Pre-requisites for the NPTEL course on Classical Field Theory
• An open mind!
• A willingness to attempt the problem sets.

Most students who take the course at IITM have done at least one course in Classical Mechanics, Electromagnetism and Quantum Mechanics. I have had students who didn't have such a background but nevertheless managed to do well after huffing and puffing through the initial part of the course. I don't assume any mathematical background beyond some knowledge of vector calculus. In more detail, the following equations should seem familiar to you.

(1)
\begin{eqnarray} L &=& \tfrac12 m |\dot{\mathbf{x}}|^2 - V(\mathbf{x})\ . \\ p &=& \frac{\partial L}{\partial \dot{q}}\quad,\quad H = p \dot{q} - L \\ \nabla \cdot \mathbf{E} & = & 4\pi \rho \quad,\quad \nabla \times \mathbf{E} +\frac{1}{c}\frac{\partial \mathbf{B}}{\partial t}=0 \\ \nabla \cdot \mathbf{B} & = &~0~~\quad,\quad \nabla \times \mathbf{B} -\frac1{c}\frac{\partial \mathbf{E}}{\partial t}=\frac{4\pi}{c} \mathbf{J}\\ \frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{J}&=&0 \\ \epsilon_{ijk} \epsilon_{ilm} &=& \delta_{jl}\delta_{km} - \delta_{jm}\delta_{kl} \\ \int_V dV\ \nabla\cdot \mathbf{A} &=& \int_{S=\partial V} \mathbf{dS}\cdot \mathbf{A} \end{eqnarray}

If Maxwell's equations as written above look a bit unfamiliar, it is because they are written in Gaussian_units that is natural to special relativity. In these units, charge is measured in statcoulombs and $\mathbf{E}\textrm{ and } \mathbf{B}$ are measured in the same units among other things.