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SF1686 Calculus in Several Variable 7.5 credits

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Headings with content from the Course syllabus SF1686 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Euclidian n-space. Functions of several variables and vector-valued functions, including the following concepts: Graph, level curve, level surface. Limits and continuity, differentiability, partial derivatives, the chain rule, differentials. Tangent planes and linear approximation. Taylor’s Formula. Gradient and directional derivative. Jacobian matrix and Jacobian determinant. Invertibility and implicitly defined functions. Coordinate changes.

Extreme-value problems. Multiple integrals. Line integrals and Green’s theorem. Flux integrals and the divergence theorem. Stokes’ theorem. Applications.

Intended learning outcomes

After finishing the course the student is expected to

  • Be able to use terminology, results and methods to solve, and present solutions of, problems in calculus in several variables described within the course contents.
  • Read and understand mathematical text.

Course disposition

No information inserted

Literature and preparations

Specific prerequisites

Completed course SF1625 Calculus in One Variable or SF1685 Calculus in One Variable.


Recommended prerequisites

Basic knowledge of calculus in one variable and linear algebra as presented in SF1624 Algebra and Geometry and SF1625 Calculus in One Variable.


No information inserted


Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F


  • TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. 

Other requirements for final grade

Written exam, possibly with the possibility of continuous examination.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1686

Offered by

Main field of study


Education cycle

First cycle

Add-on studies

No information inserted

Supplementary information

Language: English

Mandatory for first year, can not be read by other students