Analytic Number Theory

### The Abel Summation Formula

Sums, Integrals, and Series

Analytic Number Theory

Sums, Integrals, and Series

Calculus

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

And Deriving a Beautiful Identity in the Process

Calculus

How to Derive the Equation of the Catenary

Calculus

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

Calculus

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

Feynman

A Clever Way to Quickly Take Derivatives Used by Richard Feynman

Calculus

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

Calculus

Intuitive ideas about the derivative

Calculus of Variations

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

Calculus

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

Calculus

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