Infinitesimal Calculus
of One Complex Variable

This page is a sub-page of our page on Infinitesimal Calculus.

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The sub-pages of this page are:

Complex Derivative
Complex trigonometry
Conformal Mapping
Inversion
Möbius transformations
Conformal Mapping
Stereographic Projection
The Riemann Zeta function

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Related KMR-pages:

Einstein for Flatlanders

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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.

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The complex exponential function

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Electromagnetic radiation

A planar electromagnetic wave:

The interactive simulation that created this movie.

The electric part of the wave: \, E(\mathbf{\hat{k}}, \mathbf{x}, \omega, t) \, = \, e^{ \, i \,(\mathbf{\hat{k}} \cdot \mathbf{x} \, - \, \omega \, t)} \,

The magnetic part of the wave: \, B(\mathbf{\hat{k}}, \mathbf{x}, \omega, t) \, = \, e^{ \, i \, (\mathbf{\hat{k}} \cdot \mathbf{x} \, - \, (\omega \, + \, \pi/2) \, t)} \,

The entire wave: \, E_m(\mathbf{\hat{k}}, \mathbf{x}, \omega, t) \, = \, E(\mathbf{\hat{k}}, \mathbf{x}, \omega, t) \, + \, B(\mathbf{\hat{k}}, \mathbf{x}, \omega, t) \,

Its Poynting vector : \, S \, = \, \frac{1}{{\mu}_0} \, E \, \times \, B

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Electromagnetism

Maxwell and Dirac theories as an already unified theory

Conceptual background:

Geometric Algebra

Clifford Algebra

Historical background:

The Evolution Of Geometric Arithmetic

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Angels and devils: exp(z + p) for different values of p (moving black dot):

Devil transformed by exp(z+p) for different values of p (moving red dot):

Interactive simulation of the devil transformed by exp(z).

Complex trigonometric functions

Devil transformed by complex sin: sin(z+p) for different values of p (moving red dot):

Interactive simulation of the devil transformed by sin(z).

Angels and Devils transformed by complex sin:

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