1. The problem statement, all variables and given/known data a) Assuming the presence of sources (J flux density) and (p charge density) , write out Maxwell’s equations in the time domain in terms of and only for a lossless, but inhomogenous medium in which ε = ε(r) , μ = μ(r). b) Derive the vector differential equation (wave equation) satisfied by E(r,t) in a source-free, lossless, inhomogenous medium. (There are lines on the "r"s indicating that they are position vectors) 2. Relevant equations maxwell's equations and the equations that relate D&E and B&H (I am not sure about which forms should be used) 3. The attempt at a solution I am blowing my mind over this but couldn't see what is being meant by inhomogeneous medium. Obviously I am not asked for the inhomogeneous wave equation (it is not in the curriculum), so I thought this was about anisotropic medium where ε&μ are different for different positions, but when I read about it, I've encountered lots of stuff I haven't even heard about (like tensors). Please give me a starting point. D=εE , but if ε is not constant, it is not a scalar. If it's not a scalar, how is D=εE true? Or is ε a tensor and since it is a matrix I should treat it like a scalar? Then what is the difference of the answer from constant ε&μ wave equation? Please help I am desperate.