Simple Fields of Physics by FEA

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Have you ever solved a partial differential equation?

The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the di [...]
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New version with color inside

Have you ever solved a partial differential equation?

The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the distribution of gravitation in free space. Other PDEs, for the electric and magnetic fields etc., are somewhat similar but more complicated.

Few of these equations have exact solutions, which explains why they do not receive the attention they deserve in the academic curriculum. Only in recent years has it become possible to solve PDEs numerically on an ordinary PC by finite element analysis (FEA).

The present book is unique in its approach. It is not another volume on conceivable algorithms of FEA. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots.

The main topics treated are the following.

Plotting Functions

Laplace and Poisson PDEs

Electricity

Magnetism

Heat

Problems in 3D Space

Electromagnetic Waves

Wave Mechanics

Fluid Dynamics