714-0386/01 – Numerical Mathematics (NM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorMgr. Zuzana Morávková, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2000/2001Year of cancellation2018/2019
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
MOR74 Mgr. Zuzana Morávková, Ph.D.
RYH40 RNDr. Irena Rychtarová
TAN30 Mgr. Miloslava Tannenbergová
SVO19 Mgr. Ivona Tomečková, 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 12+4

Subject aims expressed by acquired skills and competences

The aim of this course is to acquaint students with the numerical solution of mathematical problems that arise in the other courses of their study and in the technical practice. The main accent lays in explanations of fundamental principles of numerical methods with emphases their general properties. It should lead to the ability in concrete situations to decide whether a numerical procedure is a suitable tool for solving a particular problem. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programs specialized for numerical computations. The graduate of this course should know: • to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method; • to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies; • to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The course is devoted to basic numerical methods of the linear algebra and mathematical analysis: iterative methods for solving of nonlinear equations, direct and iterative methods for solving of linear systems, eigenvalue problems, interpolation and approximation of functions, numerical computation of derivatives and integrals, solving of ordinary differential equations. The programming system Matlab is used during the course.

Compulsory literature:

1. Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005. ISBN 80-248-0803-X

Recommended literature:

1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN 978-3-540-34658-6. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003, ISBN 0-521-00794-1. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573.

Way of continuous check of knowledge in the course of semester

Tests and credits ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of three written tests, 0-15 CP - completion of two programs, 5 CP Exam ---- - written exam 0-60 CP, successful completion at least 25 CP - oral exam 0-20 CP, successful completion at least 5 CP Exam Questions ============== 1st Give examples of discrete and continuous problems. What is it a discretization? 2nd Define the absolute, relative error and their estimates? How does the round-off error influence the arithmetic operations? 3rd Explain what is it meant by stable and unstable computations? What is it the condition number? 4th Derive the computer epsilon. What is its usual value on standard PC? 5th Explain how to separate roots of one nonlinear equation in real domain. 6th Bisection method: formula and stopping criterion. 7th Regula-falsi method: derive the formula, stopping criterion. 8th The Newton method: derive the formula, stopping criterion. 9th Derive an order of the Newton by the Taylor expanssion, the global convergence theorem. 10th Fixed-point method, Brower fixed-point theorem. 11th The convergence analysis of the fixed-point method by contractivity. 12th Gaussian elimination, phases and complexity. 13th LU-decomposition via Gaussian elimination. 14th Using the LU-decomposition to solve linear systems, to calculate the inverse matrices and determinants. 15th Matrix norms and condition number. An example of ill-conditioned matrix. 16th Eigenvalues and eigenvectors. The definition and calculations. 17th Iterative methods for solving systems of linear equations, Jacobi and Gauss-Seidel. 18th The convergence analysis of general linear iterative method. 19th Interpolation polynomials. Existence and uniqueness. 20th Interpolation error for polynomials. The Runge example. 21st Interpolation splines. 22nd Least square method. System of normal equations. Existence and uniqueness of the solution. 23rd The Newton-Cotes formulas for numerical calculation of integrals. 24th Error in numerical integration. 25th The precision control in the numerical calculation of integrals. The Richardson extrapolation. 26th Numerical differentiation formulas. Order. Behavior of error. 27th The Cauchy problem for ODE. Existence and uniqueness of the solution. The Euler method. 28th One-step methods.Local and global error, order. 29th Multi-step methods. Explicit and implicit formulas. 30th Build predictor-corrector algorithm.

E-learning

Další požadavky na studenta

homework, tests and others

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0366 MI Mathematics I Recommended
714-0367 MII Mathematics II Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Week. Lecture ------------- 1st Course contents, the issue of errors, stability of calculations. 2nd Solution of nonlinear equations, separation of roots, the simplest methods. 3rd Newton's method and fixed-point iterations. 4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition. 5th Eigenvalues and eigenvectors, numerical calculation. 6th Iterative methods for solving linear equations. 7th Interpolation by polynomials and splines. 8th Least squares approximation. 9th Numerical differentiation and integration. 10th Extrapolation in the calculation of integrals. Gaussian integration formulas. 11th One-step methods for solving initial value problems for ordinary differential equations. 12th Multistep methods. 13th Ordinary differential equations of higher order. 14th Systems of differential equations. Program of tutorials ==================== Week. Tutorial -------------- 1st Introduction to mathematical software. 2nd Separation of roots, the simplest iterative methods. 3rd Newton's method and fixed-point iterations. 4th Systems of nonlinear equations. 5th 1st examination. Calculation of LU-decomposition. 6th Application of LU-decomposition. 7th Iterative methods for solving linear systems. 8th Elementary, Lagrange and Newton interpolation polynomials. 9th 2nd examination. Interpolation by splines. 10th Least squares approximation. 11th The numerical calculation of integrals, extrapolation. 12th One-step methods for solving differential equations. 13th 3rd examination. Multistep methods. 14th Credits.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2011/2012 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (10) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment (10) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2008/2009 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2341) Engineering (2301R040) Industrial Engineering K Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2007/2008 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Šumperk 3 Compulsory study plan
2007/2008 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2007/2008 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2301R013) Robotics (71) P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Šumperk 3 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (71) P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 3 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 3 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering K Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 3 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 3 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner