Calculus is widely regarded as one of humanity's greatest intellectual achievements. Developed to model continuous change and motion, it serves as the mathematical foundation for modern physics, engineering, computer science, economics, and data science. In the late 17th century, two mathematical…
Episode: 1633 In which a Cambridge don doubts his own calculus teaching. Today, a mathematician misses the point. To embed this piece of audio in your site, please use this code: This article is part of the podcast Engines of Our…
When we study mathematics, or encounter its philosophy, we feel as if we are looking at some cold, detached 'puzzle of symbols.' However, if we stare intently at the systems of that abstract world and bring them back to human…
Opening a calculus textbook can be intimidating. A single chapter may contain dozens of exercises. A complete textbook may contain …
Derivatives and integrals form the heart of introductory calculus. One describes how quantities change …
A University of California, Berkeley teaching professor says some students arrive in calculus with gaps in mathematics extending to fractions and basic algebra, intensifying a debate over the UC system's test-free admissions policy. Zvezdelina Stankova set out the claim on…
The Assam Tribune In school, I was not taught how to solve such equations
This post provides a couple examples to go along with two earlier posts. The pattern we’re illustrating is families of polynomials pn(x) that each satisfy a differential equation and a three-term recurrence. The differential equations have a second solution…
Special functions often have arcane names that not very helpful without some context. The previous post goes into some reasons for this. This post will expand on a point at the end of the post about “modified” functions. Things are…
In science and engineering classes, you might describe a system using Newton’s laws and end up with a differential equation. You then solve the differential equation, analytically or numerically, to see how the solutions behave. You might also do the…
Analysis and differential equations: functions, series, Fourier analysis and calculus ideas, and research on the equations of change.
An article joins this feed when it matches these terms. Each one is also a search of its own.