Fundamentals of Scientific Computing
About the course
This course introduces the fundamentals of mathematical modelling, numerical analysis, and optimization for engineering science.
This course is suitable for engineering and natural science PhD programs.
The objective of the course is to introduce some of the basic notions and methods in mathematics modelling, numerical analysis, and optimization. The main topics are those used in scientific computing, for example, the Newton, Ritz, Galerkin, and least squares methods, polynomial approximations in Sobolev spaces, the Fourier transform, and spectral methods. Construction of numerical methods for optimization, algebraic equations, and for classical PDEs associated with wave, heat, and fluid dynamics. Methods based on rigorous numerics using interval analysis.
Admission requirements
General admission requirements for PhD.-program at UiT.
Offered irregularly. The course will be cancelled if less than five participants.
Objectives of the course
Knowledge:
After passing the course, the student is expected to be able to
- Give an account of basic concepts and definitions in the mathematics of modelling, numerical analysis, and optimization.
- Formulate results covered by the course.
- Exemplify concepts in specific cases.
Skills:
After passing the course, the student is expected to be able to
- Interpret concepts in specific cases.
- Describe the main features of the proofs of the main theorems.
Competence:
After passing the course, the student is expected to be able to
- Use the theory and methods of the course to solve problems in applied mathematics.
Teaching methods
Lectures and problem-solving sessions.
Acquisition (face-to-face presentations and lectures, demos, reading paper books).
Investigation (using text-based study guides, analysing the ideas and information in a range of materials & resources, searching and evaluating information and ideas, using digital resources for scaffolding, using digital tools to collect and analyse data).
Practice ("field" trips, using models, simulations, practising exercises, doing practice-based projects).
Discussion (tutorials, seminars, class discussions, online tutorials)
Collaboration (individual project, online forums, wikis, chat rooms, etc.).
Production (reports, models, oral exam).
Language of instruction and examination
EnglishSchedule
The schedules are normally finalized and published well in advance of the start of the semester, often a few weeks beforehand. This gives students the opportunity to organize their studies and prepare for upcoming activities.
It is recommended to check the schedule regularly, as changes may occur.
Examination
| Oral exam |
Grade: Passed / Not Passed |
To take an examination, the student must have passed the following coursework requirements
| Hand-in assignment | Grade: Approved – not approved |
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