*Conducted in term:*2021L

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*14

*Language:*Polish

*Organized by:*Faculty of Physics

# Mathematics II 1100-1AF22

**Program:**

1. Complex numbers

operations on complex numbers, roots, complex plane, moduluds and argument of a complex number.

2. Vector spaces,

linear independence, basis, dimension, linear operators, matrices,

systems of linear equations, determinant, Cramer formulas, scalar product, vector product.

3. Functions of many real variables

the space R^n, convergence, continuity, derivative, directional derivative, gradient, higher order derivatives, extrema,

local invertibility, implicit functions, constrained extrema.

4. Ordinary differential equations (ODE)

the initial problem, examples, elementary methods, existence and uniqueness of the solution, different types of first order differential equations, systems of linear equations with constant coefficients, higher order linear equations.

5. Multiple integrals

Updated by Katarzyna Grabowska, November 2010

## Main fields of studies for MISMaP

## Mode

## Course coordinators

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

- Astronomy, first cycle programme
- Applications of Physics in Biology and Medicine, first cycle programme
- Physics, full-time, first cycle programme
- Geophysics in Geology, full-time, first cycle programme

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: