It's fair to say that vector-calculus is a pre-requisite for differential geometry.dextercioby said:Actually everything comes from differential geometry.U'll see that the laplacian is the trace of the hessian and it can be written in terms of differentials and codifferentials.
Vector calculus is not compulsory for PDE-s.Linear algebra,multivariable calculus (partial derivatives),complex analysis (and special functions) and ODE-s are.
There are several reasonsNusc said:Could anyone tell me why Vector Calculus would be a prequisite or a co-requisite? Specifically, what topics are required to know vector calculus in PDE's?
I suspected a course in ODE's would be enough.