Common topics for Bachelor degree state examination (for all specializations)
Solving systems of linear equations, Gaussian elimination. Vector space of solutions of homogeneous systems. Linear dependence and independence of vectors, basis of a vector space. (X01ALG)
Matrices, basic operations with matrices. Rank of a matrix and Frobenius theorem about solvability of systems of linear equations. Inverse matrix, determinant. Linear mapping, its matrix with respect to a given basis. (X01ALG)
Sequences of real and complex numbers. Relation between boundedness and convergence of a sequence. Series of numbers, criteria of absolute convergence. (X01MA1)
Functions of one variable, limit and continuity. Derivative, its properties and meaning. Derivative and the graph sketching. Local and global extrema. (X01MA1)
Antiderivative, definite integral. Methods of computing: substitution and per partes. Interpretation and applications of integral. (X01MA1)
Series of functions. Power series, radius of convergence. Fourier series, its sine, cosine and complex form. Periodic extension of a function by means of Fourier series. (X01MA2)
Ordinary differential equations of the 1st order. Method of separation of variables. Linear differential equations of the n-th order with constant coefficients. Variation of constants and estimation method. Using Laplace transform for solution of systems of differential equations. (X01MA2)
Mechanics - Newton.s laws, rotational motion. Conservation laws. Velocity, acceleration, linear momentum, force. Kinematics and dynamics of the system of particles and rigid body. Equation of motion. Rotational motion of the rigid body (torque, angular momentum, moment of inertia). Work and energy. Conservation laws. (X02FY1)
Field concept - intensity, potential, electric currents. Field concept. Description of the field using vector (intensity) or scalar (potential) quantity. Relation between these quantities. Gravitational field, examples. Electrostatics. Stationary electric field. Electric current, current density. Conduction of electricity in conductors, liquids and gases. Joule´s law. (X02FY1)
Electromagnetic field and its energy, Maxwell equations. Maxwell equations in the differential and integral form, explanation of basic principles (Gauss theorem, Ampere law, Biot-Savart law) and their application to simple geometrical problems - a charged sphere, a conductor with passing current, radiation of an open ended transmission line. Forces and energy in an electromagnetic field, density of energy. Motion of particles in an electromagnetic field. Electric and magnetic properties of materials. (X02FY1, X17TEP, X17VVE)
Electric circuit elements and analysis, resistors, capacitors, inductors, coupled inductors, circuit equations - Kirchhoff's current law, Kirchhoff's voltage law. (X31EO1)
Harmonic steady state - voltage and current phasors, complex immittance. (X31EO1)
Transient event analysis, impulse and transient characteristic, transient response in first and second order circuits. (X31EO2)
Frequency characteristic - relation between time and frequency domain, amplitude and phase frequency response. (X31EO2, X37SAS)
Circuits with distributed parameters - infinite lossless transmission lines, transmission lines of finite length, wave reflex. (X31EO2)
Basic properties of semiconductors, electronics of digital circuits. Junction PN, bipolar transistors PNP and NPN, unipolar transistors JFET, MOSFET. Gate structure, characteristics, and parameters. More gates junction. Exciters of buses. Flip-flop circuits, memory cells SRAM, DRAM, EPROM, EEPROM, FLASH. (X34ELE, X34ESS)
An algorithm and its properties, means of representation of algorithms. Variables, expressions, control structures, subroutines, iterative and recursive computations. Text and binary files, pointers, static and dynamic data structures. (X36ALG)
Programming languages. Syntax and semantics, simple data types, structured data types, arrays, functions and procedures and their parameters. Structured programming. The C language, basic data types, the language concepts. (X36ALG)
Object oriented programming. Objects, classes, inheritance, polymorphism, exceptions. The Java language, basic data types, the language concepts. (X36ALG)
Programming techniques. An abstract data type, its specification and implementation. Data types stack, queue, table, tree, list. Basic algorithms for sorting and searching. The complexity of algorithms. (X36ALG)