Calculus – Cantor's Archive

Analytic Number Theory

The Abel Summation Formula

Sums, Integrals, and Series

Calculus

The Best Numerical Derivative Approximation Formulas

Approximating derivatives is a very important part of any numerical simulation. When it is no longer possible to analytically obtain a value for the derivative, for example when trying to simulate a complicated ODE. It is of much importance though, as getting it wrong can have detrimental effects on the

Calculus

Exploring a Different Kind of Calculus

And Deriving a Beautiful Identity in the Process

Calculus

Determining the Shape of a Hanging Cable Using Basic Calculus

How to Derive the Equation of the Catenary

Calculus

Two Myths of Numerical Integration, Debunked

Many programmers believe that the use of higher order integration algorithms, combined with a large number of integration interval…

Calculus

An Easier Way to Deal with Derivatives

An easier method to evaluate the product and quotient rule, and display their symmetry.

Feynman

Finding Derivatives of Complicated Functions According to Feynman

A Clever Way to Quickly Take Derivatives Used by Richard Feynman

Calculus

The Famous Problem of the Brachistochrone

From Newton’s “Lion Claws” to the Modern Solution

Calculus

Calculus You Forgot (Or Never Learned): Derivatives

Intuitive ideas about the derivative

Calculus of Variations

Introduction to the Brachistochrone Problem — Finding the Time to Slide Along a Path

It seems like the most common introduction to the Calculus of Variations is to talk about the Brachistochrone problem. It goes like this.

Calculus

Let’s Derive the Power Rule from Scratch!

From nothing but the definitions of derivatives and exponentiation, we’ll prove one of the first derivative rules you’ll learn in college

Calculus

The Intuition Behind Integration

An introduction to integral calculus with a focus on the core concepts and the beautiful intuition that lies behind the algebra.