Algorithms of numerical analysis (classes) (ćwiczenia) - 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.
Prerequisites
Introduction to differential and integral calculus
Linear algebra with analytic geometry
Basic knowledge of programming methods
Learning outcomes
KNOWLEDGE
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.
SKILLS
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.
SOCIAL COMPETENCE
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
Discussion, problem solving, own work with a computer
Course content description
1. Horner scheme. Polynomial interpolation. Lagrange and Newton polynomials. Neville\\\'s algorithm. Hermite interpolation.
2. Gaussian elimination. LU decomposition. Cholesky decomposition. The Cholesky algorithm avoiding taking square roots.
3. Householder orthogonalization.
4. Chebyshev systems. The method of least squares. Linear least squares solutions by Householder transformations.
5. Numerical differentiation and integration. Quadrature rules based on interpolating functions. Composite Newton–Cotes formulas.
6. Methods for solving nonlinear equations. Bisection method. Newton\\\'s method. The secant method. Regula falsi method.
7. Newtons method for solving system of nonlinear equations.
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
HOURLY EQUIVALENTS OF ECTS POINTS
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
REQUIRED READING
W. Cheney, D. Kincaid, Numerical Mathematics and Computing, 6th ed., Thomson Brooks/Cole, 2008
RECOMMENDED READING
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: 0
Form of assessment: Grade