CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Overview of Mathematics and Physics

Code Completion Credits Range Language
F7PMSPMF Z,ZK 4 2P+2S Czech
Garant předmětu:
David Vrba
Lecturer:
Jana Urzová, David Vrba
Tutor:
Matouš Brunát, Jana Urzová, David Vrba
Supervisor:
Department of Biomedical Technology
Synopsis:

Students will acquire basic knowledge of linear algebra (vectors, matrices, systems of linear equations), and differential and integral calculus of the functions of one variable (limit, continuity, derivation, function path, integrals).

They will be able to solve systems of linear equations and apply linear algebra and differential methods and integral calculus to practical examples.

In the teaching of physics, emphasis is placed on the context of individual physical disciplines and the application of mathematics. Through lectures and numerical exercises, students will acquire basic knowledge of physics with a focus on medical practice.

Upon completion of the course students will be ready to study other technical subjects.

Requirements:

Conditions

1 Active participation in seminars (maximum 2 absences allowed)

2. Min. 50% successful mathematical credit test (max. 20 points) and min. 50% success rate of the test of physics (maximum 20 points)

3. For an active approach during the exercises, it is possible to get max. 10 points (1 point / exercise)

Exam conditions: The exam (max. 50 points) consists of two parts: written and oral.

The written part contains 4 questions from mathematics and 4 questions from physics. At least 50% points must be earned from each part, ie the student must earn at least 50% points from mathematics and at least 50% points from physics.

In the oral part the student defends the mark from the written part. Understanding the substance and the logical context should be proven.

ECTS Rating for the sum of all points (max. 100 points)

Syllabus of lectures:

MATHEMATICAL PART

• Numbers and functions: natural, whole and real numbers, intervals, numeric systems, functions, polynomial, functions of two or more variables, composite and inverse functions.

• Matrix calculation: matrices and vectors, matrix operations, commutative, associative and distributive laws, unit and zero matrices, transposed and inverse matrices.

• Limit, continuity and derivation: Derivatives as the rate of change, such as the tangent to the curve, the notion of limits, limit calculation, infinity, infinite limits, continuity of functions.

• Derivatives of constants, linear and power functions, rules for calculating the derivative of the sum, the difference, the multiplication and the division of functions, the derivative of the composite function, the derivative of the functions of more variables, the partial derivative.

• Function of one variable: definition field, local and absolute extremes, monotone functions, convexity, concavity and inflection points.

• Fundamentals of integral calculus: indefinite integral, definite integral, infinite integral; integral as generalized sum, integral as area under graph; properties of the integral

PHYSICAL PART

• Value, SI system, kinematics of the material point, average and instantaneous velocity, acceleration, equally accelerated motion, vertical and oblique cast (vectors).

• Mechanics: Newton's laws, force, momentum of a body and impulse of force, shear friction, centripetal force mechanical work, energy: kinetic energy, potential energy, law of preservation of mechanical energy, work of elastic force, power and efficiency.

• Mechanics: Uniform motion along a circle, solid body mechanics, rotational motion, moment of force, momentum of momentum, moment of momentum preservation, moment of inertia, kinetic energy, Newton´s law of gravity, Kepler's laws.

• Vibrations: waves, harmonic movement, speed and acceleration, forced oscillation - resonance, waves, wave types, gradual wave equations, sound, ultrasound in medicine.

• Optics: wave and electromagnetic nature of light, reflection and refraction of light, fundamentals of geometric optics, plane mirror, spherical mirror, lenses, optical instruments, eye as an optical system.

• Thermodynamics, kinetic theory of substances - basic concepts (internal and external state variables, length and volume thermal expansion, internal energy, calorimetric equation), thermodynamic laws, microscopic physics, photoelectric effect, X-ray, laser, radionuclides

• Electricity and magnetism: electric charge, Coulomb law, electrostatic field, electric field in dielectrics and conductors, electric current, Ohm's law, resistor connection, magnetostatic field and force, magnetic properties of coil, magnetic properties of substances.

