Syllabus
SYLABUS EN:
* Coordinate systems.
The most common coordinates in plane and space: Cartesian, polar, cylindrical and spherical. Definition and motivation: planetary motion ...
* Function and its derivative.
* Recalling functions and limits. Differentiation and elementary methods of calculus. Physical applications, differential equations and examples (radioactive decay, discharging, harmonic oscillations). Three important generalizations: higher-order derivatives (Taylor expansion of functions), differentiation of functions of several variables (partial derivative), derivatives of vectors (velocity and acceleration in non-Cartesian coordinates).
* Integration.
A primitive function (motivation: shape of water surface in a rotating glass), indefinite integral. Elementary rules and methods of calculus (per partes method, substitution, partial fractions). Definite integrals and their properties. Newton-Leibniz formula. Various physical and geometrical applications. Unbounded integrals: Euler-Poisson-Laplace integral and velocities of molecules.
Annotation
Explanation and exercising of various mathematical methods used in the introductory physics course. Practical applications and solution of particular physical problems are emphasized.
For the 1st year of the Bc study Physics aimed at Education (Physics-Mathematics).