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
Weight
10 ECTS
Year of study
2023/2024
Curriculum
SPRING 2024
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

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course, the student:

  • knows how mathematical models can be derived from facts and first principles.
  • has a repertoire of methods to solve and/or analyse both ordinary differential equation (ODE) systems and certain partial differential equations (PDEs).
  • is able to apply analytical and/or numerical solution methods for PDEs to models of heat transfer, wave propagation and diffusion-convection and discuss the relevance of these models to real-world phenomena.
  • is able to construct and develop relevant models and discuss the validity of the models.

Skills

On successful completion of the course, the student can:

  • can determine steady states of ODE systems and use linear approximation to elucidate the stability properties of these states.
  • can solve and/or analyse selected PDE models.
  • is able to implement and use some numerical methods for solving relevant PDEs.
  • can devise the solution of certain composite quantitative problems.
  • can disseminate results and findings in an accessible manner – both orally and in writing.

General competence

  • is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation.
  • is able to discuss properties of a system using the equations of the mathematical model that describes the system.
  • can explain and use numerical methods, know their strengths and weaknesses and interpret results of numerical simulations.

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 following required coursework must be approved before the student can take the exam:

  • Completion of an extensive individual project in the specialised module.

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

Pass or fail.

Examiners

Two examiners. External examiner is used periodically.