Analytic ODEs in real and complex domain: similarities and differences.
- Background on holomorphic functions. Weierstrass compactness principle.
- (Ordinary) Differential Equations and their solutions.
- Contracting mapping principle (recall).
- Picard integral operator and its contractivity.
- Existence/uniqueness theorem.
- Example: Matrix exponent and its computation.
Holomorphic vector fields and their trajectories. Equivalence of vector fields. Flow box theorem and rectification theorem for nonsingular vector fields.