course-details-portlet

TMA4110

Mathematics 3 - Linear algebra

Choose study year
Credits 7.5
Level Foundation courses, level I
Course start Autumn 2025
Duration 1 semester
Language of instruction Norwegian
Location Trondheim
Examination arrangement School exam

About

About the course

Course content

Complex numbers and the complex exponential function. Second order linear differential equations. Systems of linear equations, Gauss-Jordan elimination, reduced echelon form, matrix algebra, determinants. Vector spaces, subspaces, linear dependence and independence. Inner products, orthogonality, orthogonal projections, Gram-Schmidt orthogonalization, and the method of least squares. Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms. First order systems of differential equations.

Learning outcome

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from linear algebra in Euclidean spaces and systems of differential equations.

2. Skills. The student is able to apply his or her knowledge of linear algebra and systems of differential equations 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. Parts of this course can be taught in English.

Compulsory assignments

  • Exercises

Further on evaluation

Grade based on 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 semester.

Credit reductions

Course code Reduction From
SIF5009 7.5 sp
SIF5010 7.5 sp
MA1201 3 sp Autumn 2009
MA1202 3 sp Autumn 2009
MA0003 1.5 sp Autumn 2009
TMA4115 7.5 sp Autumn 2006
MA6201 3 sp Autumn 2012
MA6202 3 sp Autumn 2020
TMA4101 3.7 sp Autumn 2020
TMA4106 3.7 sp Autumn 2020
TMA4400 2 sp Autumn 2025
TMA4410 5.5 sp Autumn 2025
TMA4411 5.5 sp Autumn 2025
TMA4413 7.5 sp Autumn 2025
TMA4422 5.5 sp Autumn 2025
IMAT3011 2.5 sp Autumn 2025
IMAG3011 2.5 sp Autumn 2025
IMAA3011 2.5 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

  • Technological subjects

Contact information

Course coordinator

Lecturers

Department with academic responsibility

Department of Mathematical Sciences

Examination

Examination

Examination arrangement: School exam
Grade: Letter grades

Ordinary examination - Autumn 2025

School exam
Weighting 100/100 Examination aids Code C Duration 4 hours Exam system Inspera Assessment
Place and room
The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.

Re-sit examination - Summer 2026

School exam
Weighting 100/100 Examination aids Code C Duration 4 hours Exam system Inspera Assessment
Place and room
The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.