# Topics for the Final State Examination of the Bachelor Study Program Cybernetics and Robotics

## Common theoretical part

- Functions of single variable, limits and continuity. Derivative, its properties and geometrical meaning. Connection between derivative and graph of a function. Local and global extrema. (AE3B01MA1)
- Indefinite and definite integral. Basic techniques: substitution and integration by parts. Applications of integral. (AE3B01MA1)
- Linear dependence and independence, basis, dimension. Linear mappings, kernel and image, dot product and vector product. (AE0B01LAG)
- Matrix, determinant, inverse matrix, eigenvalues and eigenvectors of a matrix. Systems of linear equations. (AE0B01LAG)
- Function series and power series, basic criteria of convergence. Taylor expansion of functions, Fourier series. Functions of several variables, gradient, derivative of a composite function. Local and constrained extrema, method of Lagrange multipliers. (AE3B01MA2)
- Double and triple integrals. Fubini's theorem and theorem on substitution. Line and surface integrals, their meaning and application. Potential of vector field, Gauss.s theorem, Green.s theorem and Stokes.s theorem. (AE3B01MA2)
- Newton.s laws. Kinematics and dynamics of mass particles and rigid bodies. Equation of motion. Rotational motion. Work and energy. Conservative fields. Lagrange's equations of the 2nd order. Hamilton's canonical equations. Motion in the field of central force. Kepler's laws. (AE3B02FY1)
- Simple harmonic motion, damped and forced oscillations. Resonance. Introduction to the mechanics of fluids. Fundamentals of theory of relativity. Lorentz transformation, relativistic kinematics and dynamics. (AE3B02FY1)
- Physical fields. Description of a field, potential. Gravitational field. Fundamental quantities of the electrostatic field (AE3B02FY1)
- Electric current, current density. Conservation of an electric charge law. Ohm's law, Joule's law. Maxwell's equations. Gauss's law. Ampere's and Biot-Savart's law. Faraday's law of induction. Energy of the electromagnetic field. (AE3B02FY1)
- Thermodynamics. Temperature, heat, kinetic theory of gases, ideal gas law, thermal expansion of matter. Work, internal energy, 1st and 2nd law of thermodynamics, entropy and probability, 3nd law of thermodynamics. (AE3B02FY2)
- Fundamentals of waves theory (phase velocity, group velocity, dissipation and dispersion of waves) general wave equation. Superposition of waves. Huygens' principle, diffraction of waves. Doppler's effect. Rays approximation. Acoustic waves, fundamental acoustic quantities, linear wave equation of acoustics. Geometrical and wave optics. Fundamentals of photometry. (AE3B02FY2)
- Introduction to quantum mechanics. Black-body radiation, photoelectric and Compton's effect. Bohr's model of atom. Wave properties of matter. Schrodinger's equation. Uncertainty principle. Tunnel effect. Quantum numbers. Band theory of solids. Lasers. Fundamentals of nuclear physics, radioactivity, sub-nuclear particles. Accelerators. Fusion and fission. (AE3B02FY2)
- Imperative programming, software, compiler, interpret, internal form, programming language, syntax, semantic, variables, expressions, input, output, control structures, simple data types, assignment statement, functions, procedures, parameters, problem decomposition, recursion and iterative principals (AE0B36PR1)
- Object access principals, class as: programming unit, source of functions, data type, object structure, constructors, overloading, instance of class, hierarchy of class, heritage, composition; abstract class, polymorphism, interface, interface as variable type, interface type. (AE0B36PR1)
- Events, source and listener of events, events propagation, owner.s events, more sources and listeners, source resolution. Exceptions and their processing, propagation of exceptions, hierarchy of exceptions, checked and unchecked exceptions. Files and streams, primitive data types and objects (strings) in files. Serialisation. (AE0B36PR2)
- Graphical user interface (GUI), principals, type of communication, AWT and SWING library in Java, components, containers, placement administrator, handling action listener, applets, properties, use, activation, life cycle of applet, access applets parameters, applet restriction. (AE0B36PR2)
- Programming language C, characteristic, compilation model, program structure. Macros, conditional compilation, syntax of language, structures, unions, enumerated types, pre-processor, basic libraries, basic input and output, dynamic memory, array, functions and pointers. (AE0B36PR2)
- Syntax and semantic of propositional and predicate logic. Semantical consequence and tautological equivalence of formulas. Boolean calculus. Resolution method. (AE0B01LGR)
- Directed and undirected graphs, connectivity, strong connectivity, trees and spanning trees. Euler graphs and Hamilton graphs. Independent sets and colourings. (AE0B01LGR)
