The aim of studying and bibliography

The main aim of study: To acquaint students with selected topics in higher mathematics. Students will have one of two topics to choose, which will be given before the end of the second semester

The general information about the module: Semester 5,The module is implemented in the form of lectures (30 hours) and exercises (15 hours).

Bibliography required to complete the module

Bibliography used during lectures

1	A. Kiełbasiński, H.Schwetlick	Numeryczna algebra liniowa	WNT, Warszawa.	1992
2	D. Kincaid, W. Cheney	Analiza numeryczna	WNT, Warszawa .	2006

Bibliography used during classes/laboratories/others

1	A. Bjorc, G. Dahlquist	Metody numeryczne	PWN, Warszawa .	1987
2	A. Maćkiewicz	Algorytmy algebry liniowej. Metody bezpośrednie	Wydawnictwo Politechniki Poznańskiej, Poznań.	2002

Bibliography to self-study

1

Z.Fortuna, B.Macukow, J.Wąsowski

Metody numeryczne

WNT .

2001

Basic requirements in category knowledge/skills/social competences

Formal requirements: Completion of the course Mathematical analysis and Linear algebra. The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: A student has mathematical knowledge which allows him/her to understand the lectured material.

Basic requirements in category skills: Ability to use fundamental mathematical tools and the knowledge obtained during the first level studies.

Basic requirements in category social competences: Ability of individual and group learning.

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	Student knows the basic terminology and facts about linear mappings and matrices.	lectures, problem exercises	written test	K_W01+ K_U01+ K_K01+ K_K05+	P6S_KK P6S_KO P6S_UW P6S_WG
02	Knows main methods of exact and approximate solving of systems of linear equations	lectures, problem exercises	written test	K_W01+ K_W08+ K_U01+ K_U10+ K_K01+	P6S_KK P6S_UW P6S_WG
03	Knows main methods of calculation of eigenvalues	lectures, problem exercises	written test	K_W01+ K_W08+ K_U01+ K_U10+ K_K01+	P6S_KK P6S_UW P6S_WG

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
5	TK01	Bounded linear operators and their norms. Eigenvalues and eigenvectors of operators and matrices, characteristic polynomial and spectral radius. Hermitian, normal, unitary, positive-definite matrices, similarity of matrices. Householder matrices, transforming the matrix into a triangular form, diagonal form of matrix, Jordan matrix.	W1-W15 C1-C7	MEK01
5	TK02	Numerical solution of systems of linear equations (Gauss's algorithm, Cholesky–Banachiewicz algorithm)	W16-W22 C8-C11	MEK02
5	TK03	Some methods of calculating of eigenvalues, algorithms of reduction of any matrix to a Hessenberg form and three-pronged matrix, methods of calculation of characteristic polynomial, the methods GR and its improvments, Jacobi's method.	W23-W30 C12-C15	MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 5)		contact hours: 30.00 hours/sem.	Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 5)	The preparation for a test: 10.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 4.00 hours/sem.
Advice (sem. 5)
Credit (sem. 5)

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	A credit for the lecture is based on attendance at the lectures.
Class	A credit for the exercises is based on the results of tests and oral answers.
The final grade	The final grade is a grade for the exercises.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: no