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Applied mathematical modelling and analysis PET933

The course introduces methods for deriving and analyzing mathematical models of systems and processes within science and engineering, focusing on how such models can be used to motivate, design and interpret experiments. Fundamental conservation principles will be used to derive mathematical models followed by dimensional analyses and scaling for solving the model analytically by perturbation methods or numerically. The course concludes with certain topics from statistics, including linear and nonlinear regression methods.

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, advection and diffusion processes, or general viscous flows in two-dimensional geometries.


Course description for study year 2021-2022. Please note that changes may occur.

Facts
Emnekode

PET933

Vekting (SP)

10

Semester undervisningsstart

Autumn

Antall semestre

1

Vurderingsemester

Autumn

Undervisningsspråk

English

Tilbys av

Faculty of Science and Technology, Department of Energy and Petroleum Engineering

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.
Content

The course introduces methods for deriving and analyzing mathematical models of systems and processes within science and engineering, focusing on how such models can be used to motivate, design and interpret experiments. Fundamental conservation principles will be used to derive mathematical models followed by dimensional analyses and scaling for solving the model analytically by perturbation methods or numerically. The course concludes with certain topics from statistics, including linear and nonlinear regression methods.

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, advection and diffusion processes, or general viscous flows in two-dimensional geometries.

Required prerequisite knowledge
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.
Eksamen / vurdering

Oral exam and project assignment

Vurderingsform Vekting Varighet Karakter Hjelpemiddel
Oral exam 40/100 Pass - Fail
Project assignment 60/100 Pass - Fail None permitted

Course teacher(s)
Course coordinator: Hans Joakim Skadsem
Head of Department: Øystein Arild
Course coordinator: Hans Joakim Skadsem
Method of work
Lectures, voluntary exercises and a mandatory project assignment.
Open for
Technology and Natural Science - PhD programme
Course assessment
Standard UiS procedure.
Literature
Search for literature in Leganto