# FYS3140 – Mathematical methods in physics

Choose semester

## Course content

This course addresses a number of important mathematical methods often used in physics. Central topics are: basic complex analysis, differential equations, Fourier series and –transforms, tensor calculus, variational calculus, orthogonal functions, Laplace transformations.

## Learning outcome

After completing this course you will:

• have a good grasp of the basic elements of complex anaysis, including the important integral theorems. You will be able to determine the residues of a complex function and use the residue theorem to compute certain types of integrals.
• be able to solve ordinary second order differential equations important in the physical sciences; solve physically relevant partial differential equations using standard methods like separation of variables, series expansion (Fourier-type series) and integral transforms.
• have learned how to expand a function in a Fourier series, and under what conditions such an expansion is valid. You will be aware of the connection between this and integral transforms (Fourier and Laplace) and be able to use the latter to solve mathematical problems relevant to the physical sciences.
• have received basic training in tensor calculus. You will be familiar with examples of how to formulate certain physical laws in terms of tensors, and how to simplify them using coordinate transformations (example: principal axes of inertia).
• be able to solve basic classical variational problems.
• have received training in clear argumentation, reasoning and presentation, and how to present your results in a tidy way.
• have practiced cooperation, formulating good questions and explaining to others.

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

## Prerequisites

### Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

• Mathematics R1 (or Mathematics S1 and S2) + R2

And and in addition one of these:

• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

## Overlapping courses

Be aware that the information about overlapping courses is not complete. Contact the Department if there are uncertainties.

## Teaching

This course lasts a full semester with eight classroom hours per week (four hours of lectures, four hours of problem solving sessions). Twelve  problem sets for handing in.

## Examination

To be eligible for exam, a minimum six out of twelve problem sets must be passed.

Written assignment with approximately 25% weight of the final grade. Final 4-hour written exam with approximately 75% weight, which must be passed in order to pass the course.

### Examination support material

• Approved calculator.
• Øgrim and Lian or Angell and Lian: "Fysiske størrelser og enheter".
• Rottman: "Matematisk formelsamling".
• Two A4 sheets with notes (you can write in both sides of the sheet).

### Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

Bachelor

Every spring

Every spring

### Teaching language

Norwegian (English on request)

## Contact

Department of Physics