- Random variable and random vector. Distribution function, density, and probability mass function of a random variable. Mean and variance of a random variable and their estimates. Joint characteristics of a random vector. Correlation and independence of random variables. Method of maximum likelihood. Basic principles of statistical hypotheses testing. Markov chains, classification of states. (AE0B01PSI)
- Entropy, mutual entropy, and conditional entropy of discrete distributions, basic properties and importance. Coding of messages, Kraft inequality. Link between entropy and mean length of code. Codes with optimal mean length. Information channel and its capacity. Shannon coding theorem. (AE0B01PSI)
- Systems and signals. Basic types, their properties and description in time and frequency domains. Convolution, correlation and application of Laplace, Fourier and z-transform. Sampling and shaping of signals, analogue and digital filters, quantisation, modulation. (AE3B31TES)
- Basic terms of electric circuits: Circuit quantities (voltage, current, instantaneous power, electric energy), definitions. Elements of electric circuits. Basic laws, priciples and theorems in electric circuits, Kirchhoff.s laws, Th'venin.s and Norton.s theorem, superposition principle. Analysis methods of electric circuits. Transients in RL, RC and RLC circuits at DC excitation. (AE3B31EOP)
- Actual elements, structures and connections: Semiconductor diode - PN junction, bipolar junction transistor (BJT), field effect transistor (JFET, MOSFET), operational amplifier (ideal/actual). Basic logical circuits - gates (TTL, Schottky, Low power Schottky, CMOS), electric characteristics, loading conditions. Memories (ROM, PROM, EPROM, EEPROM), programmable logic arrays and devices (PLA, PLD), semiconductor memories RWM, static, dynamic. (AE3B31EOP)
- Practical electric structures and connections (transistor amplifiers CE, CC, CB), linear operational networks (inverting and non.inverting voltage amplifier, voltage follower, adding amplifier, integrator, differentiator, controlled sources realizations), non.linear operational networks (logarithm amplifier), generators of periodic signals, oscillators, semiconductor switches, classic supplying sources, priciple of switched supplying source. Output amplifiers of logic elements (gates). (AE3B31EOP)
- Dynamical systems (continuous-time, discrete-time, linear, nonlinear) and their models (differential/difference equations, transfer function, state space descritption). Model construction and transformations. Linearization. Discretization, discrete-time equivalents. Simulation. Identification and verification. (AE3B35ARI)
- Systems response to input signal (impulse, step, ramp, harmonic, general input signal) and nonzero initial conditions. Frequency response, Bode and Nyquist diagrams. Fundamental systems properties (order, DC gain, stability, poles and zeros, damping, non-minimim phase etc.) and their analysis. Software for analysis and imulation of dynamical systems. (AE3B35ARI)
- Control systems: structure and properties. Feedback. Control goals: specifications in time, frequency and complex domains. Tracking and steady state error. Control systems properties (stability, margins etc.) and their analysis. Simple controllers (PID, lead-lag) and their design. Root locus and dynamics compensation. State space and polynomial design methods. Sensitivity, uncertainty, loopshaping. (AE3B35ARI)
- Discrete time systems and their properties. Discrete systems control. Digital contrl of continuous-time systems. Nonlinear systems and controls, equilibria and their stability. MIMO systems, properties and control issues. Time-delay systems. Software tools for control laws design. (AE3B35ARI)
- Minimization of logic functions. Combinational logic circuits and their hazards. Sequential logic circuits. Logic circuits in computer systems. Programmable circuits FPGA. Synthesis of finite automata as sequential logic circuits. (AE0B35SPS)
- Computer architecture: CPU: machine code instructions, address space, buses, memories, interrupts, and exceptions, DMA. Programmable logic controllers PLC. (AE0B35SPS)
- Operating system, process, thread, scheduling algorithms. Inter-process communication, time-dependent errors, critical sections, synchronization primitives, deadlock problem and possible approaches. Memory management, virtual memory, paging and page-replacement policies, segmentation. File systems, external storage organization principles, file protection. Distributed computing, client/server concept (AE3B33OSD)
- Databases and their types. Data models, E-R models, data flow diagrams, decomposition and normalization. Relation, relational model, integrity constraints, data model quality. Object-oriented and object-relational databases. Query languages. Relational algebra and calculus. SQL. Data in XML. Parallel data access, transactions, error recovery, parallel access coordination. Physical data organization, indexes as B-trees, bitmap indexes, linkage to OS approaches. (AE3B33OSD)
