Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After the course the student will

- know how to calculate approximations with the aid of partial derivatives

- be able to solve systems of equations with Newton s method

- know and understand the basic ideas of optimization

- be able to use Lagrange multipliers

- be able to calculate double and triple integrals

- be able to change the order of integration in double integrals

- know how to change variables in double and triple integrals

Credits: 5

Schedule: 12.01.2021 - 22.02.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Jarmo Malinen

Teacher in charge (applies in this implementation):

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Functions of several variables and their derivatives, optimization of functions with several variables, double and triple integrals.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Lectures, exercises, midterm exams/final exam.

  • Valid 01.08.2020-31.07.2022:

    24+24 (4+4)


Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Together with the course MS-A03XX substitutes the courses Mat-1.1020, Mat-1.1220, Mat-1.1320, Mat-1.1420, Mat-1.1520, Mat-1.1620, Mat-1.1720.

    Together with the course MS-A04XX Foundations of discrete mathematics or the course MS-A01XX Differential and integral calculus 1 substitutes the course Mat-1.1110.

    Substitutes the courses MS-A02XX Differential and integral calculus 2.

  • Valid 01.08.2020-31.07.2022:

    MS-A00XX Matrix algebra, MS-A01XX Differential- and integral calculus 1.



Registration and further information