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Elements of Complex Analysis
The most important theorems and tools for applications in physical field theory

Some fundamental theorems of complex analysis, in particular Cauchy's integral theorem and the residue theorem, are of outstanding usefulness for physical field theory. We discuss and give reasons for these mathematical tools without going excessively into the details, but still with sufficient accuracy, so that the physicist is not only enabled to apply the formulas correctly, but also to understand their context and background.
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Electromagnetic Units
In electrodynamics, various systems of units are commonly used, in which not only different numerical values, but different physical dimensions are assigned to quantities like charges or fields. We describe in this article, how the formulas of electrodynamics can be translated simply and efficiently in-between the various systems of units.
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The Partial Derivative
A misleading use of this notion, which differs from the conventional mathematical definition, is widely-used in physics.

According to a naming convention, which is widespread in physics, the notion “partial derivative” is being used for a type of derivative, which according to the naming convention prevailing in mathematics should better be called “explicit derivative” (more precisely: derivative with respect to the explicit variable).
We explain both naming conventions, and in particular put straight the notion “partial derivative”.
In the last section we point out, how ambiguous results can be avoided due to correct use of the partial derivative.
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Rotations and Translations
Proper Rotations, Mirrorings, und Translations of Cartesian Coordinate-Systems and Spherical Coordinate-Systems

The transformation matrices, which describe proper rotations, improper rotations (i.e. mirrorings), and translations in 3-dimensional Euklidean space, are derived for Cartesian coordinates and for spherical coordinates.
This article is written in german.
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Ekliptical and Equatorial Coordinates
The Conversion inbetween both Coordinates Systems

The definitions of both coordinates systems are explained, and a formula for conversion inbetween them is presented.
This article is written in german.
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