Multivariable Calculus and Differential Equations, 4 credits (TATA90)

Flervariabelanalys och differentialekvationer, 4 hp

Main field of study

Mathematics Applied Mathematics


First cycle

Course type

Programme course


Jesper Thorén

Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CMJU Computer Science and Software Engineering, M Sc in Engineering 4 (Spring 2017) 2 4 Swedish Linköping o

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level


Course offered for

  • Computer Science and Software Engineering, 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.


Calculus in one variable 1, Linear Algebra

Intended learning outcomes

Gain familiarity with mathematical concepts, reasoning and relationships in multivariable calculus and linear differential equations in one variable, and gain the calculation and problem solving skills needed for further studies. After completing this course you should be able to

  • cite and explain the definitions of the course's key concepts, such as topological fundamental concepts, functions, limits, continuity, partial derivatives, multiple integrals, functional determinants etc..
  • handle differential equations (first order linear, separable and higher order linear equations with constant coefficients).
  • quote, explain and use the course central theorems, such as the chain rule, change of variables in multiple integrals, the relationship between gradients and directional derivatives, theorems concerning multiple integral properties etc..
  • solving some partial differential equations using the chain rule.
  • verify that results are correct or reasonable.
  • calculate the directional derivatives and tangent-, normal- and tangent plane equations and explain and use the concepts geometrical significance in problem solving.
  • compute multiple integrals using repeated integration, change of variables (e.g. polar, spherical and linear).

Course content

The space R ^ n. Basic topological concepts. Functions from R ^ n to R ^ p. Function surfaces, level surfaces and level curves. Limits. Partial derivatives. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Multiple integrals. Repeated integration. Variable Substitution. Functional determinants. Ordinary Differential Equations. First order linear and separable equations. Linear equations of higher order with constant coefficients.

Teaching and working methods

The course consists of lectures and classes.


TEN1Written examinationU, 3, 4, 54 credits


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


Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén


Jesper Thorén

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 71 h
There is no course literature available for this course.
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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