Vector Integral Calculus

This chapter discusses line, surface, and volume integrals, and describes the evaluation of these integrals in a particular coordinate system. It first reviews the concept of indefinite and definite integrals, and then discusses line integrals. The concept of a line integral is a simple generalization of the concept of a definite integral. If the curve is a constant-coordinate curve, the line integral reduces to the definite integral. The concept of a surface integral is a simple generalization of the concept of a double integral. The evaluation of the surface integral is quite difficult. If the surface is a constant-coordinate surface, this surface integral reduces to the double integral. The volume integral is a generalization of the triple integrals, which can be evaluated by three successive integrations. The chapter also discusses the divergence theorem of Gauss, Stokes's theorem and EMC applications.