## 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