# Basic Equations of Ideal One-Fluid Magnetohydrodynamics (Part III & IV)

Derivation of the continuity equation and the vorticity equation and a “proof” of one of its consequent equations.

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# Basic Equations of Ideal One-Fluid Magnetohydrodynamics (Part III & IV)

# Solution to Laplace’s Equation

# Solution to Legendre’s Differential Equation

# Solution to the three-dimensional Heat Equation

# Deriving the speed of light from Maxwell’s equations

# Electron Scattering of a Step Potential

# Basic Equations of Ideal One-Fluid Magnetohydrodynamics (Part II)

Derivation of the continuity equation and the vorticity equation and a “proof” of one of its consequent equations.

This post deals with the familiar (to the physics student) Laplace’s equation. I am solving this equation in the context of physics, instead of a pure mathematical perspective. This problem is considered most extensively in the context of electrostatics. This equation is usually considered in the spherical polar coordinate system. A lot of finer details […]

Solution to the Legendre Differential Equation by Power Series Method

Solution to the Three-Dimensional Heat Equation in Rectangular Coordinates

Derivation of the speed of light from Maxwell’s equations

Electron Scattering of a Step-Potential.

Continuing with the derivation of the ideal one-fluid MHD equations, the next equation governs the motion of a parcel of fluid (in this case plasma). This momentum equation stems from the Navier-Stokes’ equation. The derivation of this equation will be reserved for a future post. However, the solution of this equation will not be attempted. […]