# Applied Mathematical Modelling and Analysis (PET933)

The course introduces methods for deriving and analyzing mathematical models of systems and processes within science and engineering. The course focuses on the development of approximate solutions to problems in physics and engineering by the use of dimensional analysis, scaling and perturbation methods.

Course description for study year 2023-2024. Please note that changes may occur.

Facts

PET933

1

10

Autumn

1

Autumn

English

Time table

## Content

• Dimensional analysis and the Pi-theorem
• Non-dimensionalization and scaling
• Regular and singular perturbation theory
• Fixed points, stability and bifurcations in nonlinear dynamical systems
• Derivation and analysis of partial differential equations from conservation principles

The course will focus on the development and analysis of mathematical models, as well on how these models can be used to motivate, design and interpret experiments. Throughout the course, example problems from classical mechanics and/or fluid mechanics will be used to illustrate the application of both analytical and numerical methods. Examples may include mechanical vibrations of slender structures, population (predator-prey) models, advection and diffusion processes, or general viscous flows in two-dimensional geometries.

## Learning outcome

Upon successful completion of the course, the student will be able to:

• Apply conservation principles to derive mathematical models of a wide range of physical systems and processes,
• Use dimensional analysis and scaling to analyze and simplify models,
• Solve mathematical models using regular and singular perturbation techniques, as well as numerical methods,
• Actively use mathematical models to design experiments and analyze measurements.

None

## Recommended prerequisites

MAT100 Mathematical Methods 1, MAT200 Mathematical Methods 2, STA100 Probability and Statistics 1
Basic knowledge of physics and mathematics, including statistics. Basic knowledge of numerical methods is recommended.

## Exam

Oral exam and project assignment

Øystein Arild

## Method of work

Lectures, voluntary exercises and a mandatory, individual project assignment. The topic for the individual projects will be agreed between course responsible and candidate, and may be linked to the PhD project of the candidate. The outcome of the project will be a short project report and presentation.

## Open for

Technology and Natural Science - PhD programme

## Course assessment

There must be an early dialogue between the course coordinator, the student representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

## Literature

Search for literature in Leganto