Course syllabus for Linear algebra and differential equations

Course syllabus adopted 2024-02-05 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra och differentialekvationer
  • CodeMVE580
  • Credits7.5 Credits
  • OwnerTIMEL
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 67125
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0119 Examination 7.5 c
Grading: TH		0 c7.5 c0 c0 c0 c0 c
  • 16 Jan 2025 pm L
  • 14 Apr 2025 pm L
  • 18 Aug 2025 pm L

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

The course LMA401 Calculus, or equivalent knowledge.

Aim

The aim of the course is to, in a logically coherent way, give basic knowledge of differential equations and linear algebra. The course will also give necessary prerequisites for mathematical treatment of technical problems in future profession and supply a good base for further studies.

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

  • define, describe and prove basic concepts in matrix and vector algebra.
  • solve systems of linear equation.
  • determine if a matrix is invertible and, if so, determine the inverse.
  • calculate determinants.
  • calculate scalar and vector product.
  • apply vectors within space geometry.
  • use the least squares method.
  • calculate with complex numbers on both rectangular and polar form.
  • set up and solve simple differential equations.
  • find eigenvalues and eigenvectors

Content

  • Linear equation systems: row equivalents for matrices, the elimination method on matrix form.
  • Matrix algebra: addition, subtraction, multiplication, inverse matrix.
  • The least squares method.
  • Linear combination, linearly independent / dependent.
  • Determinants: conditions for invertability, laws of calculation, Cramers rule.
  • Geometric vectors: addition, subtraction, scalar and vectorial product, applications in space geometry.
  • Complex numbers: rectangular coordinates,  laws of calculation, algebraic equations, polar coordinates, de Moivre's formula, Euler's formulas, binomial equations.
  • Eigenvalues and eigenvectors

Organisation

The course includes lectures, tutorials, quizzes and homework.

Literature

J. Månsson & P. Nordbeck, Linjär algebra, 1st ed., Studentlitteratur
J. Månsson & P. Nordbeck, Övningar i linjär algebra, 1st ed., Studentlitteratur
J. Månsson & P. Nordbeck, Endimensionell analys, 1st ed., Studentlitteratur
J. Månsson & P. Nordbeck, Övningar i endimensionell analys, 2nd ed., Studentlitteratur

Examination including compulsory elements

Examination consists of a written exam. Quizzes giving bonus points may be offered. Grades TH.

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.