470-4506/02 – Selected Chapters on Numerical Methods (VKzNM)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year2Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

The aim of the course is to introduce fundamental numerical methods for solution of engineering problems that lead to large-scale linear systems, nonlinear systems, or eigenvalue problems. Further, we shall present interpolation methods and an approximation by the method of least squares. Finally, we shall focus on numerical derivatives, quadrature, and we introduce methods for solution of boundary value problems for partial diferential equations. Each topic will be motivated by an engineering problem. The algorithms will be implemented in Matlab. The students will be also introduced to some libraries of numerical linear algebra such as BLAS, LAPACK, and MUMPS.

Teaching methods

Lectures
Tutorials

Summary

The course covers fundamental methods of numerical linear and nonlinear algebra, methods of interpolation and approximation, and numerical analysis including an introduction to solution of boundary value problems for partial differential equations.

Compulsory literature:

- Quarteroni, A. – Sacco, R. – Saleri, F. Numerical Mathematics. Springer, 2000.

Recommended literature:

- W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.

Way of continuous check of knowledge in the course of semester

test, project

E-learning

Další požadavky na studenta

Basic knowledge of linear algebra, derivatives, and integrals

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 1. Numerical linear algebra - iterative methods for solution to linear systems 2. Numerical linear algebra - the method of conjugate gradients, preconditioning 3. Numerical linear algebra - sparse matrix solvers, parallel frontal method 4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method 5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS 6. Nonlinear systems - bisection, fixed-point iterations, Newton's method 7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares 8. Numerical analysis - numerical derivative, numerical quadrature 9. Numerical analysis - introduction to numerics for partial differential equations 10. Numerical analysis - principle of the finite element method Exercises: 1. Numerical linear algebra - iterative methods for solution to linear systems 2. Numerical linear algebra - the method of conjugate gradients, preconditioning 3. Numerical linear algebra - sparse matrix solvers, parallel frontal method 4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method 5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS 6. Nonlinear systems - bisection, fixed-point iterations, Newton's method 7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares 8. Numerical analysis - numerical derivative, numerical quadrature 9. Numerical analysis - introduction to numerics for partial differential equations 10. Numerical analysis - principle of the finite element method

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan

Occurrence in special blocks

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