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Algorithmization of engineering computations

Type of study Bachelor
Language of instruction Czech
Code 228-0234/01
Abbreviation AIV
Course title Algorithmization of engineering computations
Credits 5
Coordinating department Department of Structural Mechanics
Course coordinator prof. Ing. Martin Krejsa, Ph.D.

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.

E-learning

Studijní opory k dispozici v IS edison a na lms.vsb.cz

Literature

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.

Advised literature

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.