VB6110 - Mathematical methods 3


Examination arrangement

Examination arrangement: School exam
Grade: Letter grades

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

Course content


Limits and continuity. Directional derivative and the gradient. Tangent planes and tangent lines. Linear approximation and differentiability. The chain rule. Parametric curves in the plane and in space. Curvature and torsion.


Double integrals and iterated integration using cartesian and polar coordinates. Triple integrals and iterated integration using cartesian, cylinder- and spherical coordinates. Integration on curves and surfaces in space, curve length, surface area, volume and centroids.

Vector analysis

Static vector fields. Divergence,curl, gradient fields and potentials. Conservative and curl free vector fields. Work/circulation and flux. Green theorem, Stokes' theorem and Gauss' Theorem. Applications of vector analysis in fluid mechanics and/or electro-magnetism (Maxwell's equations)

Learning outcome


The candidate knows concepts, theorem, and methods from calculus in several variables related to differentiation, integration, and vector analysis for static vector fields.


The candidate can

  • use mathematical language to formulate problems in mathematics and science related to calculus in several variables.
  • apply methods from multivariable calculus to find analytic solutions to mathematical and engineering problems.
  • use mathematical software to visualise and solve relevant problems in calculus in several variables.

General competencies

The candidate can

  • use mathematical language to communicate about problems in engineering.
  • translate between a mathematical language and a language suitable for use with mathematical software

Learning methods and activities

Lectures and exercises.

The lectures may be given in English.

Compulsory assignments

  • Exercises

Further on evaluation

4 hour individual exam in Inspera, graded using the scale A-F.

Exam aids: Simple calculator

In order to take the exam, 70% of all compulsory assignments, including one compulsory computer assignment must be passed. Re-sit Exam: May/June.

Python will be available during the exam.

Specific conditions

Admission to a programme of study is required:
Continuing Education, Faculty of Engineering Science and Technology (EVUIVE0)

Course materials

To be announced.

Credit reductions

Course code Reduction From To
IMAG2100 7.5 AUTUMN 2021
More on the course



Version: 1
Credits:  7.5 SP
Study level: Third-year courses, level III


Term no.: 1
Teaching semester:  AUTUMN 2024

Language of instruction: Norwegian

Location: Gjøvik

Subject area(s)
  • Engineering
  • Mathematics
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Mathematical Sciences

Department with administrative responsibility
Section for quality in education and learning environment


Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD School exam 100/100 D INSPERA
Room Building Number of candidates
Spring UTS School exam 100/100 D INSPERA
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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