way to start with calculus is th

I sort of dislike this kind of "philosophical" introduction to calculus. Maybe I don't have the spirit of an artist. The best way to start with calculus is the one by Gilbert Strang, who explains everything on the first page of his book (and the rest of the book are "just" examples). The first half of the first page shows a drawing of the speedometer and odometer of a car and it explains what they are, and that they are not independent but related in a special way. On the second half of the first page it says that differential calculus is the task of computing the speed from the distance, and integral calculus is the task of computing the distance from the speed. Then it says a lovely sentence "this is not an analogy, this is the real deal and we have already started with the subject, and this is actually all there is to it". Then in the rest of the page it explains in a couple of sentences how can you compute speeds from distances and vice-versa, and why you need a constant of integration, and so on. It also proves the fundamental theorem of calculus. The rest of the book consists in concrete examples and a few more constructions, up to Taylor series.

lewisjoe 7y ago
https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ https://ocw.mit.edu/resources/res-18-001-calculus-online-tex... I guess this is the one?
- enriquto 7y ago
  Yes, this one! Just read pages 1 and 2 of the pdf (I was writing from memory and my explanation is not exact).
GuiA 7y ago
Different people learn differently. Very few people learn all they know from a single source. Therefore, having many sources presenting a same subject in many different ways is a wonderful thing. Gilbert Strang’s book is wonderful! Some will find it to be the “best book” to learn calculus, others won’t. No need to poo-poo others’ work just to value signal. (I’m sure the authors would appreciate any constructive feedback though!)
- enriquto 7y ago
  But I'm not "poo-pooing" Kleitman's book! It's just that after reading the beginning I did not find it very engaging personally. It starts with numbers, and properties of real and complex numbers. The definite integral is not defined until half the book (while it is a simpler concept than the derivative). I prefer to start with calculus, and the relationship between integrals and derivatives right away. And then, much later, when you need some crucial property of real numbers, introduce it as required. You can do a great deal of calculus without needing to know the definition of real number!
  - adamsea 7y ago
    ... somebody on the internet is wrong! ;) ... the question is who? Is it them? Is it me? Is it you?
TheOtherHobbes 7y ago
I can't imagine someone with an arts background getting anything at all out of this introduction. The Gilbert Strang approach is much clearer - although it's still not obvious why an artist would ever need calculus. In fact there are some applications in generative design and 3D animation, but it's still low on the list of essential art skills. And if you really need those effects - and know enough math to understand how to code them - you can copy code from a cookbook without having to derive it from first principles.
- Chazprime 7y ago
  These types of tutorials are pretty popular among VFX artists who may suddenly need to brush up on complex math, but don’t work with it consistently. Knowing the fundamentals of calculus comes in very handy when suddenly you’re tasked with working in Houdini for six months and have never touched the software before.
- commandlinefan 7y ago
  I don’t believe that anybody can really learn any math (much less calculus) by just reading about it without doing a lot of practice problems. It’s nice of this guy to put this together and all, and I guess it could pique somebody’s curiosity, but they’ll really need to pick up a good book with a LOT of sample problems to understand it any better than they understood it before they read this introduction.
- mathgenius 7y ago
  Artists may not need calculus, but calculus would certainly benefit from artists.
- jacobolus 7y ago
  There are a bunch of mathematical artists who don’t do “generative design” or “3D animation”. Textiles, sculpture, painting, architecture, ... Many of them use calculus in one way or another. Check out the Bridges conference, http://bridgesmathart.org/ http://bridgesmathart.org/
- adamsea 7y ago
  Conceptual artists
emmelaich 7y ago
I hesitate to agree with you because this (website) is a nice interactive presentation. But it depends on the audience and more the depth of result required. If I was to introduce calculus to non-mathematicians, I'd use almost no maths at at. Not even symbols! I'd use area and slope, with specific examples - probably just distance, velocity and acceleration. I think you'd be able to reveal the magic relationship between slope and area with just that.
randomsearch 7y ago
Brilliant example. Strang is a great teacher, his book on linear algebra being another key text.
- enriquto 7y ago
  Yeah, I love the one that starts "All of linear algebra deals with the four following problems: Ax=b (where A either is square, tall rectangular or wide rectangular) and Ax=lx where A is square."
mulmen 7y ago
This is the exact example that made calculus “click” for me. Before that math was a chore and after this example it all seemed so much more useful. I wish I had seen it in junior high instead of college.

