Analytic Number Theory
The Abel Summation Formula
Sums, Integrals, and Series
Calculus
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.