Algorithms of numerical analysis (lecture) (wykład) - 2019/2020

Course description
General information
Lecturer:dr Małgorzata Nowak-Kępczyk
Organising unit:Faculty of Science and Health - Instytut Matematyki, Informatyki i Architektury Krajobrazu
Number of hours (week/semester): 2/30
Language of instruction:English
Course objective
The main aim of the course is to familiarize students with the methods of numerical analysis with emphasis on algorithm construction, analysis and implementation. Students are able to apply these methods in practice.
Introduction to differential and integral calculus
Linear algebra with analytic geometry
Basic knowledge of programming methods
Learning outcomes
W1 - Students know basic concepts of numerical analysis K_W01, K_W03, K_W06.
W2 - Students have knowledge in using methods of interpolation, approximation, numerical integration, solving linear and nonlinear equations K_W03, K_W06.
W3 - Students know meaning of numerical methods for practical use K_W03, K_W06.
U1 - Students are able to use basic concepts of numerical analysis K_U04, K_U07, K_U20, K_U22.
U2 - Students are able to use methods of numerical analysis and implement numerical algorithms K_U04, K_U07, K_U08, K_U11, K_U20, K_U22.
K1 - Students are aware of the level of their knowledge and skills, understand the need of further training and improving both professional and personal competence K_K01
K2 - Students understand necessity of application of numerical methods for solving practical problems K_K04
Teaching method
Multimedia presentation.
Course content description
1. Horner\'s scheme. Polynomial interpolation. Lagrange interpolation formula. Newton interpolation formula. Neville\'s iterative formula. Hermit interpolation.
2. Methods of solving systems of linear equations. Gaussian elimination method. Matrix distribution methods based on Gaussian elimination. Choleski distribution method A = LL * positively determined matrices. Choleski method without square roots.
3. Householder orthogonalization method
4. Approximation. Least squares method. Chebyshev systems. Householder\'s method of numerical solving of the method of least squares.
5. Numerical integration. Interpolation quadratures. Newton-Cotes quadratures.
6. Methods of solving nonlinear equations and their systems. Bisection method. Secant method, regula falsi method. Newton\'s method. Newton\'s multidimensional method.
7. Linear programming. Simplex method. Integer programming.
Forms of assessment
Examination (for those who have completed the classes) in written form. Below 40% - insufficient rating.

W1 - exam, preparation for classes
W2 - exam, preparation for classes
W3 - exam, preparation for classes
U1 - test, preparation for classes, final project
U2 - test, preparation for classes, final project
K1 - work and activity in classes, final project
K2 - work and activity in classes, final project
Hours implemented as part of the study program
Lecture 30
Exercises 30
Total number of hours with the participation of an academic teacher 60
Number of ECTS credits with the participation of an academic teacher 2

Own work
Preparation for classes 15
Studying literature 15
Preparation for test 15
Preparation for the exam 15
Preparation of the final project 15
Total number of hours 75
Number of ECTS points 3
Total number of ECTS points for module 5
Required reading list
W. Cheney, D. Kincaid, Numerical Mathematics and Computing, 6th ed., Thomson Brooks/Cole, 2008
J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, 1980.
G. Dahlquist, Å. Björck, Numerical Methods, Dover Publications, 2003.
Field of study: Informatics
Course listing in the Schedule of Courses:
Year/semester:Year II - Semester 3
Number of ECTS credits: 5
Form of assessment: Examination