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goku12today at 2:36 AM6 repliesview on HN

There ought to be something similar for calculus too. While a detailed and formal treatment of the subject can be delayed till the age at which it's introduced now, I feel that the intuition and feel for calculus can be formed more efficiently at an earlier age.

If nothing else, it may help them understand where to seek solutions for the common problems they encounter. I started learning Electronics at a fairly young age using undergraduate level textbooks that I found lying around. The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.

PS: If anybody is wondering, those books were from an earlier generation engineer. They were very interesting, to say the least. All the circuits (amplifiers, rectifiers, oscillators, multivibrators, mixers, various RF Txr and Rxr designs, etc) were using vacuum tubes! Diodes, triodes, pentodes, thyratrons, magnetrons, TWTs, etc were used liberally in them. It had a description of an early form of the Instrumental Landing System (ILS). There were also descriptions of some early generation semiconductor devices and their similarity to vacuum tubes. I don't think ICs were in much use back then, because the book had no mentions about them.

I used to spend hours at a time with those books when I was a child. Later I graduated in Electronics engineering and went on to work on the avionics for a satellite launcher. Vacuum tubes were museum pieces by the time I was born. But I was the only one in my undergraduate class who had seen or knew anything about vacuum tubes, when we had lessons on CRTs, magnetrons, etc. I can't stress how deeply those books influenced my education and career. Sweet memories!


Replies

smj-edisontoday at 4:31 AM

> The need for and relationships between concepts in calculus, logarithms and trigonometry were a recurrent problem for me.

Oh my gosh, this was me growing up! I loved tinkering with electronics and programming, but I kept bumping against my lack of knowledge wrt more advanced math topics. I usually hacked around it, or more often just switched to a different project.

Now that I'm taking calculus, I feel like I always have a corresponding application for each topic we cover. It's very exciting!

cultofmetatrontoday at 7:20 AM

> There ought to be something similar for calculus too.

mathacademy.com very thourough and highly effective.

globular-toasttoday at 8:47 AM

They shouldn't teach calculus like they taught it to me and my peers. Basically we just one day started "differentiating" equations. We learnt a completely mechanical process. Like how to chop an onion, except it doesn't actually feed you or taste delicious.

It took me a while to realise the point. It's all about rates of change. They should start with that. No need to bother with the maths, just look at graphs and be like "that's a steeper slope than that", and, ooh, that one's sloping in the opposite direction. This is a fundamental intuition that's so useful to have. Most people don't understand that braking is acceleration. They just don't have the mental model that lets them see fuel burn and braking as opposite things. The sooner this intuition is there the better. Then teach the maths.

in_cahootstoday at 3:32 AM

My father introduced this book to me when I was around 10. I will forever be grateful.

https://www.worldofbooks.com/products/calculus-the-easy-way-...

WalterBrighttoday at 4:18 AM

Basic integration and differentiation would fit right in with algebra class. You can teach it in about half an hour.

WalterBrighttoday at 4:14 AM

The tube circuits I studied were marvels of clever engineering.