Course syllabus for Linear algebra and numerical analysis

The course syllabus contains changes
See changes

Course syllabus adopted 2020-02-12 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra och numerisk analys
  • CodeTMA672
  • Credits7.5 Credits
  • OwnerTKTFY
  • Education cycleFirst-cycle
  • Main field of studyMathematics, Engineering Physics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 57117
  • Maximum participants190
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0119 Laboratory 1.5 c
Grading: UG		 1.5 c
0219 Examination 6 c
Grading: TH		 6 c
  • 31 Maj 2021 pm J
  • 10 Okt 2020 am J
  • 26 Aug 2021 am 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.

Course specific prerequisites

A first course in Linear algebra and geometry

Aim

To present an introduction to linear spaces concepts such as linear dependence/independence, basis, dimension, orthogonality and spectral theory. To give the basics in numerical analysis and computational mathematics.

Learning outcomes (after completion of the course the student should be able to)

  • use linear algebra concepts for solving problems in engineering and science.
  • use mathematical models for numerical solution of real world problems.
  • critically analyze and give advice regarding different methods and algorithms with respect to efficiency and reliability.

Content

  • Vector spaces: Basis, dimension, sub-spaces.
  • Inner product, orthogonality.
  • Linear mappings.
  • Eigenvalues and eigenvectors, spectral theory, quadratic forms.
  • Applications in analysis; systems of ordinary differential equations.
  • Numerical techniques for solution of linear systems, least squares problems and eigenvalue problems.
  • QR-factorization and SVD.
  • Numerical equation solving and optimization, search methods.
  • Interpolation, and its use for numerical integration and differentiation, splines.
  • Numerical solution of differential equations, explicit and implicit methods, stability.

Organisation

Lectures, lessons, and computer exercises.

Literature

- Kjell Holmåker och Ivar Gustafsson, Linjär Algebra: fortsättningskurs, 1st ed., Liber - Ivar Gustafsson och Kjell Holmåker, Numerisk Analys, 1st ed., Liber

Examination including compulsory elements

Written examination with problems of theoretical and applied nature. Computer exercises. Homework assignments giving credit points for the examination may exist.

The course syllabus contains changes

  • Changes to course rounds:
    • 2020-11-15: Max number of participants Max number of participants changed from 180 to 190 by PA
      [Course round 1]