Multivariable Calculus, 4 credits (TATA76)

Flervariabelanalys, 4 hp

Main field of study

Mathematics Applied Mathematics


First cycle

Course type

Programme course


Fredrik Andersson

Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CDDD Computer Science and Engineering, M Sc in Engineering 4 (Spring 2017) 1 4 Swedish Linköping o
6CITE Information Technology, M Sc in Engineering 4 (Spring 2017) 1 4 Swedish Linköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level


Course offered for

  • Computer Science and Engineering, M Sc in Engineering
  • Information Technology, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.


Linear Algebra, Calculus, one variable

Intended learning outcomes

The student should acquire the proficiency in multivariable calculus required for subsequent studies. After completing the course the student should be able to:

  • define and explain the central concepts of the course e.g., basic topological notions, function, limit, continuity, functional determinant, volume, area, mass, potential and the different kinds of derivatives and integrals that are used in the course.
  • quote, explain, use and in occurring cases prove the central theorems of the course e.g., the theorem of global extrema, differentiability implies existence of partial derivatives, the chain rule, variable substitution in multiple integrals and the connection between gradients and directional derivatives.
  • verify that results and partial results are correct or reasonable.
  • calculate limits for functions of several variables
  • solve partial differential equations by using the chain rule.
  • calculate directional derivatives and equations for tangents, normals and tangent planes as well as explain and use the geometric interpretations of these objects and use them to solve problems.
  • calculate multiple integrals by means of iterated integration and variable substitutions (e.g., polar, spherical and linear substitutions).

Course content

The space R^n. Fundamental notions from topology. Functions from R^n to R^p. Function graphs, level surfaces and level curves. Definitions of limit and continuity. Partial derivatives. Differentiability and differential. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Multiple integrals. Iterated integration. Variable substitution. Area, volume and mass.

Teaching and working methods

Lectures and lessons.


TEN1Written examinationU, 3, 4, 54 credits


Four-grade scale, LiU, U, 3, 4, 5


Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén


Fredrik Andersson

Education components

Preliminary scheduled hours: 46 h
Recommended self-study hours: 61 h

Course literature

Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund. Problemsamling utgiven av MAI.
Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund. Problemsamling utgiven av MAI.
TEN1 Written examination U, 3, 4, 5 4 credits

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LiU’s rule book for education at first-cycle and second-cycle levels is available at 

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