228-0234/02 – Algorithmization of engineering computations (AIV)
| Gurantor department | Department of Structural Mechanics | Credits | 5 |
| Subject guarantor | prof. Ing. Martin Krejsa, Ph.D. | Subject version guarantor | prof. Ing. Martin Krejsa, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 3 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
Summary
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.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Written and oral exam.
E-learning
Other requirements
Ability of partial self-study
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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