Calculus with Python

Here is my class on Calculus with Python. This is not a normal Calculus I class, but rather a contemporary approach that values topics from probability and statistics in addition to the classical concepts. We use the computer and code to explore exact and approximate approaches.

Syllabus

Lesson I
Area

This lesson aims to develop formulas for area of simple geometric shapes.

Lesson 2
Number

In this lesson, we introduce less friendly numbers. Specifically, we are interested in exploring irrational numbers and approximating square roots by hand.

Lesson III
Getting Transcendental

Now, we turn our attention to approximations of pi. From Babylonian approximations to Ulam's Monte Carlo experiments, we dedicate time to a particularly special constant.

Lesson IV
Pascal's Triangle

Now, we move to explore combinations and counting. From ancient Egyptian games to crypto kitties, we encounter problems that express themselves in the classic triangular tool.

Lesson V
Integer Summations and Patterns

Now, we turn to examine patterns in summations and connect these to some early problems in area approximation.

Lesson VI
Functions and Area

Using our work with summations, we approximate and evaluate exactly areas defined on closed intervals. We essentially develop the machinery of the Riemann integral, and explore its development with code as well.

Lesson VII
Average Value and Monte Carlo

In this section, we explore approximation strategies for approximating integrals. In these examples, we