The aim of studying and bibliography

The main aim of study:

The general information about the module: The module contains the content of methods of solving linear and nonlinear systems equations, interpolation, numerical integration, solving the initial value problems for ordinary differential equations.

Bibliography required to complete the module

Bibliography used during lectures

1	D. Kicaid, W.Cheney	Analiza numeryczna	WNT, Warszawa .	2006
2	Z. Fortuna, B. Macukow, J. Wąsowski	Metody numeryczne	WNT, Warszawa.	2002

Basic requirements in category knowledge/skills/social competences

Formal requirements: A course of mathematical analysis and algebra, programming languages.

Basic requirements in category knowledge: Basic knowledge of mathematical analysis and matrix calculations, programming languages.

Basic requirements in category skills: The ability to solve selected problems in the field of linear algebra, differential and integral calculus, differential equations and the use of computational packages.

Basic requirements in category social competences: It can appropriately determine the priorities for the realization of one's own or other tasks

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	Knows the basic concepts and numerical problems as well as selected methods of constructing numerical algorithms.	lectures, laboratory exercises, employments practical	pass the part practical	K_W02+ K_W04+	P6S_WG
02	Knows the basic computational techniques that support the analyst's work, understands their role and limitations.	lectures, laboratory exercises, employments practical	pass the part practical	K_W03+	P6S_WG
03	Knows selected software packages for symbolic and numerical calculations necessary for modeling and solving engineering problems (e.g. SciLab)	lectures, laboratory exercises, employments practical	pass the part practical	K_W02+	P6S_WG
04	Can formulate a problem in the language of mathematics, analyze it, select and use appropriate software and IT tools to solve it, and then visualize and interpret the obtained results.	lectures, laboratory exercises, employments practical	pass the part practical	K_U05+ K_U06+ K_U07+ K_U08+ K_U25+ K_K02+	P6S_KK P6S_KO P6S_UU P6S_UW
05	Can analyze the algorithms and their correctness and computational complexity.	lectures, laboratory exercises, employments practical	pass the part practical	K_U11+ K_K02+	P6S_KK P6S_KO P6S_UW

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
3	TK01	Mathematical modeling and numerical calculations. Write numbers in the computer. Classification of calculation errors.	W1	MEK02 MEK05
3	TK02	Direct methods for solving systems of linear equations. The method of Gaussian elimination. Calculations determinants and inverse matrices. Elimination method for systems with tridiagonal matrix. Iterative methods. The methods of successive approximations (simple iteration), Jacobi, Gauss-Seidel, upper relaxation. Convergence of Iterative methods	W1-W10, L1-L10, C1-C3	MEK01 MEK02 MEK03 MEK04 MEK05
3	TK03	Methods for solving nonlinear equations. Methods bisection, successive approximations (simple iteration), Newton’s, secant. Methods for solving systems of nonlinear equations. The method of successive approximations, Newton’s	W11-W14, L11-L14, C4-C6	MEK01 MEK02 MEK03 MEK04
3	TK04	Function approximation. Interpolation polynomials of Lagrange and Newton. Estimation of the error of the interpolation polynomial. The method of least squares. Spline interpolation. Numerical differentiation.	W15-W20, L15-L20, C7-C9,	MEK01 MEK02 MEK03 MEK04 MEK05
3	TK05	Numerical integration. Newton-Cotes quadrature. Formulas of rectangles, trapezoids, Simpson. Composite quadrature formulas. Gauss quadratures. Practical estimation of the error at quadrature formulas.	W21-W24, L21-L24, C10-C12	MEK01 MEK02 MEK03 MEK04 MEK05
3	TK06	Methods of numerical solution of the initial value problem for ordinary differential equations. Taylor series and Runge-Kutta methods. Linear multistep methods. Order of approximation and stability of linear multistep methods. Numerical integration of stiff systems of ordinary differential equations. Implementation of linear multistep methods	W25-W30, L25-L30, C12-C15	MEK01 MEK02 MEK03 MEK04 MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 3)	The preparation for a test: 2.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 2.00 hours/sem. Studying the recommended bibliography: 2.00 hours/sem.
Class (sem. 3)	The preparation for a Class: 2.00 hours/sem. The preparation for a test: 2.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 2.00 hours/sem.
Laboratory (sem. 3)	The preparation for a Laboratory: 2.00 hours/sem. The preparation for a test: 2.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Making the report: 2.00 hours/sem.
Advice (sem. 3)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Credit (sem. 3)	The preparation for a Credit: 3.00 hours/sem.	The written credit: 1.00 hours/sem.

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

The type of classes	The way of giving the final grade
Lecture	Written work (tasks).
Class	Work in the classroom.
Laboratory	Written laboratory works
The final grade	Average rating: written work (50%), written laboratory works (50%)

Sample problems

Required during the exam/when receiving the credit
kolok1.pdf

Realized during classes/laboratories/projects
Zad1.pdf

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