Syllabus
1. Differential calculus. Elementary functions. Derivatives, their properties and applications. Taylor series. Partial derivatives.
2. Integral calculus. Indefinite and definite integral. Geometric meaning. Methods of integration.
3. Euclidean geometry. Coordinates. Points, curves, surfaces. Geometric vectors, scalar and vector products.
4. Linear algebra. Vector space, basis, dimension. Rows, columns, matrices. Linear operators.
5. Differential equations. Classification. Solution, its existence and uniqueness. Linear ODEs with constant coefficients.
6. Surface and volume integrals. Differential operators. Gauss and Stokes theorems.
Annotation
The course Mathematical methods in natural sciences will cover basic topics of mathematics necessary for understanding fundamental physical theories such as classical mechanics and Maxwell theory of electromagnetic field, as well as topics relevant for chemistry and biology.