calculus_playground

messing around with colab activities for calculus

Class Activities to find differentials using Colab, sheets, and Desmos:

1. Estimating Justin Jefferson's Position using a video on Youtube

2. Plotting the position and velocity of a ball dropped in the WSU Atrium

3. Finding the relationship between dA, s, and ds for the area of a square. This is extended for volume, a higher-dimensional volume s^7, and a square root function s^{0.5}. [ This uses a limiting process by shrinking dt ]

4. Finding relationships between dQ, t, and dt for exponential, logarithm, sine and cosine functions.

Basic Tempaltes for Colab

Basic Template: Desmos and Colab

Basic Template: Desmos and Google Sheet in Colab

Github and Colab Notes

Directions for having students sign up for Github and Colab

Desmos Notes

To have Desmos find the coefficients in your model using best-fit: 1) Create a table in Desmos. Change the table headings to something appropriate (e.g. x_1, t_1, l_1, or d_x1 or d_f1 2) Put in a function, like y = b + m x, that models the data. Do NOT use the sliders, and cancel sliders for b and m. 3) Change the = to a ~ and the variables to use the variables in the table (e.g. p_1 and t_1 instead of x and y) 4) Desmos gives you the best parameters for b and m. 5) This works for (any?) model you like. [ Trig functions might cause problems...]

Possible problems:
a) A missing value in the table
b) Dividing by zero causes problems - of course!  Be careful for things like y_1 ~ (1/x_1) sin(x_1) if 0 is one of the x_1 values.

Sheet Notes:

To let students work on a copy of a sheet:

Change the "edit" to "copy" in the url for the sheet.

Invite people to make a copy of a file in Docs, Sheets, Slides, or Drawings"" In Google Drive, open the file. Copy the file link from the address bar. In Gmail, click Plus Compose​. Paste the file link in the email and in the link, change edit to copy. When your email is ready, click Send. Note: If you haven’t shared the file, you’re prompted to share it now.

When the recipient clicks the link in the message, they’re instructed to click Make a copy. They can then work on a copy of the original document.

Approximation using derivatives

https://github.com/awangberg/calculus_playground/blob/main/Linear_and_higher_order_approximation.ipynb