Numerical Analysis
Deriving the Quadratic Equation From the Roots Up
Solving Quadratics using gradients at the roots
Numerical Analysis
Numerical Analysis
Sextic Polynomials — A Practical Approach
At a young age a builder taught me how to mark out a right angle using the 3,4,5 triangle rule with a tape measure. That math practicality has stuck with me and recently I have been working to decipher it into its ‘LEGO block’ constituents to increase intuitive
Numerical Analysis
The Simplest Cubic Root
A very simple Cubic polynomial root approximation using architectural symmetry and similar triangles
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
Differential Equations
Numerical Solvers for ODEs
An introduction to Euler methods
Linear Algebra
A Guide to Inverting Matrices for Analysts
One of the oldest and most thoroughly studied problems in both linear algebra and numerical analysis is finding solutions for Ax = f. In a first linear algebra class, one might learn about how to identify what matrices are invertible, and calculate inverses by hand (very likely by means of Gaussian
Numerical Analysis
Cubic Polynomials - Rotation to Calculate Roots
Exploiting the amazing symmetry of cubic polynomials to quickly find the first root using Newton’s method.