Recommended literature on the subjects of the study program.
The final examination is realized by the student's discussion with the members of the commission on two topics from the content of the examination. Assessed: illustration of concepts on suitable examples / contexts / situations 0-3 points; correctness of physics terminology 0-3 points; intelligibility of discussion 0-3 points; responding to commission questions regarding selected topics 0-3 points; responding to other commission questions / broader context 0-3 points. Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
The exam is successfully passed if the student obtains at least 50% of points.
Slovak and English.
Physics:
Movement in two dimensions. Even movement in a circle. Movements in a homogeneous gravitational field, oblique litter. Newton's laws of motion. Relationship between free fall and motion of bodies in the radial field of the Earth.
Mechanical work, kinetic energy, work of gravitational force (in homogeneous gravitational field), work of elastic force, power, potential gravitational energy, potential energy of elasticity, law of conservation of mechanical energy, conservative and non-conservative forces, work of friction force.
Fluid mechanics, pressure, compressive force, pressure induced by fluid gravity, Archimedes' law, Pascal's law, continuity equation, Bernoulli's equation.
Elastic and inelastic collisions, momentum, impulse of force, law of conservation of system momentum, elastic and inelastic direct collisions, oblique collisions, explosion (in two parts).
Moment of force with respect to the axis of rotation, momentum of the moment for rotation around a fixed axis (second impulse theorem), rolling, rotation of bodies around a fixed axis, rolling on an inclined plane. Momentum, momentum of a particle system, momentum of a rigid body with respect to a fixed axis, the law of conservation of momentum.
Coulomb's law. Electric field. Scalar and vector fields. Electric fields, lines of force. Point charge field. Superposition of electric fields. Electric dipole field. Application of Gauss' s law.
Electric potential. Electric potential energy. Potential, voltage, equipotential surfaces. Electron volt. Work performed by an external force when moving the charge in the el. field. Point charge potential. Potential energy and potential of a system of point charges. Faraday's cage. Capacity. Capacitor and capacity. Capacitor charging process.
Circuits with unidirectional el. current. Electromotive voltage. Internal battery resistance, terminal voltage. Battery power, power dissipation, battery charging and discharging. Loop rule, node rule, current calculation in resistor circuits by voltage method. Serial and parallel connection of resistors. Connection of ammeters and voltmeters, ideal ammeter and ideal voltmeter.
Magnetic field. The essence of magnetism and the magnetic field, the absence of a magnetic monopole. Magnetic induction, Lorentz force. Induction lines. Bar magnet. The trajectory of a charged particle in mag. field. Earth's magnetic field, aurora borealis. Cyclotron and synchrotron. Charged particle separator according to velocities, mass spectrometer. Hall map. Force acting on a current conductor in a magnetic field (Ampere's force).
Electromagnetic induction. Induced current, induced electromotive voltage. Experiments demonstrating electromagnetic induction. Faraday's law of electromagnetic induction. Lenz's law. Induction energy transfer. Alternator. Faraday's law of electromagnetic induction in integral form. Eddy currents.
Electromagnetic oscillations and alternating current circuits. LC oscillations, energy transfer, energy conservation, mechanical analogy. Damped oscillations in a serial RLC circuit. Circular frequency of undamped and damped oscillations. Power in RLC circuit with AC source. Effective voltage, power factor, resonant frequency of the source.
Mechanical vibration, kinematics - instantaneous deflection, speed and acceleration of oscillating motion, equation of motion for harmonic motion, energy of harmonic oscillator. Torsional oscillations, mathematical and physical pendulum, damped and forced oscillations, resonance.
Waves, superposition principle, wave speed propagating on a rope, reflection and transmission of a wave at an interface, standing waves, sound, resonance in tubes, Doppler effect, sound shock waves. Doppler phenomenon in connection with sound and in connection with light. Body velocity measurement. Infrared shift when exploring distant stars.
Electromagnetic waves, light, spectral regions of light and electromagnetic waves, Interference in space, basic assumptions of two-beam interference, Young's two-slit experiment, intensity profile in interference, interference on thin films. Sound wave interference. Bending (diffraction) of light at the aperture, Rayleigh criterion, diffraction grating.
