Curvilinear Coordinates

In many applications physical systems possess symmetry. For instance, the magnetic field of an infinite vertical wire with a current flowing through it has a cylindrical symmetry (i.e. the field depends only on the distance from the wire), while the field radiated by a point source has the characteristic spherical symmetry (i.e. depends only on the distance from the source). In these and many other cases Cartesian coordinates is not the most convenient choice; a special choice of the coordinates (such as e.g. cylindrical or spherical ones for the two examples mentioned above, respectively) may however simplify the problem considerably and hence enable one to obtain a closed solution. In particular, investigation of a large number of physical problems require solving so-called partial differential equations (PDE).