Vector Calculus, 5 cr

Core content

• Gradient, divergence and curl, and identities containing these operators.
• Curve and its parametrization, derivative and smoothness, orientation of curves, curve length, line integral of a real-valued function and of a vector field. Green's theorem and two-dimensional divergence theorem.
• Conservative vector field, potential function and how to find it, gradient theorem and path independence.
• Surface and its parametrization, surface area, surface integral of a real-valued function, orientation and border curve of a surface, flux of a vector field and divergence theorem.

Complementary knowledge

• Mass and center of mass of a curve.
• Mass and center of mass of a surface, Stokes' theorem.
• Using a computer program as a tool in solving the exercise problems.