Brief descriptions do not work,. You need to learn it.
A differencial equation, with several variables.(2) Partial Differential Equations and Applications
What Riemann made, it is use in General Relativitty. It is a more abstract approach to what a surface is and what the next thing you asked.(3) Differential Geometry
Calculus does not only need to be done in the standard xy-plane. Meaning on a sheet, it generalizes to Manifolds which are a much more general type of structure on which Calculus can do done.(4) Calculus on Manifolds
Also known as Calculus I.(5) Differential Calculus
The other course are extremely advanced and are only studied by people going into math in full detail.