# Geometry and Analysis III

5 credits

Syllabus, Bachelor's level, 1MA212

Code
1MA212
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Pass with distinction, Pass with credit, Pass, Fail
Finalised by
The Faculty Board of Science and Technology, 28 September 2023
Responsible department
Department of Mathematics

## Entry requirements

3 credits mathematics. Participation in Geometry and Calculus II.

## Learning outcomes

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.

## Content

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.

## Instruction

Lessons in large and small groups.

## Assessment

Written examination at the end of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

## Other directives

The course may not be included in the same higher education qualification as Calculus of several variables.