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Numerical Methods


Some basic information about the module

Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Medical Engineering
The area of study:
technical sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
The degree after graduating from university:
inżynier
The name of the module department :
Departament of Topology and Algebra
The code of the module:
9736
The module status:
mandatory for teaching programme
The position in the studies teaching programme:
sem: 2 / W15 L15 / 2 ECTS / Z
The language of the lecture:
Polish
The name of the coordinator:
Krzysztof Pupka, PhD

The aim of studying and bibliography

The main aim of study:

The general information about the module:

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. Wasowski Metody numeryczne WNT, Warszawa. 2002
Bibliography used during classes/laboratories/others
1 L. Jaroszyński, M. Łanczont Laboratorium metod numerycznych Politechnika Lubelska, Lublin . 2014
Bibliography to self-study
1 J. i M. Jankowscy Przegląd metod i algorytmów numerycznych WNT, Warszawa. 1988

Basic requirements in category knowledge/skills/social competences

Formal requirements:
The student satisfies the formal requirements set out in the study regulations

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

Basic requirements in category skills:
Ability to solve simple tasks of of mathematical analysis, the ability to perform calculations on arrays, the ability to use the calculator and computer.

Basic requirements in category social competences:

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
MEK01 Student knows the basic methods of numerical integration, and numerical solution of differential equations. lecture, laboratory examination the written part K-U01+
K-U04+
K-K01+
 P6S-KO
P6S-UK
P6S-UU
P6S-UW
MEK02 Can to solve numerically a simple problem, using the CAS Maxima. laboratory examination the written part K-W09+
K-W14+
K-U01+
K-K05+
 P6S-KK
P6S-KO
P6S-UO
P6S-UU
P6S-UW
P6S-WG
P6S-WK
MEK03 Knows the basic numerical methods for solving equations and systems of linear equations. lectures, laboratory work examination the written part K-U01+
K-U04+
K-K01+
 P6S-KO
P6S-UK
P6S-UU
P6S-UW

The syllabus of the module

Sem. TK The content realized in MEK
2 TK01 Mathematical modeling and numerical calculations. Write numbers in the computer. Classification of calculation errors. W01 MEK02
2 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. W01- W02, L01, L02 MEK03
2 TK03 Methods for solving nonlinear equations. Methods bisection, successive approximations (simple iteration), Newton’s, secant. Methods for solving systems of nonlinear equations. W03-W04, L03,L04 MEK03
2 TK04 Function approximation. Interpolation polynomials of Lagrange and Newton. Estimation of the error of the interpolation polynomial. The method of least squares. W05, L05 MEK01 MEK02
2 TK05 Numerical integration. Newton-Cotes quadrature. Formulas of rectangles, trapezoids, Simpson. Composite quadrature formulas. W06, L06 MEK01 MEK02
2 TK06 Methods of numerical solution of the initial value problem for ordinary differential equations. Taylor series and Runge-Kutta methods. W07, L07 MEK01 MEK02

The student's effort

The type of classes The work before classes The participation in classes The work after classes
Lecture (sem. 2) contact hours: 15.00 hours/sem.
 complementing/reading through notes: 3.00 hours/sem.
Studying the recommended bibliography: 3.00 hours/sem.
Laboratory (sem. 2) The preparation for a Laboratory: 5.00 hours/sem.
 contact hours: 15.00 hours/sem.
 Finishing/Making the report: 5.00 hours/sem.
Others: 5.00 hours/sem.
Advice (sem. 2) The preparation for Advice: 1.00 hours/sem.
 The participation in Advice: 1.00 hours/sem.
Credit (sem. 2) The preparation for a Credit: 5.00 hours/sem.
 The written credit: 2.00 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).
Laboratory
The final grade

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