It's Time For An Intuition-First Calculus Course

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Kalid,

I am just about finished with your book, “Math, Better Explained.” I love it! The way you present the topics is incredibly easy to follow. I’m very fortunate to have stumbled upon this website (not literally) to see that there is a wealth more of your stuff to learn from.

Certainly helps that you’ve got some wit and humor. Helps me maintain motivation to really grasp a concept. Look forward to perusing your website and am excited for your intuitive calculus course.

Thanks,
Derek

Thanks Derek, I really appreciate the kind words. I try to write things as I wish a teacher told them to me – and if someone isn’t having a good time when they’re explaining, you’re probably not having a good time when learning! =). The course should be out in the very near future. Thanks!

It seems there is a mistake:
2pi(r + 1) - 2pir = 2pi+1 (not just 2pi).

Isn’t it?

I need help in INTUITING DARK ENERGY. I know what it is. My phone is 301 774 9256 or send me an E-mail with a contact number. My wife looks at E-mails, I do not.

Sorry, it was right… You can delete my previous comment =)

I really don’t understand how the effort would be same when there is a change in shape there will be a change in effort too…you mean to say putting a fence around a 200 meter circle and 400 meter circle will require the same effort is same…

Calculus Zen master: I see the true nature of things. We’re changing a 1-dimensional radius and watching a 1-dimensional perimeter. A dimension in, a dimension out, it’s like making a fence 1-foot longer: the initial size doesn’t change the work needed. The gap could be made around a circle, square, rectangle, or Richard Nixon mask, and it’s the same effort for similar shapes. (And, silly me, I’d forgotten the equation for circumference anyway!)

Thanks Tim, I agree. I like introducing derivatives and integrals together – they’re a pair – and then the FTOC seems like a natural conclusion (they really are a pair!). I don’t like teaching limits, derivatives, and integrals in isolation and then “glue them together”. I think we can have a natural intuition that the parts fit together, without waiting for the FTOC to tell us.

Taylor’s Theorem is a good follow-up too, and I like the philosophical implications of it (successively refining imperfect models to recreate the original).

Today was an important day in my understanding of calculus. It took me a long, hard year to understand the fundamental theorem, and then it took me three more months to understand Taylor’s theorem. But today I could roughly see how the nth derivative of c , always somewhere between a and b, decreases the error term in direct relation to the number of terms, and as the denominator becomes proportionately large.

In my own experience, the fundamental theorem should be introduced in the beginning, maybe just a glimpse or two, so the student knows where the derivatives and integrals are going. Likewise, with the Taylor theorem, it wouldn’t hurt to see, however abstract, the remainder theorem first.

I’m glad to have stumbled across your website (from the interview on Coursera: Learning How to Learn). I absolutely love math and used to go off topic during classes to find the very intuition you explain here. There was never enough time to do both learning and completing the course requirements. So I’m super excited to finally get to understand!! Thank you so much :slight_smile:

H Kalid,
When asked ‘what is the best book for calculus(beginners)?’ , Arjun, my friend told me about your website.and I was like’ what difference is it gonna make? ’ but i saw the difference. I was amazed by the way You began a calculus course…i was wondering for days, ‘What actually is this calculus?’ and i was enlightened after reading your intro.
I am gonna read the whole of your calculus book…

sry, that was Hi Kalid