FYS3140 – Mathematical Methods in Physics

Teaching and exams spring 2022

In light of the most recent infection control regulations, we will at the start of the spring semester 2022 increase our online teaching, while we at the same time try to maintain in-person teaching where this is possible. We hope to go back to more in-person teaching later on in the semester. You will be informed about any changes in teaching or examinations on the semester page, in Canvas or through your regular channels.

Read more about postponed exams for the autumn semester 2021.

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:

  • have a good grasp of the basic elements of complex analysis, 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.
  • are 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, 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). You will be able to apply integral transforms and series expansion methods to solve differential equations 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).
  • are 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.

Admission to the course

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.

Special admission requirements

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 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


This course lasts a full semester with 8 hours of teaching per week:

  • 4 hours of lectures 
  • 4 hours of problem-solving sessions

This course has 12 mandatory assignments, of which at least 6 have to be approved before you can sit the final exam.

Regulations for mandatory assignments can be found here.


  • Midterm home exam which counts 25 % towards the final grade.
  • Final written exam, 4 hours, which counts 75 % towards the final grade.

A minimum of 6 out of 12 mandatory assignments must be approved before you can sit the final exam. You must pass the final exam in order to receive a final grade in the course.

When writing your exercises make sure to familiarize yourself with the rules for use of sources and citations. Breach of these rules may lead to suspicion of attempted cheating.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: FYS4140 – Mathematical methods in physics (discontinued)

Examination support material

  • Approved calculator
  • Rottman: "Matematisk formelsamling"
  • Øgrim and Lian or Angell and Lian: "Fysiske størrelser og enheter"
  • 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.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

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.

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Jan. 18, 2022 11:15:15 PM

Facts about this course

Teaching language
Norwegian (English on request)