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 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.

Apply for guest student status if you are admitted to another Master's programme, or have completed a master in Economics at UiO or another Norwegian University.


Formal prerequisite knowledge

  • Bachelor's degree in Economics, or equivalent.

Recommended previous knowledge

ECON3120 – Mathematics 2: Calculus and Linear Algebra / ECON4120 – Mathematics 2: Calculus and Linear Algebra, or equivalent.

A working knowledge of elementary calculus of functions of one and several variables, the definition of the integral, elementary vector and matrix algebra, and determinants.

Overlapping courses


Lectures and seminars.


A 3-hour written school exam.

Previous exams and examiner guidelines

Exam papers with comments from examiner

Examination support material

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

From spring 2018 there are two calculators allowed for examinations:

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

It is recommended to request an explanation of your grade before you decide to appeal.



The deadline to request an explanation is one week after the grade is published. For oral and practical examinations, the deadline is immediately after you have received your grade.

The explanation should normally be given within two weeks after you have asked for it. The examiner decides whether the explanation is to be given in writing or verbally.

Ask for explanation of your grade in this course

Ask for an explanation of your grade for postponed exam in this course.

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