Multivariable calculus 7.5 credits

First cycle, M0055M
Course syllabus valid: Autumn 2020 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.

Syllabus established
by Niklas Lehto 15 Feb 2019

Last revised
by HUL Niklas Letho 14 Feb 2020

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.

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 scaleHPStatusFrom periodTitle
0001Written examG U 3 4 56.00MandatoryA19
0002Assignment reportU G#1.50MandatoryA19