**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.~~

Attached is Section 1. It will be available on these pages for a limited time and is password-protected from printing 😦 … I must obey the requirements of the Publisher.