# TMA4115 - Mathematics 3 - Linear algebra

### Examination arrangement

Examination arrangement: School exam

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

### 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. The lectures may be given in English.

• Exercises

### Further on evaluation

Grade based on written final written examination. Retake of examination may be given as an oral examination.

### Course materials

Will be announced at the beginning of the semester.

### Credit reductions

Course code Reduction From To
SIF5010 7.5
MA1201 3.0 AUTUMN 2009
MA1202 3.0 AUTUMN 2009
TMA4110 7.5 AUTUMN 2006
MA0003 1.5 AUTUMN 2009
MA6201 3.0 AUTUMN 2012
TMA4101 3.7 AUTUMN 2020
TMA4106 3.7 AUTUMN 2020
More on the course

Facts

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

Coursework

Term no.: 1
Teaching semester:  SPRING 2024

Language of instruction: English, Norwegian

Location: Trondheim

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

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 100/100 2024-05-16 09:00
Summer UTS School exam 100/100
• * 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.
Examination

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

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