Study unit

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3315160 Vectors and matrices, 5 Cp 
Code 3315160  Validity 01.02.2021 -
Name Vectors and matrices  Abbreviation Vectors and mat 
Credits5 Cp  Date of expiry  
TypeGeneral Studies Subject0510 Mathematics 
ClassStudy Unit  Hours  
Study right   Grading0-5 
Recommended scheduling 
   
Organisation Physics and Mathematics(J) 

Teachers
Name
Janne Gröhn 

Description
Learning outcomes 

Upon successful completion of the course, the student is able to solve systems of linear equations by the Gaussian elimination. The student knows how to represent the system of equations in a vector or matrix form and is also capable of analyzing its solutions. The student understands the concepts of the subspace of a Euclidean space, the basis vector and the dimension of the space. The student knows how to verify whether given vectors are linearly independent. The student can do basic matrix computations and knows how to compute the determinant and the inverse of a given square matrix. The student is also capable of computing eigenvalues. The student knows how to represent geometric problems in terms of vectors and to solve them with tools of linear algebra. The student is able to prove basic properties of vectors and matrices by justifying each step of the argument.

The student can apply linear algebra in the context of practical problems, for example, by applying the method of least squares. The student is able to compute by hand and also by symbolic software.

 
Content 

Systems of linear equations and their solutions via Gaussian elimination, linear independence of vectors in a Euclidean space, subspace of a Euclidean space, basis vectors and dimension of a Euclidean space, straight lines and planes, matrices, determinant of a square matrix, eigenvalues and diagonalization, dot product of vectors, cross product of vectors and vector triple product.

 
Modes of study 

This course is available only to M.Sc. (Tech.) students. Either course examination and active participation in exercises or general examination.

 
Teaching methods 

Online material, small group sessions 14 h, exercises 14 h.

 
Study materials 

Poole, David: Linear Algebra: A Modern Introduction (2nd ed.).

 
Evaluation criteria 

0-5

 
Teachers 

Janne Gröhn

 
Prerequisites 

The basic studies in mathematics in university of applied science (tech.), long mathematics syllabus in high school or equivalent initial knowledge.

 
Time 

Each year in period 4.

 
Campus 

Campuses of Joensuu and Kuopio

 


Letter (J, K) in front of the name of the course/exam indicates the campus on which teaching or exam takes place: J = Joensuu, K = Kuopio.

Present and future teaching
Functions Name Type Cp Teacher Timetable
No registration in WebOodi Vectors and matrices  Lecture and exercise course  Janne Gröhn  21.03.22 -31.05.22

Future exams
Functions Name Type Cp Teacher Timetable
Registration not started Vectors and matrices  General examination  Janne Gröhn 
22.10.21fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn 
14.01.22fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn 
10.06.22fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn 
26.08.22fri 12.00-16.00