*Conducted in term:*2022L

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*9

*Language:*Polish

*Organized by:*Faculty of Physics

*Related to study programmes:*

# Analysis II E 1100-1Ind05

The aim of the course is to supply on extended level the necessary knowledge concerning differential and integral calculus of several variables, ordinary differential equations and elements of general theory of integration.

Program:

1. Differential calculus of functions of several variables

a) Continuity of many variable functions

b) Norms in vector spaces

c) Derivatives of functions of several variables (strong, directional,

partial derivative)

d) Derivation of a composite function

e) Repeated differentiation, Taylor's formula

f) Extreme values of functions of several variables

g) The local inversion theorem

h) Functions represented implicitly

i) Surfaces, exttreme values on surfaces, Lagrange multipliers

2. Differential equations

a) The existence and uniqueness of the Cauchy problem

b) Linear differential equations

c) Higher order differential equations

d) Examples of imposing additional conditions for differential equations

e) Equations (the systems of equations) with constant coefficients

3.Theory of integration

a) Iterated integrals

b) Fubini theorem

c) Change of coordinates

d) Sets of zero measures

e) Integrals depending on parameters

f) Improper integrals

g) Differential forms, external derivative, Poincare Lemma

h) Stokes theorem

## Main fields of studies for MISMaP

astronomy

## Mode

## Prerequisites (description)

## Course coordinators

## Learning outcomes

1. Mastering the basics of mathematical analysis.

2. Gaining competence in reading and understanding mathematical

texts.

3. Obtaining elementary techniques of analysis of functions of many variables.

4. Training in basic methods of solving the ordinary differential equations.

5. Obtaining skill and experience of identifying crucial mathematical

properties of objects under study.

## Assessment criteria

Two mid - terms, final written exam, final oral exam.

Grading criteria: mastering the subject, solving problems.

## Practical placement

none

## Bibliography

K. Maurin: Analisys

P. Urbański, Analiza II i III

## 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:

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