diff --git a/src/2_coordinates.md b/src/2_coordinates.md index 9018b5964f0772f10e1a61ff4eb3374eb5258074..53b6c4eccd4949a3649ca02e5135ad9c374916da 100644 --- a/src/2_coordinates.md +++ b/src/2_coordinates.md @@ -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: $$dV = r^2 \sin(\theta) dr d\theta d\varphi.$$