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.
Disclaimer. In full compliance with the strike rules (were it still be underway), this meeting is defined as a research/orientation seminar on a novel teaching technology. 🙂