Physics with Mathematics I, lecture

obligatory courses

Graduation from secondary school, interest in science,readiness to hard work during the whole semester

Classroom

Acquaintance with the basic concepts and theorems of classical mechanics and thermodynamics, as well as with mathematical tools for solvation of typical problems of both areas.

This basic lecture, together with the laboratories presents fundamental concepts and theorems of classical mechanics and thermodynamics. Paralell to the physical phenomena, their mathematical description will be presented. Also practical mathematical tools will be discussed and practised.

Programme

1. Mathematics: calculus with elements of linear algebra

1.1. Linear vector space, basis,dimension, scalar product,

length of a vector, metrical spaces, coordinate systems

1.2. Functions and their graphs, sequence, limit of a sequence,

limit of a function,

continuous function

1.3. Derivatives of a function,differences, study of a variability

of a function, extrema of functions

1.4. Functions of several variables, partial derivatives

1.5. Scalar and vector fields, gradient

1.6 Indefinite integral, finite integral. fundamental theorem

of calculus, multiple integrals

1.7. Differential equations

2. Physics (mechanics)

2.1. Desription of location and description of a path during a motion

2.2. Newtonian laws of motion, inertial systems

2.3. Laws of conservation: mechanical energy, momentum and

angular momentum

2.4 Conservative and central forces, potential forces,potential

energy, concept of work

2.5. Noninertial systems

2.6. Mechanics of a rigid body

3. Thermodynamics

3.1 Boltzmann distribution

3.2. Kinetic theory of ideal gases

3.3. Concept of entropy,

3.4 Internal energy, heat and work

3.5. Laws of classical thermodynamics

3.6 Thermodynamic potentials amd equillibrium

3.7. Carnot cycle and heat en8iones

Regular hard work is needed during the whole semester.

Lectures: 7 hours every week = 105 hours

Repetition of every lecture at home = 9 hours per week

Together: 135 hours per week

Preparation for the exam = 30 hours

Alltogether about 270 hours

After the course:

Knowledge:

1. Fundamental concepts of diffrential and integral calculus

and linear algebra

2. understanding classical laws of mechanics and thermodynamics

Ability:

1. to calculate limit of a sequence

1. to calculate derivatives of function of several variabkles

2. to determine minima and maxima of a function

3. to calculate areas and volumes using the integrals

4. to determine path for simple motion

5. to analyse forces acting in simple mechanical systems

6. to use the conservation laws to solve the simple mechanical

problems

Written exam:

20 test questions

Possiblility of improving the final notes in the form of oral exam.

None