“Auxiliary Lesson” #1 שעור עזר (Oct. 25, 2007)

Analytic ODEs in real and complex domain: similarities and differences.

1. Background on holomorphic functions. Weierstrass compactness principle.
2. (Ordinary) Differential Equations and their solutions.
3. Contracting mapping principle (recall).
4. Picard integral operator and its contractivity.
5. Existence/uniqueness theorem.
6. Example: Matrix exponent and its computation.
7. Holomorphic vector fields and their trajectories. Equivalence of vector fields.
8. 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.

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.