Schedule, syllabus and examination date

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Course content

Functions of a complex variable, complex integrals, the residue theorem and its applications. Linear-, ordinary- and partial differential equations of second order. Fourier series. The Laplace and Fourier integral transformations. Green's functions. Tensor analysis. Orthogonal functions. Calculus of variations.

Learning outcome

Learning objectives: After finishing the course the student should be able to:

• master the basic elements of complex mathematical analysis, including the integral theorems, obtain the residues of a complex function and to use the residue theorem to evaluate definite integrals
• solve ordinary differential equations of second order that are common in the physical sciences
• expand a function in terms of a Fourier series, with knowledge of the conditions for the validity of the series expansion
• apply integral transform (Fourier and Laplace) to solve mathematical problems of interest in physics, use Fourier transforms as an aid for analyzing experimental data
• solve partial differential equations of second order by use of standard methods like separation of variables, series expansion (Fourier series) and integral transforms
• formulate and express a physical law in terms of tensors, and simplify it by use of coordinate transforms (example: principal axes of inertia)
• Solve some simple classical variational problems.


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.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


Formal prerequisite knowledge

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

One of these:

  • Mathematics R1
  • Mathematics (S1+S2)

And and in addition one of these:

  • Mathematics (R1+R2)
  • 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. Read more about special admission requirements (in Norwegian).

Recommended previous knowledge

Knowledge corresponding to the following courses at the University of Oslo: MAT1100 - Calculus, MAT1110 - Calculus and linear algebra and MAT1120 - Linear algebra.

Overlapping courses

10 credits overlap against FYS211, which was offered for the last time in fall semester 2003.


The course extends over a full semester with 6 hours of teaching per week (lectures and problem solving).


Written assignment with approximately 25% weight of the final grade. Final 3-hour written exam with approximately 75% weight, which must be passed in order to pass the course. Twelve weekly assignments, of which six have to be approved in order to sit for the final exam.

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).

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.

Explanations and appeals

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

Application form, deadline and requirements for special examination arrangements.


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

Facts about this course






Every spring


Every spring

Teaching language

Norwegian (English on request)