Rutherford scattering, Bohr model of the atom, electron transitions between energy levels, emission and absorption spectra of gases. Franck-Hertz experiment. X-rays.
Interaction and radiation detection. Photoelectric effect, Compton scattering, pair formation and annihilation.
The nucleus of an atom and its properties. Weight loss and binding energy. nuclear fusion and fission. Isotopes.
Radioactive transformation. Alpha, beta and gamma radiation. Law of radioactive transformation, activity. Absorption characteristics of alpha, beta and gamma rays.
Ideas about the microworld. Basic substance characteristics (molar quantities). Equation of state of an ideal gas. Heat and temperature, Kelvin temperature scale. Thermal processes with an ideal gas - state changes and energy aspects. Ideal gas pressure, barometric equation. Kinetic theory of substance structure. Maxwell-Boltzmann distribution. The law of conservation of energy in terms of thermodynamics.
Didactics:
Science literacy, scientific work skills. Examples of the development of scientific skills in teaching physics.
Objectives and content of science and physical education.
Bloom's taxonomy of goals and its application in the creation of physical problems.
Basic pedagogical documents and teaching aids, their structure and function.
The model of ontogenesis of thinking according to J. Piaget and its importance for the creation of the physics curriculum.
Empirical and theoretical cognition in school physics. Selected methods of access to methods and ways of cognition.
Graphic method of communication between two quantities. Examples of the use of graphs in the introduction of some physical concepts.
Classification of physical tasks. The importance of the physical role in the cognitive process.
Complex physical problems, function of complex tasks in introducing ideas about natural phenomena.
Complete scheme of the school physics experiment planned by the teacher - the teacher's activity.
Pupil's activity in various phases of planning, implementation and data processing of a school physics experiment. Pupil-planned experiment.
Classification of school physics experiments (cognitive functions, organization, means used, data obtained).
Assessment and classification of students in physics teaching. Assessment of the degree of development of students' scientific abilities.
Key experiments on the topic of "fluid statics".
Key experiments on the topic of "calorimetry".
Key experiments on the topic of "molecular physics".
Key experiments on the topic of "movement and force".
Passing the exam represents fulfilling the profile of the graduate.
Geometry
1. Study of affine space by analytical method
(subspaces - linear varieties, their parametric and general equations, intersections and mutual positions)
2. Study of Euclidean space by analytical method
(scalar product of vectors and metrics, perpendicularity of subspaces, distances of subspaces, angles)
3. Affine representations of spaces
(analytical expression of affine mapping, invariants of affine transformations, group of similarities of Euclidean space)
4. Axiomatic construction of geometry: incidental and ordered plane
(axioms of incidence and arrangement and their consequences, models of incident and ordered plane.)
5. Axiomatic construction of geometry: Hilbert's and Euclidean planes
(axioms of similarity and their consequences: triangles of similarity of triangles, properties of a triangle, construction of perpendiculars and parallels; axioms of parallelism and axioms of continuity)
Combinatorics, probability and statistics
1. Mathematical induction (principle of mathematical induction; connection with good arrangement of natural numbers; examples of use).
2. Pigeon/Dirichlet principle (formulation and some applications).
3. Combinatorial principles (addition principle, multiplication principle, bijection principle, counting in two ways).
4. Binomial coefficients and binomial theorem (definition and formula for binomial coefficients and some of their properties; binomial theorem formulation).
5. Principle of inclusion and exclusion (formulation and examples of use).
6. Probability, its basic properties. Conditional probability and independence of events. Complete Probability Theorem, Bayes Theorem.
7. Probability distributions, their properties and characteristics (distribution function, density, mean value, dispersion). Special types of distributions (alternative, binomial, geometric, exponential, normal). Central limit theorem.
8. Descriptive statistics (location and variability characteristics). Point estimates (random selection; estimates of mean and dispersion and their properties).
9. Confidence intervals for the mean value. Hypothesis testing, one-choice tests on the mean value.
Algebra and theoretical arithmetic
1. Linear representations and their matrices, product of matrices, inverse matrices.
2. Vector spaces and subspaces, linear combinations of vectors, linear representations.
3. Finite-dimensional vector spaces, base and dimension of finite-dimensional vector space.
4. Systems of linear equations, the existence of a solution of an inhomogeneous system of linear equations, the structure of the set of solutions of a homogeneous system of linear equations.
