Our first 5 weeks of Calculus

Here are the 11 projects calculus-related projects that we’ve done to start the school year:

(1) Working through Calculus with my older son

The concepts in this project were based on ideas discussed in Grant Sanderson’s amazing video series “Essence of Calculus”.   The specific video we were working with here was the “Geometric Derivatives” one.

Here’s the project:

Working through Calculus with my older son

(2) What a kid learning calculus can look like

The problem here is finding a line that is perpendicular to a parabola. Here’s the project:

What a kid learning calculus can look like

(3) A beginning Calculus example

In this project my son works through a common introductory calculus problem about finding the largest area for a rectangle with a given perimeter.

A beginning calculus example

(4) An Introductory implicit differentiation example thanks to Patrick Honner

I mentioned on twitter that we were working on implicit differentiation and Patrick Honner gave me a good challenge problem to share with my son:

An introductory implicit differentiation example thanks to Patrick Honner

(5) Working through a challenging calculus problem

This was a pretty challenging problem I found in the calculus book we are using – Stewart edition 3.   The problem is about a light casting a shadow as it shines on ellipse.

Working through a challenging calculus problem

(6) Struggling through a related rates problem

This was a neat trig problem about finding the 3rd side of a triangle changes as the angle between the two known sides changes:

Struggling through a related rates problem

(7) Learning about approximations

For this project we explored how to use calculus to find approximations to values of some common functions:

Learning about approximations

(7.5) Playing around with Newton’s Method

This was a project that I did with both my younger and older son.  The topic was Newton’s method.  I didn’t want to skip it because it was a neat application of calculus, but I also didn’t want to dive too far into the details and thought my younger son would enjoy learning a bit about it, too.

Playing Around with Newton’s Method

(8) Applied Max / Min problems

This project showed how to use calculus to find the largest square that you could inscribe in an equilateral triangle (with one side on the base of the triangle).

Applied Max / Min Problems

(9) A fun calculus project -> folding a circle wedge into a cone

This project was a classic -> finding the largest volume you could make by folding up a wedge of a circle into a cone.

Folding a circle wedge into a cone

(10) Finding the Area of a Circle using Riemann Sums

The motivation for this project was showing how a seemingly impossibly to sum Riemann sum could actually be understood as giving the area of a circle.

Finding the Area of a Circle using Riemann Sums