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