MATA182 Vector calculus 2 (5 cr)

Two and three dimensional integration, iterated integrals. Change of variables. Polar, cylindrical and spherical coordinates. Improper integrals. Vector fields, line integrals, the fundamental theorem for line integrals, Green's theorem. Parametric surfaces and surface integrals. Stokes' theorem and the divergence theorem.

After successful completion, the student 

• is able to calculate integrals of functions of two and three variables as iterated integrals, and change the order of integration if necessary
• knows how to use polar, cylindrical and spherical coordinates with integrals, and knows the general change of variables theorem
• is familiar with the multidimensional improper integral 
• can find and use parametrizations for curves and surfaces 
• can calculate curve and surface integrals of real-valued functions and vector fields (incl. calculation of curve length and surface area) 
• can apply the most important integration theorems for vector fields (Green's and Stokes' theorems, divergence theorem)

Calculus 1-3. (or Introduction to mathematical analysis 1-3 and Calculus 3). Vector calculus 1.

Adams: Calculus, chapters 14-16.

Stewart: Calculus, chapters 15-16.