On successful completion of the course, the student should be able to
explain the significance of completeness of the reals and consequences thereof, like the Bolzano-Weierstrass property
apply definitions of limits and continuity of real sequences and functions and to some extent generalize the definitions to metric spaces
explain the difference between pointwise and uniform convergence and continuity, and know results where this difference is essential
explain and use the definition of differentiability
decide integrability in the sense of Riemann and compute Riemann integral of real functions
explain the intermediate value theorem, the mean value theorem and the fundamental theorem of analysis and show how these results are connected with continuity, differentiability and integrability
Explain how the rational numbers extends to a complete ordered field.
Work on examples that lead to understanding of the real numbers and to the concept of limit on the real line and in metric spaces. Further work on real functions and sequences of functions in order to study connections between continuity, differentiability and integrability.
Lectures, work in small groups and compulsory assignements. The course has an expected workload of around 200 hours.
Required assignments must be approved, see Canvas for more information.
Assessment methods and criteria
5-hour written examination. Graded assessment.
The study programme manager, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.