Abstract: In the textbook of mathematical physics method, the divergence and curl of vector field in orthogonal curvilinear coordinates are widely used but there is no general proof. Based on the definition and physical meaning of the divergence and curl, this paper gives the proof and typical application of the divergence and curl of the vector field in the orthogonal curvilinear coordinates using the basic calculus method,which is a good reference for students to understand and apply.

Key words: orthogonal curvilinear coordinates, divergence, curl, vector field