Vector Calculus (5cr)

Objectives

On this course the students learn to calculate the gradient, divergence and curl, and to apply identities containing these operators, especially for spherically symmetric vector fields. The students learn to parametrize curves, calculate line integrals of real- and vector-valued functions, find the potential function of a conservative vector field and use it in calculating the line integral. The students learn to parametrize surfaces using for example cylindrical and spherical coordinates, to find a normal vector to a surface, calculate surface integrals of real- and vector-valued functions, and use the Green theorem and divergence theorem.

Content

Core contentGradient, 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 knowledgeMass 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.

Further information

Partial completions of the course must be carried out during the same implementation round.This course belongs to the SEFI 2 level of engineering mathematics.