Course syllabus for Linear algebra and experimental mathematics

Course syllabus adopted 2021-02-18 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra och experimentell matematik
  • CodeSEE085
  • 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 74120
  • Maximum participants65
  • Open for exchange studentsNo

Credit distribution

0120 Examination 7.5 c
Grading: TH		 7.5 c
  • 03 Jun 2023 am J
  • 08 Okt 2022 pm J
  • 25 Aug 2023 pm J

In programmes

Examiner

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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 and tutorials

Literature

Matematisk analys och linjär algebra, del III”, av Larsson, Logg och Målqvist

Examination including compulsory elements

Written exam. Voluntary tasks giving bonus points on the exam can be handed out.

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 on educational support due to disability.