 MATHEMATICAL METHODS IN ENGINEERING Summer Term 2012 / 2013 Room A335: Tuesday 9:00-12:30 Assessment: 2 / 0 / 2   z, Zk Lectures: Prof. Ing. Aleš Procházka, CSc                  Laboratories: Ing. Mohammadreza Yadollahi

Week Lectures Laboratories   Texts   Files    Projects
1 Introduction: Software support of mathematical methods, numerical, symbolical and simulation tools. MATLAB environment: basic operations, commands, matrix operations, programming methods, fundamental algorithms MATLAB: Interactive and programming methods, selected functions and commands, editor, programming  2 MATLAB environment: Two-dimensional and three-dimensional graphics, visualization, object hierarchy, color selection, data import and export, GUI MATLAB: Visualization of functions, definition of color sets, data import, GUI  3 MATLAB environment: Structured data sets. Fundamentals of symbolic mathematics, manipulation with expressions, substitution, symbolic operations MATLAB: Multidimensional variables. Symbolic mathematics, operations  4 Modelling in the SIMULINK environment: Modelling of mathematical operations, visualization, construction of SIMULINK models, applications SIMULINK: Basic blocks, initialization, interaction with MATLAB  5 Linear algebra: Finite and iterative methods for solution of systems of linear algebraic equations, symbolic and numeric methods, sparse matrices Linear algebra: Symbolic methods, algorithms, sparse matrices  6 Approximation of functions: Method of the least squares, algorithms, symbolic and numeric methods Aproximation of functions: Symbolic methods, numerical solutions, algorithms  7 Linear and nonlinear approximation: Generalization, gradient method, visualization, contour plots Computer project M1:
Function approximation   8 Nonlinear equations: Basic algorithms, symbolic and numeric methods, simulation Nonlinear equations: Symbolic and numeric methods, programming  9 Systems of nonlinear equations: Principals of symbolic and numeric solutions, visualization Computer project M2:
Solution of nonlinear equations   10 Interpolation, differentiation, and integration: Basic algorithms, symbolic and numeric methods, modelling Interpolation, differentiation, and integration: Symbolic and numeric methods  11 Solution of ordinary differential equations and their systems: Basic algorithms, symbolic and numeric methods, modelling in the SIMULINK environment Solution of diferential equations: Symbolic and numeric solution, modelling, basic blocks  12 Boundary-value problem for ordinary differential equations: Basic algorithms, finite difference method, shooting method, visualization Computer project M3:
Solution of differential equations   13 Remote data processing, MATLAB WWW server, database systems Graphical user interphase, basic functions, solution of differential equations  14 Conclusion. Applications of computational methods Conclusion INFORMATION ABOUT EXAM Dates: http://student.vscht.cz Conditions: Examination system, sample test