This chapter covers
- Modeling algebraic expressions as data structures
- Writing code to analyze, transform, or evaluate algebraic expressions
- Finding the derivative of a function by manipulating the expression that defines it
- Writing a Python function to compute derivative formulas
- Using the SymPy library to compute integral formulas
If you followed all of the code examples and did all the exercises in chapter 8 and chapter 9, you already have a solid grasp of the two most important concepts in calculus: the derivative and the integral. First, you learned how to approximate the derivative of a function at a point by taking slopes of smaller and smaller secant lines. You then learned how to approximate an integral by estimating the area under a graph with skinny rectangles. Lastly, you learned how to do calculus with vectors by simply doing the relevant calculus operations in each coordinate.