lewisjoe 7y ago

https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ https://ocw.mit.edu/resources/res-18-001-calculus-online-tex... I guess this is the one?

enriquto 7y ago
Yes, this one! Just read pages 1 and 2 of the pdf (I was writing from memory and my explanation is not exact).

GuiA 7y ago

Different people learn differently. Very few people learn all they know from a single source. Therefore, having many sources presenting a same subject in many different ways is a wonderful thing. Gilbert Strang’s book is wonderful! Some will find it to be the “best book” to learn calculus, others won’t. No need to poo-poo others’ work just to value signal. (I’m sure the authors would appreciate any constructive feedback though!)

enriquto 7y ago
But I'm not "poo-pooing" Kleitman's book! It's just that after reading the beginning I did not find it very engaging personally. It starts with numbers, and properties of real and complex numbers. The definite integral is not defined until half the book (while it is a simpler concept than the derivative). I prefer to start with calculus, and the relationship between integrals and derivatives right away. And then, much later, when you need some crucial property of real numbers, introduce it as required. You can do a great deal of calculus without needing to know the definition of real number!
- adamsea 7y ago
  ... somebody on the internet is wrong! ;) ... the question is who? Is it them? Is it me? Is it you?

TheOtherHobbes 7y ago

I can't imagine someone with an arts background getting anything at all out of this introduction. The Gilbert Strang approach is much clearer - although it's still not obvious why an artist would ever need calculus. In fact there are some applications in generative design and 3D animation, but it's still low on the list of essential art skills. And if you really need those effects - and know enough math to understand how to code them - you can copy code from a cookbook without having to derive it from first principles.

Chazprime 7y ago
These types of tutorials are pretty popular among VFX artists who may suddenly need to brush up on complex math, but don’t work with it consistently. Knowing the fundamentals of calculus comes in very handy when suddenly you’re tasked with working in Houdini for six months and have never touched the software before.
commandlinefan 7y ago
I don’t believe that anybody can really learn any math (much less calculus) by just reading about it without doing a lot of practice problems. It’s nice of this guy to put this together and all, and I guess it could pique somebody’s curiosity, but they’ll really need to pick up a good book with a LOT of sample problems to understand it any better than they understood it before they read this introduction.
mathgenius 7y ago
Artists may not need calculus, but calculus would certainly benefit from artists.
jacobolus 7y ago
There are a bunch of mathematical artists who don’t do “generative design” or “3D animation”. Textiles, sculpture, painting, architecture, ... Many of them use calculus in one way or another. Check out the Bridges conference, http://bridgesmathart.org/ http://bridgesmathart.org/
adamsea 7y ago
Conceptual artists

emmelaich 7y ago

I hesitate to agree with you because this (website) is a nice interactive presentation. But it depends on the audience and more the depth of result required. If I was to introduce calculus to non-mathematicians, I'd use almost no maths at at. Not even symbols! I'd use area and slope, with specific examples - probably just distance, velocity and acceleration. I think you'd be able to reveal the magic relationship between slope and area with just that.

randomsearch 7y ago

Brilliant example. Strang is a great teacher, his book on linear algebra being another key text.

enriquto 7y ago
Yeah, I love the one that starts "All of linear algebra deals with the four following problems: Ax=b (where A either is square, tall rectangular or wide rectangular) and Ax=lx where A is square."

mulmen 7y ago

This is the exact example that made calculus “click” for me. Before that math was a chore and after this example it all seemed so much more useful. I wish I had seen it in junior high instead of college.