On completion of the course, the student should be able to
account for basic concepts and theorems within the vector calculus;
demonstrate basic calculational ability concerning the concepts in the previous point such as to be able to calculate line and surface integrals and manipulate formulae involving the nabla operator;
account for basic concepts in the theory of infinite series;
demonstrate basic calculational ability concerning the concepts in the previous point such as to be able to use convergence criteria and handle power series.
Vector fields. Cartesian and curvilinear coordinates. The nabla operator. Divergence and rotation. Line integrals. Conservative fields. Divergence free and rotation free fields. Scalar and vector potentials. Surface integrals. Green's, Gauss' and Stokes' theorems. The Laplace operator. The equations of Laplace and Poisson. Physical interpretations. Complex number sequences and series. Convergence. Comparison criteria. The integral criterion. The quotient criterion. Absolute and conditional convergence. Power series and their properties. Applications.
Lessons in large and small groups.
Written examination at the end of the course.
The course may not be included in the same higher education qualification as Calculus of several variables.