Syllabus of tutorials:

MATHEMATICAL PART

• Numbers and functions: natural, whole and real numbers, intervals, numeric systems, functions, polynomial, functions of two or more variables, composite and inverse functions.

• Matrix calculation: matrices and vectors, matrix operations, commutative, associative and distributive laws, unit and zero matrices, transposed and inverse matrices.

• Limit, continuity and derivation: Derivatives as the rate of change, such as the tangent to the curve, the notion of limits, limit calculation, infinity, infinite limits, continuity of functions.

• Derivatives of constants, linear and power functions, rules for calculating the derivative of the sum, the difference, the multiplication and the division of functions, the derivative of the composite function, the derivative of the functions of more variables, the partial derivative.

• Function of one variable: definition field, local and absolute extremes, monotone functions, convexity, concavity and inflection points.

• Fundamentals of integral calculus: indefinite integral, definite integral, infinite integral; integral as generalized sum, integral as area under graph; properties of the integral

PHYSICAL PART

• Value, SI system, kinematics of the material point, average and instantaneous velocity, acceleration, equally accelerated motion, vertical and oblique cast (vectors).

• Mechanics: Newton's laws, force, momentum of a body and impulse of force, shear friction, centripetal force mechanical work, energy: kinetic energy, potential energy, law of preservation of mechanical energy, work of elastic force, power and efficiency.

• Mechanics: Uniform motion along a circle, solid body mechanics, rotational motion, moment of force, momentum of momentum, moment of momentum preservation, moment of inertia, kinetic energy, Newton´s law of gravity, Kepler's laws.

• Vibrations: waves, harmonic movement, speed and acceleration, forced oscillation - resonance, waves, wave types, gradual wave equations, sound, ultrasound in medicine.

• Optics: wave and electromagnetic nature of light, reflection and refraction of light, fundamentals of geometric optics, plane mirror, spherical mirror, lenses, optical instruments, eye as an optical system.

• Thermodynamics, kinetic theory of substances - basic concepts (internal and external state variables, length and volume thermal expansion, internal energy, calorimetric equation), thermodynamic laws, microscopic physics, photoelectric effect, X-ray, laser, radionuclides

• Electricity and magnetism: electric charge, Coulomb law, electrostatic field, electric field in dielectrics and conductors, electric current, Ohm's law, resistor connection, magnetostatic field and force, magnetic properties of coil, magnetic properties of substances.

Study Objective:
Study materials:

Required:

[1].Massachuttes Institute of Technology. http://ocw.mit.edu/courses/physics/

[2].The Princeton companion to mathematics. Editor Timothy GOWERS, editor June BARROW-GREEN, editor Imre LEADER. Princeton: Princeton University Press, c2008. ISBN 0691118809.

Recommended:

[3].RUDIN, Walter. Principles of mathematical analysis. 3d ed. New York: McGraw-Hill, 1976. ISBN 007054235x.

[4].FEYNMAN, Richard P., Robert B. LEIGHTON a Matthew L. SANDS. The Feynman lectures on physics. New millennium ed. New York: Basic Books, 2010. ISBN 0465023827

Note:
Time-table 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 roomKL:C-4Vrba D.Urzová J.10:00–11:50(lecture parallel1)Kladno FBMIC4, Malý sálroomKL:B-430Urzová J.Brunát M.12:00–13:50EVEN WEEK(lecture parallel1parallel nr.1)Kladno FBMIUčebna roomKL:B-430Urzová J.Brunát M.12:00–13:50ODD WEEK(lecture parallel1parallel nr.2)Kladno FBMIUčebna roomKL:B-430Vrba D.Urzová J.14:00–15:50(lecture parallel1)Kladno FBMIUčebnaroomKL:B-430Urzová J.Brunát M.16:00–17:50(lecture parallel1parallel nr.1)Kladno FBMIUčebnaroomKL:B-430Urzová J.Brunát M.18:00–19:50(lecture parallel1parallel nr.2)Kladno FBMIUčebna
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-13
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