M4180 Numerical Methods I

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
RNDr. Bc. Iveta Selingerová, Ph.D. (seminar tutor)
Mgr. Jakub Záthurecký, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Fri 8:00–9:50 online_M1
  • Timetable of Seminar Groups:
M4180/01: Mon 1. 3. to Fri 14. 5. Mon 8:00–9:50 online_MP1, I. Selingerová
M4180/02: Mon 1. 3. to Fri 14. 5. Thu 16:00–17:50 online_MP1, J. Záthurecký
Prerequisites
!( ROCNIK(1) && PROGRAM(B-MA))
Differential calculus of functions of one and more variables. Basic knoledge of linear algebra-theory of matrices and solving systems of linear equations. Basics of programming.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course together with the course Numerical Methods II provides complete explanation of numerical mathematics as the separate scientific discipline. The emphasis is given to the algorithmization and computer implementation. Some examples with graphical outputs help to explain even some difficult parts. At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines e.g. in statistical methods.
Learning outcomes
Student will be able to:
- to solve numerical nonlinear equations and to decide which method will be most suitable for the problem,
- separate the real roots of the polynomials and determine them using the appropriate numerical method,
- use iterative methods to find solutions for both linear and nonlinear systems.
Syllabus
  • Error analysis
  • Solving of nonlinear equations-iterative methods, their order and convergence, Newton method, secant method, regula falsi method, Steffensen method, Müller method
  • Solving of systems of nonlinear equations-Newton method, Seidel method
  • Roots of polynomials-Sturm theorem, application of Newton method, finding all roots of polynomials, Bairstow method
  • Direct methods for solving systems of linear equations-Gaussian elimination, LU decomposition, Cholesky method, Crout method, backward error analysis, stability of algorithms and conditioning of problems
  • Iterative methods for solving of systems of linear equations- principle of a construction of iterative methods, convergence theorems, Jacobi method, Gauss-Seidel method, relaxation methods
Literature
    recommended literature
  • HOROVA, Ivana and Jiří ZELINKA. Numerické metody (Numerical Methods). 2nd ed. Brno: Masarykova univerzita v Brně, 2004, 294 pp. 3871/Př-2/04-17/31. ISBN 80-210-3317-7. info
  • MATHEWS, John H. and Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River, N.J.: Pearson, 2004, ix, 680. ISBN 0130652482. info
    not specified
  • DATTA, Biswa Nath. Numerical linear algebra and applications. Pacific Grove: Brooks/Cole publishing company, 1994, xxii, 680. ISBN 0-534-17466-3. info
  • STOER, J. and R. BULIRSCH. Introduction to numerical analysis. 1st ed. New York - Heidelberg - Berlin: Springer-Verlag, 1980, 609 pp. IX. ISBN 0-387-90420-4. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
Teaching methods
Lecture: 2 hours weeky, theoretical preparation. Class excercise: 2 hours weekly, Theoretical exercise (1 hour)is focused on solving of problems by methods presented in the lecture, practical exercise (1 hour) in a computer room is aimed at algoritmization and programming of presented numerical methods.
Assessment methods
Attendance of class exercises is compulsory, successful tests results or elaboration the assigned tasks is required for a credit.
Exam is written.
Grading according to the achieved results:
A: 20-22 points
B: 18-19 points
C: 16-17 points
D: 14-15 points
E: 12-13 points
F: less than 12 points
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2021/M4180