Course: Numerical Mathematics

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Course title Numerical Mathematics
Course code KAP/NUM
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Lecturer(s)
  • Brzezina Miroslav, doc. RNDr. CSc.
Course content
Lectures: 1. Numerical methods - numerical model, sources of error, numerical stability, speed of computation. Paralellelization of numerical computations - basic models of parallel programming, methods of parallelization, Amdahl's law. 2. Direct methods for solving linear systems - Gaussian elimination, Gaussian elimination for tridiagonal matrix, LU decomposition, Choleski decomposition. 3. Iterative methods for solving linear systems - Jacobi method, Gauss-Seidel method, successive over-relaxation, conjugate gradient method. 4. Solving rectangular linear systems - normal equations system, singular value decomposition, pseudoinverse matrix. 5. Solving nonlinear equations - fixed-point iteration, the secant method, Newton's method. 6. Interpolation - Lagrange and Hermite interpolation, splines. 7. Numerical integration - the rectangular rule, the trapezoidal rule, Simpson's rule. 8. Numerical solution of ordinary differential equations with initial value problems - the transformation of a n-th order differential equation into a system of n simultaneous equations of the first order. One-step methods - Euler methods, Runge-Kutta methods. Stiff differential equations. 9. Boundary value problems - finite difference method. 10. classification of second-order partial differential equations. Numerical solution of elliptic partial differential equations - finite difference method. 11. Numerical solution of parabolic partial differential equations - finite difference method, method of lines, Rothe method. 12. Numerical solution of hyperbolic partial differential equations - finite difference method, method of lines.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Class attendance - 56 hours per semester
  • Preparation for exam - 45 hours per semester
  • Semestral paper - 20 hours per semester
Learning outcomes
Metric and normed spaces, Banach fix-point theorem, numerical methods, boundary value problems for differential equations.
Knowledge of fundamentals of numerical mathematics.
Prerequisites
Passing of mathematical lectures.

Assessment methods and criteria
Written exam

Credit: Working out a semestral work. Exam: Written and oral.
Recommended literature
  • Benda, J. - Černá, R. Numerická matematika, ČVUT, skriptum 1994.
  • Brezina, M. a kol. Matematika IV, Skriptum TUL, Liberec 1996.
  • Dont, M. - Něničková, A. - Opic, B. Numerické metody a matematická statistika - úlohy, ČVUT, Prha 1984.
  • MATHEWS, J.H, FINK, K.D. Numerical Methods using MATLAB, Prentice Hall, New Jersey, 2004..
  • Monahan, F. J. Numerical Methods of Statistics, Cambridge University Press, 2001.
  • Nagy, J. Soustavy obyčejných diferenciálních rovnic, SNTL, Praha 1983.
  • Stoer J., Bulirsch R.:. Introduction to Numerical Analysis. Springer. ISBN 0-387-95452-X.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Engineering (ANG) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Engineering (2018) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Nonwoven and Nanomaterials (ANG) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Engineering (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Engineering (2018) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Nonwoven and Nanomaterials (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Technology (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Technology (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Technology (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Textile Engineering Study plan (Version): Clothing and Textile Engineering (2012) Category: Textile production and clothing industry 1 Recommended year of study:1, Recommended semester: Summer