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