course-details-portlet

MA1103

Multivariate analysis and vector calculus

Assessments and mandatory activities may be changed until September 20th.

Credits 7.5
Level Foundation courses, level I
Course start Spring 2026
Duration 1 semester
Language of instruction Norwegian
Location Trondheim
Examination arrangement School exam

About

About the course

Course content

Vector-valued functions of one variable. Differentiability. Differentiation rules. Curves given by vector-valued functions. Unit tangent and normal vectors. Arc length. Curvature.

Functions of two or more variables (scalar fields). Limit. Continuity. Partial differentiation. The chain rule. Automated differentiation. Linear approximation. Differentiability. Gradient. Directional derivative. Level curves and level surfaces. Implicit function theorem. Inverse function theorem.

Optimization of functions of two or more variables (identifying maxima and minima). The extreme value theorem. The second derivative test. Lagrange multipliers.

Multiple integrals. Riemann sums. Iterated integrals. Change of order of integration. Change of variables. Jacobi determinant. Polar, cylindrical and spherical coordinates.

Vector-valued functions of two or more variables. Vector field. Conservative vector field. Line integrals for functions and vector fields.

Surface integrals. Parametrized surfaces. Orientable surfaces. Surface integral of vector fields on an oriented surface.

Vector calculus. Divergence. Curl. Vector potential. Green's theorem. The divergence theorem. Stokes' theorem. Conservation laws on integral form.

Examples of mathematical modelling and applications in science and technology.

Learning outcome

The student understands and can apply basic concepts, results and methods from multivariate calculus concerning limits, continuity, differentiation, multiple integration, line and surface integrals. The student understands and can apply basic concepts and methods from vector calculus.

The student can apply multivariate calculus and vector calculus to formulate, modell and solve simple technological problems, if necessary with the additional aid of mathematical software.

The course will primarily contribute to competence area K1; show specialist knowledge and a professionally grounded perspective. It will also contribute to competence area K2; analysing engineering problems, in collaboration with the various study programmes that the subject serves.

Learning methods and activities

Lectures and compulsory exercises. The number of exercises that must be approved will be stated at the start of the semester on the course's website. The course will be taught in Norwegian.

Compulsory assignments

  • Exercises

Further on evaluation

The grade will be based on final written exam. In the event of a re-sit exam, the written exam may be changed to an oral exam. The re-sit exam will be held in August.

Course materials

To be announced at the start of the semester.

Credit reductions

Course code Reduction From
MNFMA109 7.5 sp
TMA4105 7.5 sp
SIF5005 7.5 sp Autumn 2025
TMA4111 4 sp Autumn 2025
TMA4121 3.5 sp Autumn 2025
TMA4411 3.5 sp Autumn 2025
IMAA2012 3.5 sp Autumn 2025
IMAA2022 3.5 sp Autumn 2025
IMAA2100 5 sp Autumn 2025
IMAA3012 5 sp Autumn 2025
IMAG2012 3.5 sp Autumn 2025
IMAG2022 3.5 sp Autumn 2025
IMAG2100 5 sp Autumn 2025
IMAG3012 5 sp Autumn 2025
IMAT2012 3.5 sp Autumn 2025
IMAT2022 3.5 sp Autumn 2025
IMAT2100 5 sp Autumn 2025
IMAT3012 5 sp Autumn 2025
This course has academic overlap with the courses in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics

Contact information

Course coordinator

Department with academic responsibility

Department of Mathematical Sciences

Examination

Examination

Examination arrangement: School exam
Grade: Letter grades

Ordinary examination - Spring 2026

School exam
Weighting 100/100 Examination aids Code D Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.

Re-sit examination - Summer 2026

School exam
Weighting 100/100 Examination aids Code D Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.