Numerical mathematics


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Numerical mathematics

Code: 199956
ECTS: 3.0
Lecturers in charge: prof. dr. sc. Zoran Pasarić
Lecturers: dr. sc. Endi Keresturi - Exercises
Take exam: Studomat

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Errors in numerical computing, floating-point number system and arithmetics. Evaluation of polynomials and their derivatives, Horner algorithm. Three-term recurrence relations: properties and application to summation of series, Miller's algorithm. Some results from mathematical analysis. Polynomial interpolation: Lagrange and barycentric form. Newton's form of interpolation polynomial and the error estimate. Approximations of functions: L2 and max-norm, vector and unitary spaces, orthonormal basis. Minimal distance and abstract problem of best approximation. Applications: Chebishev and Fourier approximation, discrete approximation. Numerical differentiation, Richardson extrapolation. Numerical integration (basic and extended formulas). Basics of numerical linear algebra (systems of linear equations, matrix condition number).

Students will be able to:
explain floating-point number system, explain and compare rounding vs. cut-off error.
evaluate polynomials, calculate sum of series of functions and identify possible numerical problems.
approximately solve nonlinear equations in one unknown.
approximate functions by applying the least squares method.
numerically evaluate derivative and integral of function and estimate the associated error.

Written and oral exam.
Prerequisit for:
Enrollment :
Passed : General Physics 1
Passed : Linear Algebra 1
Passed : Mathematical Analysis 1
Passed : Mathematical Analysis 2
Passed : Mathematical Methods in Physics 1
Attended : Mathematical Methods in Physics 2

Examination :
Passed : Mathematical Methods in Physics 2
6. semester
Mandatory course - Regular study - Bachelor of Geophysics
Consultations schedule: