Course syllabus adopted 2024-02-14 by Head of Programme (or corresponding).
Overview
- Swedish nameLinjär algebra och experimentell matematik
- CodeSEE086
- Credits7.5 Credits
- OwnerTKGBS
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentSPACE, EARTH AND ENVIRONMENT
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 74123
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0123 Examination, part A 6 c Grading: TH | 6 c |
| |||||
| 0223 Project, part B 1.5 c Grading: UG | 1.5 c |
In programmes
Examiner
Rüdiger Haas- Områdesledare, Space, Earth and Environment
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
The same as for the programme that owns the course.Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Aim
Linear algebra is an essential mathematical tool in most fields of engineering and addresses in particular all kind of data analysis and modeling tasks. Global system engineers work with measurements and data of natural and societal phenomena and thus need appropriate mathematical skills to analyze and interpret these data. The students of this course learn basic linear algebra by mixing traditional theoretical learning with experiments performed using numerical software. The course deals with the basic components of linear algebra, such as vectors and matrices. Students familiarise themselves with abstract objects, verify theorems, and investigate hypotheses both formally and intuitively by switching between "paper and pen" learning and numerical experiments.Learning outcomes (after completion of the course the student should be able to)
- understand and use basic concepts in linear algebra, such as linear equation systems, vector spaces, vector algebra, linear independent base vectors, inner product, orthogonality, determinant, eigenvalues and eigenvectors.
- use numerical software to solve problems and investigate relationships in linear algebra
- have a basic understanding of how linear algebra can be used in modelling and problem solving, for example for ordinary differential equations
Content
Linear equation systems
Gauss elimination
Vectors, linear spaces (R^n) and base vectors
Scalar product, orthogonal vectors and vector product
Lines, planes and vector algebra in three or more dimensions
Matrices (linear operators), matrix algebra
Least squares method
Diagonalization, eigenvalues and eigenvectors
Spectral theorem for symmetrical matrices
Quadratic forms
Numerical analysis av linear equations
Applications
Organisation
Lectures, tutorials, and project work.Literature
Matematisk analys och linjär algebra, del III, av Larsson, Logg och MålqvistExamination including compulsory elements
Written exam of 6 hp, and project work pf 1.5 hp. Voluntary tasks giving bonus points on the written exam might be possible.The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.