Application deadline

1. september.

The course will only be available if there are students at the IVT-faculty who have the course in their PhD-plans for that particular term, and there are resources available for lecturing the course.

This course is organized as an intensive course with concentrated teaching.

Type of course

The subject can be taken as a singular course.

• The PhD course is primarily open to UiT's PhD students (Category 1).

One or more of these categories of course students may also be admitted:

• Category 2: Participants in the Associate Professor programme that fulfil the educational requirements.
• Category 3: Doctoral students from other universities.
• Category 4: People with a minimum of a master's degree (or equivalent), who have not been admitted to a doctoral programme.

Admission requirements

Course content

The objective of the course is to introduce mathematical modelling of some important types of engineering and physical problems together with a number of modern techniques in applied mathematics via examples from applied areas. This modelling usually ends up in PDE, ODE and dynamical systems. An introduction to the following areas will be given: dimensional analysis and scaling, perturbation methods, calculus of variations, dynamical systems. In addition, one aims to present some solution techniques of linear PDEs.

The course introduces a number of modern methods and techniques in applied mathematics via examples from applied areas. It consists of the following rather independent items: dimension analysis and scaling, perturbation methods, calculus of variation, elementary partial differential equations, Sturm-Liouville theory and associated theory for generalized Fourier series and Fourier's method, theory of transforms, Hamiltonian theory and isoperimetric problems, integral equations, dynamical systems (chaos, stability and bifurcations), discrete mathematics, and briefly about some other useful techniques in applied mathematics (distribution theory, similarity methods, homogenization, etc.).

Objectives of the course

Knowledge:
After passing the course, the student is expected to be able to

• Give an account of the borderland between mathematics and applied areas of heavy computations.
• Demonstrate understanding of the forefront of knowledge within the field.
• Show knowledge of a number of important methods and techniques in applied mathematics.

Skills:

After passing the course, the student is expected to be able to

• Formulate problems, plan and carry out research and scholarly development work in the borderland between mathematics and applied areas of heavy computations.
• Carry out research and scholarly research work of high international standard connected to the most common fields of applied mathematics.
• Handle complex academic issues and challenge established knowledge and practice connected to computational science.

Habits of mind:

After passing the course, the student is expected to be able to

• Formulate mathematics in a way that enable communication of research and development in applied mathematics on high level.
• Participate in debates concerning applied mathematics in international forums.
• Assess the need for, initiate and practice innovation connected practical problems by the use of applied mathematics.
• Give an account of important concepts and definitions in the area of the course.
• Exemplify and interpret important concepts in specific cases.
• Formulate important results and theorems covered by the course.
• Describe the main features of the proofs of important theorems.
• Express problems from relevant areas of applications in a mathematical form suitable for further analysis.
• Use the theory, methods and techniques of the course to solve mathematical problems.
• Present mathematical arguments to others

Language of instruction and examination

Teaching methods

Assessment

Oral exam: Passed/Not passed.

A re-sit exam will be arranged for this course

Recommended reading/syllabus