Hacker News with Generative AI: Calculus

Geometrically understanding calculus of inverse functions (2023) (tobylam.xyz)
Given a function such as \(\tan x\), could you write \(\frac{d}{dx} \arctan x\) and \(\int \arctan x \; dx\), just from \(\tan x\), \(\frac{d}{dx} \tan x\) and \(\int \tan x \; dx\)? With some caveats, the inverse function theorem answers the former while the Legendre transformation answers the later. We’ll approach this with as much geometric intuition as possible, avoiding the dry application of formulas.

Calculus, Mathematics, Geometry, Inverse Functions

126 points by tobytylam 4 days ago | 5 comments

100 Years to Solve an Integral (2020) (liorsinai.github.io)
The integral of sec(x) is well known to any beginners calculus student. Yet this integral was once a major outstanding maths problem. It was first introduced by Geradus Mercator who needed it to make his famous map in 1569. He couldn’t find it and used an approximation instead. The exact solution was found accidentally 86 years later without calculus in 1645.

Mathematics, History, Calculus

215 points by blobcode 19 days ago | 61 comments

Matrix Calculus (For Machine Learning and Beyond) (arxiv.org)
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions.

Machine Learning, Calculus, Linear Algebra, Mathematics

183 points by ibobev 40 days ago | 30 comments

Definite clause grammars and symbolic differentiation (bitsandtheorems.com)
Let's talk about calculus. It's an extremely important field for almost all branches of science, and you've probably seen at least some aspects of it during high school or possible further education. Applications range from physics, chemistry, and electrical engineering to finance, medicine, meteorology, and much more.

Mathematics, Programming, Calculus

13 points by gsky 60 days ago | 2 comments

Multiplicative Infinitesimals (github.com/Ericson2314)
This goes with Multiplicative Calculus, but where as that is mostly summarizing others work, this is original as far as I know, and so I split it out.

Mathematics, Calculus, Open Source

83 points by Ericson2314 120 days ago | 44 comments

Derivative at a Discontinuity (alok.github.io)
The title may seem like a contradiction. How can you differentiate something that’s not even continuous?

Mathematics, Calculus, Theory

134 points by yuppiemephisto 156 days ago | 62 comments

Heaviside’s Operator Calculus (2007) (deadreckonings.com)
An operational calculus converts derivatives and integrals to operators that act on functions, and by doing so ordinary and partial linear differential equations can be reduced to purely algebraic equations that are much easier to solve.

Mathematics, Calculus, Operators, Differential Equations

83 points by joebig 159 days ago | 28 comments

Ask HN: Can calculus be taught without differentiating or integrating by hand? (ycombinator.com)
Maybe the focus could be on solving Calculus problems with the help of a symbolic algebra system instead?

Education, Calculus, Mathematics, Tools

37 points by amichail 192 days ago | 99 comments

Calculus for Beginners and Artists (math.mit.edu)

Calculus, Mathematics, Education, Art

48 points by susam 286 days ago | 4 comments

Notes on Taylor and Maclaurin Series (thegreenplace.net)

Mathematics, Calculus, Education

91 points by ibobev 289 days ago | 32 comments

The algebra and calculus of algebraic data types (2015) (recurse.com)