PřF:M4180 Numerical methods I - Course Information

M4180 Numerical Methods I

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

there are 7 fields of study the course is directly associated with, display

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

• M5180 Numerical Methods II
• M9100 Numerical methods for solving ordinary differential equations
• M9140 Theoretical Numerical Analysis

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

• M5180 Numerical Methods II
  M4180 || (FI:M028)  

• Enrolment Statistics (Spring 2021, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2021/M4180