Dynamical Systems Modeling and Analysis

2.

Mathematical Foundations

2.1.

Differential Equations Background

2.1.1.

Ordinary Differential Equations

2.1.1.1.

First-Order ODEs

2.1.1.2.

Higher-Order ODEs

2.1.1.3.

Systems of ODEs

2.1.2.

Existence and Uniqueness Theorems

2.1.2.1.

Lipschitz Conditions

2.1.2.2.

Picard-Lindelöf Theorem

2.1.3.

Solution Methods

2.1.3.1.

Analytical Solutions

2.1.3.2.

Qualitative Analysis

2.2.

Linear Algebra Foundations

2.2.1.

Matrix Operations

2.2.2.

Eigenvalues and Eigenvectors

2.2.3.

Diagonalization

2.2.4.

Jordan Normal Form

2.3.

Vector Field Theory

2.3.1.

2.3.2.

Integral Curves

2.3.3.

Flow Properties

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1. Introduction to Dynamical Systems

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3. Modeling with Dynamical Systems