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
2025/2026
Course history

Introduction

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

  • has knowledge of the structure and function of biological barriers
  • has knowledge of the rate of solubility and its significance for the absorption of pharmaceuticals
  • is capable of explaining factors that can limit the bioavailability of active ingredients and influence the biopharmaceutical properties of pharmaceuticals
  • is capable of explaining the grounds for choices of type of active ingredient, formulation and route of administration made during pharmaceutical development work
  • is capable of explaining the function of common ancillary substances in pharmaceutical preparations

Skills

The student

  • is capable of discussing principles of formulation for pharmaceuticals based on information from summaries of product characteristics (SPC) and any other relevant pharmaceutical reference works
  • is capable of assessing a user perspective on different formulations, as well as shelf life and storage
  • is capable of assessing the use of different pharmaceutical formulations based on a patient's condition and needs
  • is capable of using pharmaceutical reference works written in English and Norwegian
  • masters basic skills in aseptic work technique and sterilisation procedures

General competence

The student

  • is capable of documenting and presenting his/her own work orally and in writing
  • is capable of taking a critical approach to information collected from different sources

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

Work and teaching methods include lectures, group work, question sessions and laboratory work. The lectures involve student activity and the subject matter is made relevant using clinical examples. The students are also introduced to current research, possible future formulations and unsolved problems. The students work on assignments and are met with expectations of progress in the question sessions, which are scheduled throughout the course. The laboratory work focuses on aseptic work technique. Students are followed up individually before the final practical test.

The Flipped Classroom is used as a teaching method for part of the course. Digital learning resources will be made available to students in advance and the time they spend at the university will be used to work on assignments and group work.

Learning outcomes

Bokstavkarakter A-E for bestått og F for ikke bestått.

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

Exam content: The learning outcomes

Exam form: Supervised individual written exam, 4 hours

Course requirements

Calculator

Assessment

Grade scale A-F

Permitted exam materials and equipment

One external and one internal examiner will assess at least 30 % of the papers. Two internal examiners will assess the remaining papers. The external examiner's assessment shall benefit all the students.

Grading scale

Pass or fail.

Examiners

Two examiners. External examiner is used periodically.