Invariants of linear parabolic differential equations

The paper is dedicated to construction of invariants for the parabolic equationut+a(t,x)uxx+b(t,x)ux+c(t,x)u=0.ut+a(t,x)uxx+b(t,x)ux+c(t,x)u=0.We consider the equivalence group given by point transformations and find all invariants up to seventh-order, i.e. the invariants involving the derivatives up to seventh-order of the coefficients a, b and c with respect to the independent variables t, x.