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Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TMA044 - Multivariable analysis  
Syllabus adopted 2019-02-07 by Head of Programme (or corresponding)
Owner: TKELT
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics

Teaching language: Swedish
Application code: 50246
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0114 Laboratory 1,5 c Grading: UG   1,5 c    
0214 Examination 6,0 c Grading: TH   6,0 c   30 Oct 2019 pm M   07 Jan 2020 am SB_MU   28 Aug 2020 am J

In programs

TIDAL COMPUTER ENGINEERING, Year 3 (compulsory elective)


Daniel Persson

  Go to Course Homepage


TMA042   Mathematical methods TMA043   Multivariable analysis


In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

Course specific prerequisites

Calculus in one variable and Linear algebra. The student should also have basic knowledge of Matlab and ability to use Matlab in problem solving in Calculus and Linear algebra.


The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics required in further studies as well as in the future professional career.

Learning outcomes (after completion of the course the student should be able to)

- account for the basic concepts and calculations of multivariable analysis, perform the operations and use this knowledge in problem solving.

- account for the connections between the different concepts and use these connections in problem solving.

- use and combine different concepts in problem solving.

- use the software MATLAB in problem solving.

More detailed learning outcomes are found in course-PM, see the course home page.


Functions from Rn to Rm, curves and surfaces.

Limits, continuity, partial derivatives, differentiability, the chain
rule, gradients, directional derivatives, tangent lines/planes,

Jacobian matrices/determinants.

Extreme values, optimisation on compact domains, optimisation with
constraints, Lagrange multipliers. Numerical methods for optimisation.

Multiple integration, improper integrals.

Polar och spherical coordinates, change of variables in double and triple integrals.

Some applications: volumes, center of mass, area of surfaces.

Lineintegrales and Green's theorem.

Surface and flux integrals, divergence and curl, Gauss' divergence theorem, Stokes's theorem.

Short introduction to partial differential equations: the Laplace and wave equations.

Numerical methods for problem solving using Matlab.


Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course:


Literature will be written at the course web page

before the start of the course

Examination including compulsory elements

More detailed information of the examination will be given on the course web page before start of the course.

Examples of assessments are:

-selected exercises are to be presented to the teacher orally or in writing during the course,

-other documentation of how the student's knowledge develops,

-project work, individually or in group,

-written or oral exam during and/or at the end of the course.

-problems/exercises are to be solved with a computer and presented in writing and/or at the computer.

Page manager Published: Thu 04 Feb 2021.