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.

The main contents of the course are:

• 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.

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.