EPN-V2

PENG9570 Applied Mathematical Modelling and Analysis Course description

Course name in Norwegian
Applied Mathematical Modelling and Analysis
Study programme
PhD Programme in Engineering Science
PhD Programme in Engineering Science, Elective modules
Weight
10.0 ECTS
Year of study
2021/2022
Curriculum
SPRING 2022
Schedule
Course history

Introduction

Students taking the course must have a thorough knowledge of advanced calculus, including ordinary and partial differential equations. The student should also be familiar with linear algebra and Fourier and Laplace transform theory. In terms of programming, the candidate should have some experience in implementing numerical methods, including schemes for solving partial differential equations.

The candidate should also have a certain knowledge of mathematical analysis, modern physics or physiology – depending on specialization.

The course will be offered once a year, provided 3 or more students sign up for the course. If less than 3 students sign up for a course, the course will be cancelled for that year.

Recommended preliminary courses

A thorough knowledge of advanced calculus, including ordinary and partial differential equations. It is a great advantage if students are familiar with linear algebra and Fourier and Laplace transform theory. In terms of programming, some experience in implementing various numerical methods, including schemes for solving partial differential equations is recommended. Some knowledge of mathematical analysis, modern physics or physiology is recommended, depending on their specialisation.

Required preliminary courses

None.

Learning outcomes

Through systematic work and therapeutic use of activity, the occupational therapist contributes to the possibility of activity and participation. Practical training makes up one third of the study and is a very important part of the occupational therapy programme. During this first long practical training period, the individual student will gain experience from one practical training establishment, at the same time as the class as a whole will gain insight into various forms of occupational therapy practice, as the practical training places can be in all arenas where occupational therapists work.

Content

Introductory module:

  • Principles of modelling and derivation of mathematical models
  • Analysis of ordinary differential equations (ODEs)
  • Linear partial differential equations (PDEs)
  • Prominent results from functional analysis and their application to ODEs and PDEs
  • Numerical methods for computing of solutions of PDEs

Functional analysis:

  • Completeness for normed spaces
  • Hilbert spaces, compact and diagonalisable operators
  • Theory of topological vector spaces
  • Test functions, distributions and the Fourier transform
  • Sobolev spaces and fundamental solutions of partial differential equations

Biosystems:

  • Mathematical models for biological systems
  • Analytical and numerical methods for simulation of system response
  • Actuators and sensors for stimulation and measurements of biological systems
  • Interaction of biological and measurement system

Modern physics:

  • Monte Carlo techniques
  • Splines and other expansion techniques
  • Applications of expansions in spherical harmonics
  • Numerical problems in general relativity and quantum physics
  • Manifolds with geometric structures central to physics and engineering.

Within all specializations, the content may be adjusted to accommodate for the research area of each PhD candidate.

Teaching and learning methods

The teaching is organised as sessions where the subject material is presented, and as sessions where the students solve problems using analytical and/or numerical methods. Between these sessions, the students should work individually with literature studies and problem solving.

In the last, specialised part, the students are required to complete and present a rather extensive individual project involving theoretical and practical/implementational aspects.

Course requirements

The student must have been admitted to the study programme.

Assessment

An individual, oral examination. The examination will address both general topics from within the course and the specific project developed by the student.

The oral examination cannot be appealed.

Permitted exam materials and equipment

The student's own project.

Grading scale

The practical training period takes place over ten weeks and starts with a week’s preparation as part of the programme. During a practical training week, the students spend three days at the practical training establishment and one day on teaching activities in the programme. The students will be assigned an occupational therapist as a supervisor at the practical training establishment and a contact lecturer at the university, and the students will normally follow the working hours of the practical training establishment. The preparations and sessions include skills training, case-based teaching, lectures, group seminars and workshops with digital story telling.

Examiners

Two examiners. External examiner is used periodically.