Posts Tagged ‘partial differential equations’
Thursday, September 24th, 2009
Introduction to the Fourier Series
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.
Tags: cosine, decompose, differential equations, Fourier analysis, Fourier series, function, functions, heat equation, Joseph Fourier, Math, oscillating, partial differential equations, periodic function, simple, sine, sum
Posted in Differential Equations | No Comments »
Tuesday, September 22nd, 2009
How to Solve the Helmholtz Equation
Description
A detailed tutorial on the visual representation of the Helmholtz Equation. Step by step tutorial including several examples of the visual representation of the Helmholtz Equation for reference.
Overview
The Helmholtz Equation is an elliptic partial differential equation, which can be used to calculate waves. It is similar to the wave and heat equations in that manner, but the formula is very different. The formula can be expressed as 
where k is the wavenumber and A is the amplitude. The Helmholtz Equation is often used for problems involving partial differential equations in both space and time.
Tags: amplitude, elliptic, helmholtz, helmholtz equation, partial differential equations, Physics, Science, space, time, wavenumber, waves
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Friday, September 18th, 2009
How to Solve the Wave Equation
Description
A detailed tutorial on the solving of the wave equation. Step by step tutorial including several examples of how to solve the wave equation for reference.
Overview
The wave equation is an important equation in partial differential equations. In its basic form, it is expressed as:
Every so often, for questions involving dispersion, the variable c must be changed to 
Tags: constant, dispersion, electromagnetics, hyperbolic, light wave, partial differential equations, Physics, Science, sound wave, velocity, water wave, wave equation
Posted in Differential Equations | No Comments »
