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.
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,
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
1. Mastering the basics of mathematical analysis.
2. Gaining competence in reading and understanding mathematical
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.
Two mid - terms, final written exam, final oral exam.
Grading criteria: mastering the subject, solving problems.
K. Maurin: Analisys
P. Urbański, Analiza II i III
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:
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