# Math and Physics

Code Completion Credits Range Language Instruction Semester
304CMP credit 2 2 hours (45 min) of instruction per week, 32 to 42 hours of self-study English

Martin BERNAS

Martin BERNAS

## Contents

The lectures concentrate on integrated areas that are closely related to the focus of the study program (measurement, measurement error, humidity and dewpoint, introduction to sound technique, electrical circuits and electromagnetism). With respect to the fact that most students come from non-European countries, a section on SI units and prevention of injuries by electricity has been added. The remaining lecture is dedicated to the basic kinematics and movement dynamics (from Newton to Einstein).

A.Maths part

1.The different kinds of numbers – integers and real numbers, fractions. Expressions, order of operations, rules for using brackets, working with fractions, powers, zero and infinity. Other number base - binary and hexadecimal system, conversions.

2.Simplifying expressions. Simple equations - rules for solving.

3.Introducing graphs. Relating equations to graphs. Quadratic equations, system of linear equations. Relation - direct and inverse proportion.

4.Functions - introduction, power, exponential and logarithmic functions - equations, graphs, properties. Stretching and shifting function. Logarithmic and linear scale, using logarithms in real world. Solving equations with functions.

5.Trigonometry and geometry of triangle and circle ratios (sin, cos and tan) in the right-angle triangle, Pythagoras' Theorem, area of the triangle, sine and cosine rules for any triangle. Circle - special properties of angles in the circle, circle equations area of circle.

6.Trigonometric functions - trigonometric functions, inverse functions, stretching, shifting and shrinking triggered functions, solving equations with trigonometric functions.

7.Vectors - magnitude and addition, scalar and vector products. Matrices - description, addition and multiplying matrices, system of equations and matrices, practical use.

8.Differentiation - looking for the rate of the change. Introduction, practical use. Some basic rules and formulas. Use for finding turning points and points of inflections.

9.Integration - reverse process to differentiating. Definite and indefinite integral. Some basic rules and formulas. Use to find an area under the curve. Application in photometry and colorimetry. Fourier transform and its application.

B. Selected Chapters in Physics

10.Units: US units, SI system of units - base, derived and accepted units, SI prefixes, changing units. Measurement of physical quantities, measurement errors. Humidity, temperature and dew point.

11.Motion - acceleration, velocity, displacement. Force and Motion - mass, Newton's laws. Work, energy and power. Kinetic and potential energy. Gravitation, Newton's law of gravitation. Introduction to Special Relativity. Model of atom.

12.Waves - types, frequency. Acoustics - sound, speed and intensity of sound, Doppler effect, Fletcher-Munson curves, problems with loudness.

13.Electric circuit - DC and AC current, voltage, resistor, Ohm's law. Conductors, semiconductors, insulators. Capacitance (electric field, permiticity, capacitor) and inductance (magnetic field, permeability, inductor, ferromagnetic core). Principle of magnetic recording.

14.Electromagnetic induction - transformers, electric motors. Electromagnetic waves. Electromagnetic compatibility. Electrical safety. Review of lectures.

## Learning outcomes

The mathematical part of the course intends to review secondary school mathematics with additional two chapters (Fundamentals of Differential and Integral Calculus). The coursework should provide not only a basic grasp of mathematics to the students, but also allow them to understand specialised lectures. Selected chapters in physics respect the fact that some parts of physics are discussed in detail in specialised subjects (optics, photometry, colorimetry).

## Prerequisites and other requirements

An integral part of these lectures is a practical exercise of the subject in course „Maths, Physics - practical seminars“

## Literature

Recommended Materials:

Math. A Self-Help Workbook for Science and Engineering Students. Cambridge University Press, 2003, ISBN 0 521 01707 6.

 Halliday,D.; Resnick,R.; Walker,J.: Fundamentals of Physics. 8th edition, Wiley&amp;Sons., 2008. ISBN 0-471-46508-9.

Supplementary Materials:

 Yevick, D.and H.: Fundamental Math and Physics for Scientists an Engineers. John Wiley &amp; Sons, 2015, ISBN 978-0-470-40784-4 (pbk.) – ISBN 978-1-118-98559-5 (Adobe PDF)

 Veselá, E.: Physics I. Czech Technical University Press, 2011

 Veselá, E.: Physics II. Czech Technical University Press, 2012

## Evaluation methods and criteria

Credit for 80% participation

on-line course

## Schedule for winter semester 2023/2024:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
room 225
Room No. 225

(Lažanský palác)
BERNAS M.
14:00–15:35
(lecture parallel1)
Wed
Thu
Fri
Date Day Time Tutor Location Notes No. of paralel
Tue 14:00–15:35 Martin BERNAS Room No. 225
Lažanský palác
lecture parallel1

## Schedule for summer semester 2023/2024:

The schedule has not yet been prepared