A Basic Course in Applied Mathematics
About the course
Can be taken as a single course.
Who can apply for admission?
• PhD students at UiT who wish to take a course at the PhD level.
• PhD students from other universities and institutions.
• Applicants that has already achieved a master’s degree (five year master or three year bachelor degree + two year master degree), but isn’t a PhD student.
This course provides the foundation and essential tools for the mathematical modeling and analysis of real-world engineering problems.
Admission requirements
- This course is aimed at PhD candidates from engineering and technology disciplines, but is also open to postdoc fellows if seats are available.
- PhD candidates from UiT and other universities may be admitted to the course. PhD candidates who are not registered at UiT must upload a document from their university stating that they are registered as PhD candidates.
If there are 5 applicants or fewer, the course responsible will evaluate whether the course will take place.
In addition to the general admission requirements for the PhD program at UiT, a good command of the concepts of calculus, differential equations, and matrices is a prerequisite.
The following prior knowledge is recommended:
- Mathematics 2
- Knowledge of Partial Differential Equations
- Calculus
- Fourier Series
- Transform theory
- Dynamical systems.
Objectives of the course
The objective of the course is to introduce mathematical modeling of some important types of engineering and physical problems, together with several modern techniques in applied mathematics, using examples from applied areas. This modeling 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, and dynamical systems. In addition, one aims to present some solution techniques for linear PDEs.
The course introduces several 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.).
Students should understand that each topic covered has a limited scope, not in-depth, as each topic can be studied in one or several full-length books. The course introduces mathematical methods and modeling to mature seniors and graduate students in mathematics, science, and engineering. Each topic discussed is a separate unit.
Upon successful completion of the course, the following learning outcomes are expected to be achieved:
Knowledge:
After passing the course, the student is expected to be able to
- Advanced knowledge of the overlap between mathematics and applied areas of heavy computations.
- Demonstrate understanding of the forefront of knowledge within the field.
- Knowledge of the 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 a 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.
Competence:
After passing the course, the student is expected to be able to
- Formulate mathematics in a way that enables communication of research and development in applied mathematics.
- Participate in debates concerning applied mathematics in international forums.
- Assess the need for, initiate, and practice innovation connected to practical problems using applied mathematics.
- Give an account of important concepts and definitions in the course area.
- Exemplify and interpret important concepts in specific cases.
- 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.
Teaching methods
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 | Duration: 1 Hours |
Grade: Passed / Not Passed |
To take an examination, the student must have passed the following coursework requirements
| Report | Grade: Approved – not approved |
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