M5180 Numerical Methods II

Faculty of Science
Autumn 2024
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
RNDr. Bc. Iveta Selingerová, Ph.D. (lecturer)
Guaranteed by
RNDr. Bc. Iveta Selingerová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16:00–17:50 M3,01023
  • Timetable of Seminar Groups:
M5180/01: Mon 18:00–18:50 M3,01023, I. Selingerová
Prerequisites
M4180 Numerical methods I || ( FI:M028 Numerical Methods I )
Differential and integral calculus of one and more variables. Basic knowledge of linear algebra.
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 I provides systematic explanation of numerical mathematics as the special scientific discipline. In addition to the classical methods the modern procedures suitable for algorithmization and computer implementation are also presented. During the course, a student is acquainted with advantages and disadvantages of the methods.
Learning outcomes
At the end of the course, the student will be able to: solve numerical nonlinear equations, define numerical algorithms for interpolation, differentiation, and integration; explain advantages and disadvantages of the mentioned numerical methods; use the numerical methods for solving practical problems.
Syllabus
  • Solving nonlinear equations - order of convergence, acceleration of convergence, methods for multiple roots, Quasi Newton's method, Steffensen's method
  • Roots of polynomials - Sturm's theorem, double Newton's method, Maehly's method, Bairstow's method
  • Interpolation - the error of the polynomial interpolation, iterated interpolation, Hermite interpolation polynomial
  • Approximation - B-splines, B-spline curves, NURBS curves
  • Numerical differentiation - Richardson extrapolation, continuation of curves
  • Numerical integration - Gaussian quadratures, special quadrature formula (Lobatt formula, Chebyshev formula), Romberg quadrature formula, adaptive quadratures
  • Iterative methods for systems of linear equations - Jacobi method, Gauss-Seidel method.
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
  • BURDEN, Richard L. and Douglas J. FAIRES. Numerical analysis. 3rd ed. Boston: PWS Publishing Company, 1985, 676 pp. ISBN 0-87150-857-5. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • PŘIKRYL, Petr. Numerické metody matematické analýzy. 1. vyd. Praha: Nakladatelství technické literatury, 1985, 187 s. URL info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation.
Class exercise: 1 hour weekly. Excercise is focused on examples for practicing methods presented in the lecture.
Assessment methods
Active participation and successfully written test are required for credit.
The exam is written.
The conditions may be specified according to the evolution of the epidemiological situation and the applicable restrictions.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/M5180