Introduction
Why Calculus?
Calculus is the mathematics of change. It was invented independently by Newton and Leibniz in the 17th century to solve problems that algebra couldn't — the slope of a curve at a single point, the area under an arbitrary shape, the motion of planets.
Today, calculus underpins:
- Physics -- every differential equation in mechanics, electromagnetism, and quantum theory
- Engineering -- control systems, signal processing, structural analysis
- Machine learning -- gradient descent is pure applied calculus: minimize a loss function by following the negative gradient
- Finance -- Black-Scholes option pricing, continuous compounding
- Computer graphics -- curves, surfaces, and physically-based rendering
Why Implement It in C?
Most calculus courses focus on analytic techniques: the power rule, integration by parts, u-substitution. This course takes a different angle — you implement the numerical algorithms that compute what pen-and-paper calculus describes.
This approach:
- Reveals the limit definition of the derivative as actual code
- Shows why some methods converge faster than others
- Prepares you for scientific computing, simulation, and numerical analysis
- Builds deep intuition: you can't implement something you don't understand
What You Will Learn
This course covers the core of Calculus 1 through C implementations:
- Limits & Derivatives -- Numerical limits, central difference formula, second derivative, tangent line linearization
- Derivative Applications -- Newton's method for root finding, finding critical points, the Mean Value Theorem
- Integration -- Left/right Riemann sums, midpoint rule, trapezoidal rule, Simpson's rule
- Integral Applications -- Average value, area between curves, volume of revolution (disk method)
Every function uses function pointers — C's way of passing functions as arguments. This is the gateway to understanding higher-order functions and functional programming.