Lectures related to Advanced Analysis II: Isoclines Method

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Discusses kinematic quantities and linear mass density in examples of metal wires.

Covers the representation of plane curves and the nature of obtained curves.

Explores the inverse power method for ODEs and the significance of Lipschitz continuity.