Analysis I 1100-1AF12

1. Elements of logic and set theory.
- Basic symbols and notation of logic and set theory.
- Mathematical induction.
- Equivalence relations.
- Functions and graphs.
2. Convergence
- Axioms of the real number system.
- Least upper bound and greatest lower bound.
- Sequences of real numbers.
- Metric spaces.
- Closed sets, open sets, connected sets.
- Compactness.
3. Differential calculus in one variable.
- Taylor's formula.
- De l'Hospital rule.
- Convex functions.
- The primitive.
- Analysis of functions.
- Series.
- Radius of convergence of a power series.
- Power series expansions of elementary functions.
- The Riemann integral of functions of one variable.