Description
A detailed tutorial on the Gram-Schmidt process. Step by step tutorial including a visual example of the Gram-Schmidt process for reference.
Overview
The Gram-Schmidt process is a process used for orthogonalizing a set of vectors in an inner product space. What the Gram-Schmidt process does is it takes a finite and linearly independent set and converts it to an orthogonal set that spans the same amount of space.
Description
A detailed tutorial on the solving of Fourier series. Step by step tutorial including several examples of how to solve the Fourier series for reference.
Overview
The Fourier series is very common in differential equations and partial differential equations. What a Fourier series does is decompose a periodic function into the sum of simple oscillating functions, like sine and cosine. Fourier series are part of Fourier analysis and were first introduced by Joseph Fourier to solve the heat equation. So another name for the Fourier series is the heat equation, although they are considered different things. Both the heat equation and the Fourier series are partial differential equations.
Description
A detailed tutorial of uniform convergence. Step by step tutorial including several example problems of uniform convergence for reference.
Overview
Uniform convergence is a very strong type of convergence, even stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does not depend on x. This concept is important because several properties of these functions are transferred to the limit f if the convergence is uniform.
Description
A detailed tutorial on the solving of the Dirichlet kernel. Step by step tutorial including several examples of how to solve the Dirichlet kernel for reference.
Overview
The Dirichlet kernel is this collection of functions: 
Description
A detailed tutorial on the solving of the Euler-Lagrange Equation. Step by step tutorial including several examples of how to solve the Euler-Lagrange Equation for reference.
Overview
The Euler-Lagrange Equation, sometimes just called Lagrange’s Equation, is a differential equation which has a solution that is function for which a given functional is stationary. The Euler-Lagrange Equation is an equation satisfied by a function q of a real argument t which is a stationary point of the functional 
After finding q, the derivative of q, and L, which can all be expressed by seperate equations. the Euler-Lagrange Equation can be written as an ordinary differential equation expressed by
Description
A detailed tutorial on the solving of problems using the Ritz Method. Step by step tutorial including several examples of how to solve problems with the Ritz Method for reference.
Overview
The Ritz Method, often called the Rayleigh-Ritz Method, is the finite element method used to find the eigenvalues of a Hamiltonian system. The Ritz Method starts out with a trial wave function, that is expressed as
From there, we can substitute a value for the trial wave function, which is
The final expected value can be written as:
Description
A detailed tutorial on the solving of De Moivre’s Theorem. Step by step tutorial including several examples of how to solve De Moivre’s Theorem for reference.
Overview
De Moivre’s Theorem was named after Abraham de Moivre. It states that any complex number (or any real number) x and any integer n that
This is called De Moivre’s Formula. This formula is important because it connects complex numbers with trigonometry.
Description
A detailed tutorial on the solving of Telegrapher’s Equations. Step by step tutorial including several examples of how to solve Telegrapher’s Equations for reference.
Overview
Telegrapher’s Equations, sometimes referred to simply as telegraph equations, are a pair of differential equations which meausre the voltage and current on a transmission line with regard to distance and time. An example would be a telegraph, hence the name. Instead of having an actual set of equations, Telegrapher’s Equations tend to more oftenbe expressed as a schematic, with the equations only being used for things such as loops and transmissions.
Description
A detailed tutorial on the solving of Poisson’s Equation. Step by step tutorial including several examples of how to solve Poisson’s Equation for reference.
Overview
Poisson’s Equation is a partial differential equation. It is used in sections of math that deal with engineering and physics. The formula is named after Siméon-Denis Poisson. There are a few different ways of expressing it. In general terms, this equation is expressed as:
However, in certain branches of math, it is written as 
A third way of expressing it is used in Cartesian coordinates, and it is written as:
