Course detail
Numerical Methods
FSI-2NUAcad. year: 2022/2023
Students will be made familiar with a basic collection of numerical methods. They will make sense of errors in mathematical modelling, learn to find zeros of nonlinear equation and to solve systems of linear equations. They will master the basics of approximation including the least squares method, manage to use quadrature formulas and obtain an initial insight into the unconstrained minimization.
Language of instruction
Number of ECTS credits
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Learning outcomes of the course unit
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Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
FORM OF THE EXAMINATIONS: The exam has a practical and a theoretical part. In the practical part students solve several numerical examples by hand using a scientific calculator. In the theoretical part they answer several questions to basic notions in order to check up how they understand the subject. Students will obtain 0--70 points as a result of the exam.
FINAL ASSESSMENT: The final point course classicifation is the sum of points obtained from both the seminars (15--30) and the exam (0--70).
FINAL COURSE CLASSIFICATION: A (excellent): 100--90, B (very good): 89--80, C (good): 79--70, D (satisfactory): 69--60, E (sufficient): 59--50, F (failed): 49--0.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
HEATH, Michael T. Scientific computing: an introduction survey. 2nd ed. Boston: McGraw-Hill, 2002, 563 s. ISBN 0-07-239910-4. (EN)
MATHEWS, John H. a Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River: Pearson Prentice Hall, 2004, ix, 680 s. : il. ISBN 0-13-191178-3. (EN)
MOLER, Cleve B. Numerical computing with MATLAB. Philadelphia: SIAM, 2004, xi, 336 s. : il. ISBN 0-89871-560-1. (EN)
Recommended reading
MATHEWS, John H. a Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River: Pearson Prentice Hall, 2004, ix, 680 s. : il. ISBN 0-13-191178-3. (EN)
MOLER, Cleve B. Numerical computing with MATLAB. Philadelphia: SIAM, 2004, xi, 336 s. : il. ISBN 0-89871-560-1. (EN)
Elearning
Classification of course in study plans
- Programme B-FIN-P Bachelor's 1 year of study, summer semester, compulsory
- Programme B-MET-P Bachelor's 2 year of study, summer semester, compulsory
- Programme B-ZSI-P Bachelor's
specialization STI , 1 year of study, summer semester, compulsory
- Programme LLE Lifelong learning
branch CZV , 1 year of study, summer semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
Week 1-2. Introduction to computing: Error analysis. Computer arithmetic. Conditioning of problems, stability of algorithms.
Solving linear systems: Gaussian elimination. LU decomposition. Pivoting.
Week 3-4. Solving linear systems: Effect of roundoff errors. Conditioning. Iterative methods (Jacobi, Gauss-Seidel, SOR method).
Week 5-6. Interpolation: Lagrange, Newton and Hermite interpolation polynomial. Piecewise linear and piecewise cubic Hermite interpolation. Cubic interpolating spline. Least squares method.
Week 7-8. Numerical differentiation: Basic formulas. Richardson extrapolation.
Numerical integration: Basic quadrature rules (midpoint, trapezoidal and Simpson's rule). Gaussian quadrature. Composite quadrature. Adaptive quadrature.
Week 9-10. Solving nonlinear equations in one dimension: bisection method, Newton's method, secant method, false position method, inverse quadratic interpolation, fixed point iteration.
Solving nonlinear systems: Newton's method, fixed point iteration.
Week 11-12. Minimization of a function of one variable: golden ratio, quadratic interpolation.
Minimization methods for multivariable functions: Nelder-Mead method, steepest descent and Newton's method.
Week 13. Teacher's reserve.
Computer-assisted exercise
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Elearning