First major update of src/2_coordinates.md

src/2_coordinates.md

@@ -21,7 +21,7 @@ The most common coordinates are *Cartesian coordinates*, where we use a
 number $n$ of perpendicular axes. The coordinates corresponding to these
 axes are $x_j$ where $j=1, \ldots, n$.
 
-Cartesian coordinates are simple to describe and operate in. The coordinate axes are 
+Cartesian coordinates are simple to describe and operate on. The coordinate axes are 
 straight lines perpendicular to each other. It is therefore
 very easy to do calculations in Cartesian coordinates. For example,
 the distance $\Delta s$ between two points $(x_1, x_2, \ldots, x_n)$
@@ -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:
+    symmetry or functions given in terms of these coordinates. <br/>
+    Infinitesimal distance: 
     $$ds^2 =r^2 (\sin^2 \theta d\phi^2 + d\theta^2) +  dr^2 .$$
     Infinitesimal volume:
     $$dV = r^2 \sin(\theta) dr d\theta d\varphi.$$