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 Calculus with Python
#1
Hi there. I've been using Python in my calculus class for a few semesters now and have a decent draft collection of notebooks that I'm considering moving to a book, wanted to gauge interest in such an endeavor. The main idea is to integrate much more from the world of the approximate and statistics into the traditional content. Here is what my current outline would look like, appreciate any feedback or suggestions. I'd like to try to find a way that the Neural Network is the culmination of our work and we demonstrate how this contemporary idea relies on so much from Calc I under the hood.
    Section I
  1. Introduction to Python -- representing functions as tables, graphs, formulas
  2. Introduction to Python II -- control flows and the Babylonian Algorithm
  3. The Area Problem -- approximating areas with simple geometries
  4. Summations I -- Finite examples
  5. Summations II -- Moving to the infinite
  6. Back to Areas -- Riemann Sums
  7. Probability I -- Finite Examples
  8. Probability II -- Continuous Examples
  9. Putting it Together -- Filters and Convolution
    Section II
  10. Approximating Slope -- finite examples
  11. Invoking Infinity -- definition of derivative
  12. Linear Approximation
  13. Move to 3D -- Define and plot functions
  14. Partial Differentiation -- Derivatives with respect to anything
  15. Optimization I -- introduction to finding maximum and minimum values
  16. Optimization II -- the case of Least Squares
  17. Finding Zeros -- Newton's Method
    Section III
  18. Populations I: Arithmetic and Geometric Growth
  19. Populations II: Logistic Growth
  20. Solving ODE's: Euler's Method
  21. Application: Gradient Descent
  22. Application: Logistic Regression
    Section IV
  23. Introducing ANN's: The Perceptron
  24. Using Gradients: The Chain Rule
  25. Derivatives Again: Autodiff
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#2
See also here for a similar project:
https://python-forum.io/Thread-Book-Pyth...igh-school
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#3
Dear jfkoehler,

I'm working on a similar project. You can contact me we can discuss it. I'm Arnaud Bodin from Lille University).

Thanks to heiner55 for making connection!

Best,
Arnaud
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#4
Looks like a fairly comprehensive table of contents!
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