5. Divisibility in the field of integers. Theorem on division with the rest. The largest common divisor and the smallest common multiple of two integers. Euclidean algorithm for calculating the greatest common divisor.
6. Prime numbers, their properties, theorem about the decomposition of a natural number into the product of prime numbers. Number systems.
7. Congruences, divisibility criteria of natural numbers expressed in the decimal system, Euler's theorem, small Fermat's theorem.
Mathematical analysis
1. Limits of sequence and function, basic theorems about limits.
2. Continuity, properties of continuous functions on intervals, optimization - search for global extrema of continuous functions on closed intervals, relationship between continuity and differentiability of a function.
3. Derivation of a function, Lagrange's theorem on mean value and its use in investigating the monotonicity of functions, necessary and sufficient conditions for the existence of local extrema of differentiable functions.
4. Approximation of differentiable function by polynomials, equation of tangent, equation of Taylor polynomial of n-th degree.
5. Indefinite integral and primitive function, basic integration formulas, per partes method and substitutions.
6. Riemann integral, definition and calculation, heuristic derivation of formulas for calculation of area content, length of curve, volume of rotating body and surface of rotating body.
The course 1-UMA-951/15 Fundamentals of Mathematics has two parts:
A) School mathematics test
The test uses the types of tasks from mathematics tests for the external part of the Matura exam and from mathematics tests at the entrance exams at FMFI UK, a total of 20 short-answer tasks or with a choice of several options.
B) Oral exam
The student draws an assignment, which has 3 parts - three different circuits
1. geometry, 2. combinatorics, probability and statistics, 3. algebra and theoretical arithmetic, 4. mathematical analysis.
Each part contains
- the task from the relevant area, the solution of which (including the justification of individual steps) the student will demonstrate during the oral answer,
- definition of the area of the relevant heading, which is related to the solved task; in the oral answer the student will state the basic concepts and statements of this area, or their relationship to the problem.
Maximum points:
• 20 points from the school mathematics test (1 point for each correct answer),
• 25 points for each of the three parts of the assignment (10 for solving the problem, 15 for the theoretical part),
thus a maximum of 20 + 3.25 = 95 points in total.
A student completes the course if he/she obtains at least 5 points for each of the three parts of the assignment and a total of at least 46 points.
slovak, enghlish
0/100
State exam from selected areas of the core subjects of the program.
according to the topic of the bachelor thesis
Examination: state examination
Slovak, English
Course contents:
1. Contribution of the final thesis for the given field of study applied in the collection, interpretation and processing of basic professional literature, or the extent to which the student has mastered the application of theoretical principles in practice and whether the hypotheses presented in the work are verifiable;
2. Originality of the thesis (the final thesis must not have the character of a plagiarism, must not infringe the copyrights of other authors), part of the documentation for the defense of the final thesis as a subject of state examination is the protocol of originality from the central register.
3. Correctness and correctness of citation of used information sources, research results of other authors and author groups, correctness of description of methods and working procedures of other authors or author groups;
4. Compliance of the structure of the final work with the prescribed composition defined by Internal Regulation no. 12/2013;
5. Respecting the recommended scope of the final thesis (the recommended scope of the bachelor's thesis is usually 30 - 40 standard pages - 54,000 to 72,000 characters, including spaces), the adequacy of the scope of the thesis is assessed by its supervisor;
6. Linguistic and stylistic level of work and formal arrangement;
7. The method and form of the defense of the final thesis and the student's ability to adequately respond to comments and questions in the opinions of the supervisor and the opponent.
8. In the teaching of art-educational subjects, the final work and its defense may also include the presentation of artistic outputs and performances.
0/100
When designing the bachelor's thesis, the student is able to demonstrate the ability to work creatively in the field of study in which he completed the study program. The student is able to demonstrate adequate knowledge of the issue and apply their skills in the collection, interpretation and processing of basic literature, or its application in practice or is able to solve a partial task related to the student's focus.