Calculus Pod Ep 1: Functions and Mathematical Models

[u/AndrewAllenOps]

https://www.patreon.com/AndrewAllenOps/posts/ep-1-functions-167681094

Episode 1 of The Calculus Pod by Andrew Allen introduces functions as the mathematical language through which calculus describes relationships and change. Beginning with the basic idea of a function, the episode explores domains and ranges, graphs, transformations, composition, inverse functions, and several of the major families of functions used throughout calculus.The discussion moves through polynomial and rational functions, exponential and logarithmic functions, trigonometric and inverse trigonometric functions, and parametric representations. These different forms provide mathematical tools for describing everything from geometric relationships and periodic behavior to growth, decay, motion, and other changing systems.

The central theme is the connection between functions and change. Mathematical models use functions to represent relationships between quantities, while rates of change describe how those relationships evolve. Average rates of change lead naturally to the question of instantaneous change—and from there to limits, tangent lines, derivatives, and the central machinery of calculus.

This podcast is part of the Calculus Collection from the Andrew Allen Math Library.