- Cybernetics, system theory and artificial intelligence. Fundamentals of system theory. Decision under uncertainty and risk, statistical and Bayesian decision theory. Perception and pattern recognition. Feature and structural approach. Classifiers and their learning. Cluster analysis. Game theory, minimax rule. (AE3B33KUI)
- Problem representatioon, state space, state space search, stochastic search. Knowledge representation. Heuristics. Problems solving. Expert systems, knowledge engineering. Adaptive algorithms. Neural networks, genetic and evolution algorithms. Applications of artificial intelligence. (AE3B33KUI)
- Measurement of voltage, current and frequency. Uncertainties and methods of their decreasing. Sampling, A/D converters, an oscilloscope. Measurement of electrical power and consumption. Resistive and magnetic sensors. Measurement of small voltage and resistance. Capacitive and inductive sensors. Measurement of impedance. (AE3B38SME)
- Optoelectronic and ultrasonic sensors. Sensors and transducers for measuring vibration, speed and acceleration. Measurement of revolution speed and angular position. Sensors for navigation. Measurement of force, pressure, level and flow rate. Sensors of temperature and associated measuring circuits. Sensor networks and communication buses. D/A converters and signal generators. (AE3B38SME)
- ISO/OSI model. Metallic, optical and wireless physical media, analog and digital modulations. Data transfer types, channel capacity sharing. Medium access control methods, physical and logical topologies. Source and channel coding, error detection and correction codes, ciphering. (AE3B38DSY)
- Industrial distributed systems (fieldbuses). Ethernet, active elements, VLAN, determinism of Ethernet. Wireless networks (IEEE802.11, 802.16, 802.15). Modems (PSTN, xDSL, GSM/GPRS, PLC), their basic parameters. TCP/IP protocol family. Internetworking, applications of distributed systems. (AE3B38DSY)

## Topics for the Branch Systems and Control

- Computers and processors architectures (von Neumann architecture, Harvard architecture). Base instruction types (by purpose, operands count, etc.). Machine code, address modes and instructions encoding. CISC and RISC computer architectures. Parallel data processing, SIMD and MIMD. Control units and their hardware realizations. Basic instruction cycle and control unit operation. Pipelined instructions processing and is problems, hazard types and how they can be resolved. Arithmetic operations and their hardware implementations. Computation with fixed and floating point numbers representation. (AE0B36APO)
- Memory use in computers. Hierarchical concept, data consistency. Main (primary) memory. Secondary memory and its technologies. Cache memory. Memory access types (RAM, LIFO, FIFO, associative addressing). External/secondary storage, physical principles, technologies and interfacing. Virtual memory. Peripheral devices, kinds and thein interconnection with computer system. I/O subsystem, categories and interfacing, bus topology, data transfer handshake. Bus control, addressing and access arbitration. Memory mapped peripherals and designated I/O addres-space. Direct memory access (DMA), interrupts and exceptions request and their handling. AE0B36APO)
- Bond graphs for modeling of multidomain dynamical systems: basic principles, basic elements, simple examples of of modeling of mechanical, electronic, electromechanical and hydraulic systems. Comparing signal-based and power-based modeling of dynamic systems. Modeling of mechanical systems using Lagrange methodology: Euler-Lagrange equation, generalized coordinates, holonomic and nonholonomic constraints. (AE3B35MSD)
- Object-oriented modeling of multidomain dynamical systems: basic principles and a survey of existing implementations of Modelica language. Methods for numerical simulation of continuous-time dynamical systems: basic principles of single-step and multi-step methods, survey of popular algorithms, stability of a method, order of a method. Stiff differential equations. Adaptive step-size control. (AE3B35MSD)
- Comparison of the implementation of the logical function. Comparison of the various types of the logical circuits, used voltage levels and their compatibility (TTL, CMOS, 5V/3.3V etc.). Implementations of the inputs and the outputs circuits in processor systems. Connection of the display units and keypads. (AE3B35APE)
- Types of the communication interfaces using in microprocessor systems. Peripheral circuits using in microprocessor systems. Modern power switch components using in control systems and their practical implementation. Using of the power supply units. Using of the operation amplifiers in microprocessor systems. Active filters. Rules of the correct design of the printed circuit board including electromagnetic compatibility and mechatronical aspects. (AE3B35APE)