ECON4140 – Mathematics 3: Differential Equations, Static and Dynamic Optimization

Schedule, syllabus and examination date

Choose semester

Course content

  • differential equations
  • eigenvalues
  • concave and quasi-concave functions
  • multiple integration
  • nonlinear programming
  • optimal control theory
  • difference equations
  • dynamic programming.

Learning outcome


You should know

  • linear algebra (linear independence, rank and eigenvalues)
  • calculus and static optimization (multiple integration, concavity, quasi-concavity, nonlinear programming)dynamic optimization (difference equations and discrete-time dynamic programming
  • differential equations, calculus of variations and continuous-time optimal control theory)


You should be able to

  • use problem-solving skills to a greater extent than ECON3120 / ECON4120
  • apply new theory and problem-solving techniques for static and dynamic optimization
  • understand at a deeper level why the techniques from ECON3120/ ECON4120 work, and understand at an intuitive level why the new techniques of ECON4140 work


This course should enable you to

  • read and understand the notation and analyses of a wide class of models in the scientific literature, including foundational topics in microeconomics
  • formulate and formalize a wider range of models than what is covered in ECON3120/4120
  • analyze such models in your own academic work, for example in analyses that are part of the master’s thesis


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

Students not admitted to the Master’s programme in Economics or the Master’s programme in Economic Theory and Econometrics (Samfunnsøkonomisk analyse), can apply for admission to one of our study programmes, or apply for guest student status.


Formal prerequisite knowledge

You must fulfill one of these prerequisites:

Recommended previous knowledge

Overlapping courses


Lectures and seminars.


A 3-hour written school exam.

Previous exams and examiner guidelines

Exam papers with comments from examiner

The school exam in this course is conducted on paper. You use carbon paper which is handed out in the examination room. You retain one copy, while the rest is handed in.

Examination support material

Resources allowed: Open book examination where all printed and written resources, in addition to calculator, are allowed.

There are two calculators allowed for examinations:

  • Aurora HC106 - a very simple calculator with most basic functions
  • Casio FX-85EX - a scientific calculator with 274 functions

All other calculator types will be rejected. The calculators are checked in the exam room. There is no opportunity to lend the calculator of fellow students.
You can buy the calculators at Akademika bookstore at Blindern, or online.

The same general rules for cheating also apply when using calculator.

Language of examination

The examination text is given in English.You may submit your response 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.

Explanations and appeals

Resit an examination

If you are sick or have another valid reason for not attending the regular exam, we offer a postponed exam later in the same semester.

See also our information about resitting an exam.

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.

Facts about this course






Every spring


Every spring

Teaching language