TMA4105 - Mathematics 2 - Multivariable calculus and vector analysis


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

Curves in space. Functions of several variables. Taylor's theorem in two dimensions, extremal values in several variables, Lagrange multipliers. Double and triple integrals, line and surface integrals. Vector calculus. The theorems of Green, Stokes, and Gauss.

Learning outcome

  1. Knowledge. The student is able to recognize, understand and apply concepts and methods from multi-variable mathematical analysis, including multiple integrals, line integrals, surface integrals and the integral theorems of vector analysis.
  2. Skills. The student is able to apply his or her knowledge of multi-variable mathematical analysis to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Learning methods and activities

Lectures and compulsory exercises. Information regarding the number of compulsory exercises that must be approved will be listed on the course website at the start of the course. The lectures may be given in English.

Compulsory assignments

  • Exercises

Further on evaluation

Grade based on written final written examination. Retake of examination may be given as an oral examination. The retake exam is in August.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
MA1103 7.5
SIF5005 7.5
TMA4111 3.7 AUTUMN 2022
TMA4121 3.7 AUTUMN 2022
More on the course

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I


Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
  • Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD School exam 100/100 D INSPERA
Room Building Number of candidates
Summer 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"

More on examinations at NTNU