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Multivariable calculus 7.5 credits

First cycle, M0055M
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
First cycle
Grade scale
G U 3 4 5
Subject group (SCB)

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and the course Linear Algebra and Differential Equations (M0049M) or equivalent.

More information about English language requirements


The selection is based on 1-165 credits.

Course Aim
This course covers differential, integral and vector calculus for functions of several variables. Emphasis is placed on problem solving with and without computational tools.

  • Functions of several variables: partial derivatives, differentiablity, chain rule, gradient, directional derivatives.
  • Taylor polynomials, quadratic forms, critical points.
  • Extreme value problems on restricted domains, Lagrange multipliers.
  • Multiple integrals, iterated integration, general coordinate systems, Jacobian.
  • Parametric curves and surfaces, tangent plane, arc length, surface area.
  • Line integrals in two and three dimensions. Green’s theorem with application.
  • Surface integrals, vector fields and flux integrals. Divergence and curl. Gauss’ theorem and Stokes’ theorem.
  • Visualization, computations and basic programming in Matlab.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
A written exam is given at the end of the course that includes both theory and problems. The Matlab content is examined through hand-in assignments. The final grade is based solely on the result of the written exam.

Transition terms
The course replaces M0032M.

John Fabricius

Literature. Valid from Autumn 2020 Sp 1 (May change until 10 weeks before course start)
• Robert A. Adams, Calculus: A Complete Course, Pearson Canada, senaste upplagan. ISBN: 9780134154367
• Per Jönsson, MATLAB – beräkningar inom teknik och naturvetenskap, 3:e upplagan. ISBN: 9789144069265

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0002Assignment reportU G#1.50MandatoryA19
0003Written examG U 3 4 56.00MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by Niklas Lehto 15 Feb 2019

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021