> First-semester calculus has NO applications.
That said, the central ideas of calculus are firmly grounded in daily life (as Strang points out in the video): Differential calculus is about investigating speed (or, more generally, rate of change), and integral calculus is about investigating area.
[1]: http://www.maa.org/sites/default/files/0002989051112.di99173...
Also, you can measure boobs with integrals and model their jiggle with differential equations.
...I may have been a teenager when I was first learning. But modeling boob motion is apparently serious science and actually gets extremely complex when you try to model the interactions of the different constituent tissues.
That's the thesis of Dr. Bartlett's famous lecture "Arithmetic, Population and Energy": https://www.youtube.com/watch?v=sI1C9DyIi_8
Calculus is foundational for understanding our rapidly changing, data-driven world. It gives us the ability to see.
You can apply calculus anytime you have a quantity that's changing over time, and you want to see where things are going, how things are changing, and when something is going to happen based on its rate of change -- e.g. stocks, startup growth metrics, how an idea is spreading, mass-market adoption, etc -- anytime you have time-series data and you want to see what it means -- make sense out of it, and understand its implications.
See https://en.wikipedia.org/wiki/Calculus#Applications
And Calculus gives you the ability to calculate how lifelong learning can impact your growth over time -- the significance it can have throughout your life/career -- and realize it's never too late to learn anything ;-)
In the words of Prof John Ousterhout: "A little bit of slope makes up for a lot of y-intercept."
https://web.stanford.edu/~ouster/cgi-bin/cs142-spring12/week...
For example... what are sunspots? How does the plumbing around your house work? How does a car battery work? How does a microwave oven work?
Another thought. If we are unable to find applications for a technique, should we place such an emphasis on teaching it? I look around and see all the very practical (and interesting!) math and science that is not being taught, e.g. signal processing, just because they are nontraditional. It's a shame to me.
Thinking back, I just realized the main reason that I was bored to tears in high school wasn't so much that the subjects weren't worth knowing...just that at the time I was being taught formulas without any clear understanding of why it was useful to know it. If you don't know why it's useful to know it, there's very little reason to remember it beyond passing a test.
https://www.grc.nasa.gov/www/k-12/airplane/index.html
Obviously, it could use more work, but the kernel of something really good is there.
Additionally, I think game development is a compelling way to teach math and science.
I cant think of any obvious applications of calculus to the average non-technical person's daily life. If that's what you mean, you're going to have a bad time, as I think it's a misconception of what math is supposed to be for.
Examples with classic physics problems are good too. How about F=ma => F=m*dv/dt. Everytime you apply a force to an object calculus magic is there to mathematically describe the process.
https://www.amazon.com/Everyday-Calculus-Discovering-Hidden-...
The average person may only have to use basic arithmetic in daily life, but I'd argue that pretty much everybody could benefit from using more math (including calculus) in everyday life. I mean, just think of anything in life that can be counted/measured and can be described by a function that can be optimized. Boom, there's an application for calculus - minimization and maximization.
This is why I disagree with the recently popular narrative about how "we don't need to teach all kids calculus" and "math isn't all that important", etc. Me, I wish I'd studied more math when I was younger. I feel like you almost can't teach too much math. If anything, I'd say the problem is a combination of pedagogy and not spending enough time on applications when teaching math.