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Introduction to Calculus (2016)

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Re: Introduction to Calculus (2016)

#11

Post by mcbits »

juliend2 wrote: post #2

I find it a bit paradoxical that those articles that aim to make calculus more approachable to everyday people are always assuming that those very people already know what the Sigma symbol means, or what [that]( http://juliendesrosiers.ca/uploaded/weird-math-symbol.png ) math symbol means. I see the author in this case is defining the delta and approximately-equal symbols, but I see quite a few non-obvious symbols in…

There is a footnote on page 10 that briefly explains both of those symbols, although I doubt many people would immediately understand the footnote if they weren't already familiar with the symbols and concepts.

Re: Introduction to Calculus (2016)

#14

Post by tracer4201 »

edtechdev wrote: post #9

Calculus in 20 minutes video: https://www.youtube.com/watch?v=L5GmSYipz6A More seriously though, I like the intuitive explanations and analogies used at BetterExplained: https://betterexplained.com/calculus/ Otherwise, you're just memorizing formulas you don't really understand and will forget eventually.

Ha! Fast forward 6 year after undergrad and thats me.

I'm doing the Khan academy series on calculus, starting with single variable calculus to refresh my math, to relearn the math for ML and Data Science. It's not my day job but I'm interested in the space so I can understand things under the hood instead of just using libraries.

In college, I was more obsessed with getting an A in my classes, terrified of any lessor score, and all that at the cost of not understanding much at all but just repeating formulas and techniques on tests.

For my kids some day, the biggest lesson I can teach them is that it's okay to fail. Getting straight As doesn't matter much at all, and you should always question things and think critically.

Re: Introduction to Calculus (2016)

#15

Post by ColinWright »

nso95 wrote: post #10

The early 1900s book “Calculus Made Easy” is a really good intro to calculus.

Seconded. I did calculus decades before I became aware of this book, but in reading it now I think it's excellent, and very much wish I'd known it before.

By contrast, I didn't find the submitted book very engaging, but I'm sure it's a matter of taste, and others will disagree.

Re: Introduction to Calculus (2016)

#17

Post by Koshkin »

edtechdev wrote: post #9

Calculus in 20 minutes video: https://www.youtube.com/watch?v=L5GmSYipz6A More seriously though, I like the intuitive explanations and analogies used at BetterExplained: https://betterexplained.com/calculus/ Otherwise, you're just memorizing formulas you don't really understand and will forget eventually.

On the other hand, a lot of things (not just in math) we think we understand are, in fact, simply memorized. And, by the way, that is not a bad thing - it is better to learn the multiplication table, for example, than to fail to "understand" it and give up. You can work on true understanding later; my advice, therefore, is to read as much as possible on a topic, however incomprehensible it may seem at first, just to get used to it and to make it look familiar, and do some exercises. You will soon feel that you understand something (even though you don't). That's the way we humans learn.

Re: Introduction to Calculus (2016)

#18

Post by cuckcuckspruce »

kyberias wrote: post #4

It wouldn't be that hard to make this HTML to make it much more accessible. Reading PDF on screen is horror.

The author explains his reasoning for PDF for this document here: https://arachnoid.com/latex/why_latex_pdf.html.

The author also has a Hacker News profile: https://news.ycombinator.com/user?id=lutusp

Re: Introduction to Calculus (2016)

#19

Post by iamcreasy »

nso95 wrote: post #10

The early 1900s book “Calculus Made Easy” is a really good intro to calculus.

This book is amazing. But I'd suggest everybody to read the version edited by Martin Gardner in 1998[1]. The first version written by Thompson ignored the use of limit, and it also used terms that aren't used anymore. For example, the older book used the term 'differential coefficient' which is now known as derivatives[2].

[1] https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/...

[2] More about the difference between old and the new book https://en.wikipedia.org/wiki/Calculus_Made_Easy

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