# MM533: Mathematical and Numerical Analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled

EKA: N300033102

Assessment: Second examiner: External

Grading: 7-point grading scale

Offered in: Odense

Offered in: Spring

Level: Bachelor

STADS ID (UVA): N300033101

ECTS value: 10

Date of Approval: 08-11-2018

Duration: 1 semester

Version: Archive

## Comment

## Entry requirements

## Academic preconditions

Students taking the course are expected to:

- Have knowledge of the contents of MM536
- Have knowledge of the contents of MM540 or MM505 or acquire this knowledge in parallel to the lecture

## Course introduction

The aim of the course is to enable the student to solve problems

concerning the course topics by means of mathematical and numerical

analysis. Formulate the answers (including proofs) in a correct

mathematical language. Implement algorithms as computer programs and

compute numerical approximations to mathematical problems that don't

allow a closed form solution.

The course builds on the knowledge

acquired in the courses MM536: Calculus for mathematics and MM505:

Linear Algebra or MM540: Mathematical methods for economics and gives an

academic basis for further studies in applied mathematics and

mathematics that are part of the respective degree programs. More

precisely, this includes MM545, MM546, MM547, MM548, MM549.

concerning the course topics by means of mathematical and numerical

analysis. Formulate the answers (including proofs) in a correct

mathematical language. Implement algorithms as computer programs and

compute numerical approximations to mathematical problems that don't

allow a closed form solution.

The course builds on the knowledge

acquired in the courses MM536: Calculus for mathematics and MM505:

Linear Algebra or MM540: Mathematical methods for economics and gives an

academic basis for further studies in applied mathematics and

mathematics that are part of the respective degree programs. More

precisely, this includes MM545, MM546, MM547, MM548, MM549.

In relation to the competence profile of the degree it is the explicit focus of the course to:

- Give the competence to analyse the qualitative and quantitative characteristics of a mathematical model
- Give basic understanding on how to perform computer based calculations in science, technology and economy
- Give knowledge and understanding of basic algorithms

## Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

- understand the abstract concepts of topological and metric spaces
- understand and work with the notions of compactness, continuity and convergence in the settings of topological and metric spaces
- understand the quantitative aspects of convergence in metric spaces
- analyse and conduct basic numerical methods for
- root finding
- interpolation
- integration

## Content

The following main topics are contained in the course:

- Euclidian-, metric-, and topological spaces.
- Continuity of functions.
- Convergence of sequences and series.
- Bisection and secant methods and their convergence.
- Compact sets, Heine-Borel theorem.
- Completeness of Euclidian spaces.
- Banach fixed point theorem, norms and contractions.
- Linear convergence of fixed point iteration.
- Quadratic convergence of Newton iteration.
- Uniform continuity and the Riemann integral.
- Interpolation.
- Adaptive Newton-Cotes quadrature.
- Gaussian quadrature.

## Literature

## Examination regulations

## Exam element a)

## Timing

June

## Tests

## Written exam

## EKA

N300033102

## Assessment

Second examiner: External

## Grading

7-point grading scale

## Identification

Student Identification Card

## Language

Normally, the same as teaching language

## Duration

4 hours

## Examination aids

To be announced during the course

## ECTS value

10

## Additional information

The examination form for re-examination may be different from the exam form at the regular exam.

## Indicative number of lessons

## Teaching Method

Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Educational activities

- Reading of suggested literature
- Preparation of exercises in study groups
- Contributing to online learning activities related to the course