you can check out the latest gate syllabus for ECE.

Linear Algebra:
Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Mean value theorems, Theorems of integral calculus, Evaluation of definite and
improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier
series. Vector identities, Directional derivatives, Line, Surface and Volume integrals,
Stokes, Gauss and Green's theorems.