Dynamical Systems (Module 1)

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Dynamical Systems (Module 1)

Credits

6

Prerequisites

Mathematical Analysis 2, Mathematical Physics.

Examination method

Passing an integrated exam, possibly divided into several parts, on the contents of Dynamical Systems (Module 1) and Dynamical Systems (Module 2)

Learning
objectives

To gain mastery of the main analytical techniques for the study of ordinary differential equations. Diffeomorphisms between Euclidean spaces. Fundamental notions of complex analysis. Study of evolutionary phenomena in the Applied Sciences through the use of dynamical systems.

Contents

The implicit function theorem and the inverse function theorem, with applications in particular to the study of surfaces. Outline of holomorphic and analytic functions, Cauchy-Riemann equations, Cauchy theorems. Ordinary differential equations. Local and global existence and uniqueness theorems. Classification of the critical points of a 2×2 linear system of ODEs.

Academic Year
2020/2021

Lecturer: Pietro BALDI.

Semester: first.

Syllabus: see the relevant page.