MM533: Mathematical and Numerical Analysis
Entry requirements
Academic preconditions
- Have knowledge of the contents of MM536
- Have knowledge of the contents of MM540, MM505 or MM568 or acquire this knowledge in parallel to the lecture
Course introduction
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.
- 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
- 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
- metric spaces
- open and closed sets
- limit points and convergence
- topological spaces and continuity
- compactness and uniform continuity
- uniform convergence and Cauchy's criterion
- complete metric spaces
- Banach's fixed point theorem
- Newton iteration and the order of convergence
- iterative methods for linear systems
- polynomial interpolation and quadrature
- differential equations and Runge-Kutta methods
Literature
Examination regulations
Exam element a)
Timing
Tests
Written exam
EKA
Assessment
Grading
Identification
Language
Duration
Examination aids
All common aids are allowed e.g. books, notes, computer programmes which do not use internet etc.
Internet is not allowed during the exam. However, you may visit system DE-Digital Exam when answering the multiple-choice questions. If you wish to use course materials from itslearning, you must download the materials to your computer the day before the exam. During the exam itslearning is not allowed.
ECTS value
Indicative number of lessons
Teaching Method
Teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures, class lessons) - 52 hours
- Training phase: 26 hours
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