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First major update of src/2_coordinates.md

Merged Maciej Topyla requested to merge maciejedits into master
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@@ -358,22 +358,22 @@ We have discussed four different coordinate systems:
2. !!! tip "Polar coordinates"
$${\bf r} = (r, \phi).$$ This system can be used in two
dimensions. It is particularly suitable for systems with circular symmetry or functions
given in terms of these coordinates. \\
given in terms of these coordinates. <br/>
Infinitesimal distance: $$ds^2 = dr^2 + r^2 d\phi^2.$$
Infinitesimal area: $$dA = r dr d\varphi.$$
3. !!! tip "Cylindrical coordinates"
$${\bf r} = (r, \phi, z).$$ This system can be
used in three dimensions. It is particularly suitable for systems with axial symmetry
or functions given in terms of these coordinates.
or functions given in terms of these coordinates. <br/>
Infinitesimal distance: $$ds^2 = dr^2 + r^2 d\phi^2 + dz^2.$$
Infinitesimal volume:: $$dV = r dr d\varphi dz.$$
Infinitesimal volume: $$dV = r dr d\varphi dz.$$
4. !!! tip "Spherical coordinates"
$${\bf r} = (r, \theta, \phi).$$ This sysytem can be
used in three dimensions. It is particularly suitable for systems with spherical
symmetry or functions given in terms of these coordinates.
Infinitesimal distance:
Infinitesimal distance: <br/>
$$ds^2 =r^2 (\sin^2 \theta d\phi^2 + d\theta^2) + dr^2 .$$
Infinitesimal volume:
$$dV = r^2 \sin(\theta) dr d\theta d\varphi.$$
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