Course syllabus for Linear algebra and differential equations

Course syllabus adopted 2025-02-22 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra och differentialekvationer
  • CodeMVE755
  • Credits7.5 Credits
  • OwnerTKTKE
  • 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 43116
  • Maximum participants215
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0125 Laboratory 1.5 c
Grading: UG		 1.5 c
0225 Examination 6 c
Grading: TH		 6 c

In programmes

Examiner

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

Knowledge equivalent to the content in the courses Single variable calculus and Fundamentals of program development

Aim

The aim of the course, together with the other mathematics courses, is to provide a general knowledge of mathematics that is as useful as possible in further studies and technical careers. The course should provide, in a logical and coherent way, knowledge of linear algebra and ordinary differential equations that are necessary for other courses in the Engineering Chemistry and Bioengineering programs.

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

  • explain the meaning of an ordinary differential equation and its directional field
  • apply and explain analytical methods for solving ordinary differential equations
  • account for the concepts of linear algebra given in this course
  • account for the connections between the different concepts and use these connections in problem solving
  • use the software Python in problem solving

Content

  • Linear transformations, matrix representation
  • Matrix algebra, matrix inverse and systems of linear equations
  • The Euclidean vector space Rn, linear independence, subspaces of Rn, null space (kernel), column space (range), bases, change of basis, dimension, rank
  • Eigenvalues, real and complex, eigenvectors, diagonalization
  • Orthogonal projection, orthonormal basis, method of least squares, the spectral theorem 
  • Determinants
  • Complex numbers, the fundamental theorem of algebra
  • Ordinary differential equations: First-order equation in general, analytical solution of separable and linear equations. Second-order linear equations with constant coefficients, the equations of simple and damped harmonic motion
  • Systems of first order linear differential equations with constant coefficients
  • Numerical methods for solving systems of ordinary differential equations
  • Systems of linear equations, the augmented matrix, method of elimination
  • Solving linear systems of equations with Python

Organisation

Instruction is given in lectures and classes together with computer sessions using Python. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

The laboratory moment is examined with compulsory computer laboratories during the course and gives the grade G or U.

The exam moment is examined with a written exam at the end of the course and has the grading scale U,3,4,5.

For a passing grade on the course, a passing grade is required on both moments and the final grade will then be the same as the grade on the exam moment.

During the course there may be tests that generate bonus credits on the exam. Examples of such tests include intermediate tests and hand-in assignments. Information pertaining to the actual course round is provided on the course homepage.

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.