SylabUZ
| Course name | Modelling and simulation |
| Course ID | 11.9-WE-AutP-ModSymul-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | WIEiA - oferta ERASMUS / Automatic Control and Robotics |
| Education profile | - |
| Level of studies | First-cycle Erasmus programme |
| Beginning semester | winter term 2018/2019 |
| Semester | 2 |
| ECTS credits to win | 5 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Laboratory | 30 | 2 | - | - | Credit with grade |
Mathematical Analysis, Linear Algebra with Analytic Geometry
Introduction to Maple V and Maxima. Elements of the language. Assignment. Basic types: sequences, sets, lists, tables, arrays and strings. Calling procedures. Using apostrophes. Internal data representation. Solving linear and nonlinear equations. Functions for linear algebra and mathematical analysis. Simplification of expressions: simplify, factor, expand, convert, normal, combine, map i assume. 2D and 3D graphics. Programming foundations. Applications in mathematical analysis, linear algebra, statistics and selected engineering problems.
Mathematical models of dynamic systems. Models, modelling and simulation. Classification of modelling methods. Goals and stages of modelling. Basic physical laws. Exemplary models of mechanical, electrical, economical and control systems.
Ordinary differential equations. Definitions, classification. Examples of geometric and physical problems leading to differential equations. Geometrical interpretation. Direction field. Integrals of ordinary differential equations. Existence and uniqueness of solutions. First-order equations in normal form. Equations with separated variables. Homogeneous equations. Linear equations. Bernoulli and Riccati equations. Complete differential equations. Trajectories. N-th order linear differential equations. General integrals of linear equations. Fundamental matrix and its properties. Second-order equations with variable coefficients. Systems of nonlinear ordinary differential equations.
Numerical methods of solving ordinary differentia equations. One-step methods: Euler method, trapezoid method (Crank-Nicolson), Heun method. Explicit and implicit schemes. Multistep methods: Adams methods, backward difference methods. Predictor-corrector methods. Runge-Kutta methods. Adaptive step size selection. Systems of ordinary differential equations. Stiff problems.
Continuous linear dynamic systems. Descriptions: ordinary differential equations, transfer functions. Determining responses to any inputs. Matrix transfer functions. Examples of fundamental elements. State equations of linear systems.
Discrete linear dynamic systems. Engineering examples. Difference equations. Transfer functions of discrete systems. State equations.
Matlab-Simulink and Scilab-Xcos environments. Characteristics and applications. Operations on vectors and matrices. Logical expressions. Basic mathematical functions. 2D and 3D graphics. Animation. Low-level graphical functions. Iteration instructions. Scripts and functions. Elements of programming. Debugger. Code efficiency. Recursion. Vectorization of algorithms. Operating on strings. Nonstandard data structures: sparse matrices, structures, cell arrays, multidimensional arrays. Building graphical user interfaces. Operations on files. Calling MATLAB from C programs. Selected toolboxes. Building models of continuous and discrete processes. Simulink: blocks, S-functions.
Building mathematical models based on the principle of least action. Models of mechanical systems. Models of electrical systems. Models of electromechanical systems. Models of gases and liquids. Models of thermal systems. Models of chemical and biochemical processes. Model
linearization. Implementation in MATLAB/Simulink.
Lecture, laboratory exercises
| Outcome description | Outcome symbols | Methods of verification | The class form |
Lecture – the main condition to get a pass is a sufficient mark in a written or oral exam.
Laboratory – the passing condition is to obtain positive marks from all laboratory exercises to be planned during the semester.
Calculation of the final grade: lecture 50% + laboratory 50%
Modified by dr hab. inż. Wojciech Paszke, prof. UZ (last modification: 01-05-2020 10:52)
