| Course Unit Code | 228-0234/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Third Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KRE13 | prof. Ing. Martin Krejsa, Ph.D. |
| HOR0218 | Ing. Marie Horňáková |
| Summary |
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| The course Algorithmization of engineering tasks is aimed at deepening the knowledge of programming and algorithms using the Matlab programming system with a focus on solving simple engineering problems in the field of building mechanics. The course provides information on basic and applied numerical mathematical methods. Part of the lessons is also the deepening of the theoretical knowledge in the field of building mechanics. |
| Learning Outcomes of the Course Unit |
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| Deepening the knowledge of programming and creation of engineering applications algorithms using the Matlab programming system, mastering the basic methods of numerical mathematics and their application in solving the problems of building mechanics. |
| Course Contents |
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Lectures:
1. Introduction to Matlab: Entering variables, vectors and matrices, managing variables, graphical output, creating a script.
2. Algorithm basics: Algorithm properties, elementary algorithms.
3. Calculation of function values: Calculation of polynomial value, tabulation and function graph, determination of extreme discretized function.
4. Solution of Nonlinear Algebraic Equations I.: Iteration, ending cycle, recurring relationships.
5. The solution of non-linear algebraic equations II.: Iterative methods of solving non-linear algebraic equations.
6. Methods for sorting a set of elements: Bubble sort, Selection sort, Insert sort, Quick sort, Shell sort.
7. Systems of linear equations I.: Direct methods of solving systems of linear equations - solutions of triangular system, Gaussian and Gauss-Jordan elimination method, LU and Choleski decomposition.
8. Systems of Linear Equations II.: Iterative Methods of Solutions of Systems of Linear Equations - Jacobi iteration, Gauss-Seidel iteration method.
9. Systems of Linear Equations III.: matrix band, sparse matrix, gradient method.
10. Numerical integration of a particular integral: Rectangular, trapezoidal, Simpson and Romberg\'s numerical integration method, Adaptive integration, Gaussian quadrature.
11. Numerical derivation: Finite difference method, numerical differentiation with non-constant differential, partial derivation.
12. Differential equations solving: Ordinary differential equations, Euler method, Runge-Kutta method, method of jumping frogs.
13. Interpolation and approximation: Linear interpolation, Lagrange interpolation, Newton interpolation, Approximation by least squares method - line and polynomial of m-order.
14. Examples of sample applications.
Tutorials:
1. Introduction to Matlab: Entering variables, vectors and matrices, managing variables, graphical output, creating a script.
2. Algorithm basics: Algorithm properties, elementary algorithms.
3. Calculation of function values: Calculation of polynomial value, tabulation and function graph, determination of extreme discretized function.
4. Solution of Nonlinear Algebraic Equations I.: Iteration, ending cycle, recurring relationships.
5. The solution of non-linear algebraic equations II.: Iterative methods of solving non-linear algebraic equations.
6. Methods for sorting a set of elements: Bubble sort, Selection sort, Insert sort, Quick sort, Shell sort.
7. Systems of linear equations I.: Direct methods of solving systems of linear equations - solutions of triangular system, Gaussian and Gauss-Jordan elimination method, LU and Choleski decomposition.
8. Systems of Linear Equations II.: Iterative Methods of Solutions of Systems of Linear Equations - Jacobi iteration, Gauss-Seidel iteration method.
9. Systems of Linear Equations III.: matrix band, sparse matrix, gradient method.
10. Numerical integration of a particular integral: Rectangular, trapezoidal, Simpson and Romberg\'s numerical integration method, Adaptive integration, Gaussian quadrature.
11. Numerical derivation: Finite difference method, numerical differentiation with non-constant differential, partial derivation.
12. Differential equations solving: Ordinary differential equations, Euler method, Runge-Kutta method, method of jumping frogs.
13. Interpolation and approximation: Linear interpolation, Lagrange interpolation, Newton interpolation, Approximation by least squares method - line and polynomial of m-order.
14. Presentation of semestral work. |
| Recommended or Required Reading |
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| Required Reading: |
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1. Steven C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists (4th Edition), 720 pages, 2017, ISBN-13: 978-0073397962, ISBN-10: 0073397962.
2. Sauer T. Numerical Analysis. George Mason University. Pearson Education, Inc., 2006. (669 s). ISBN 0-321-26898-9. |
1. Krejsa, M., Algoritmizace inženýrských výpočtů, učební texty v obrazovkové verzi i ve verzi pro tisk, VŠB-TU, Ostrava, 2017.
2. Algoritmus. Webové stránky zaměřené na tvorbu algoritmů. [on-line]. .
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| Recommended Reading: |
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1. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to Algorithms, 3rd Edition, 1312 pages, 2009, ISBN-13: 978-0262033848, ISBN-10: 0262033844.
2. Attaway, S., MATLAB - A Practical Introduction to Programming and Problem Solving, Elsevier, ISBN 978-0-12-385081-2, 2012.
2. Valentine, D.T., Essential MATLAB for Engineers and Scientists, Elsevier, ISBN: 978-0-12-374883-6, 2010.
|
1. Sauer T. Numerical Analysis. George Mason University. Pearson Education, Inc., 2006. (669 s). ISBN 0-321-26898-9.
2. Ralston, A. Základy numerické matematiky. 1. vydání. Academia, Praha, 1973. (635 s).
3. Wirth, N., Algoritmy a štruktúry údajov. 1. vydanie. Alfa, vydavateľstvo technickej a ekonomickej literatúry, Bratislava, 1988. (488 s). 4. Algoritmus. Webové stránky zaměřené na tvorbu algoritmů. [on-line]. . |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 35 | 18 |
| Examination | Examination | 65 | 33 |