Lectures on Dynamical Systems
Content
Chapter 1 “Dynamical Systems: Definition and Scientific Examples” Introduces the concept of dynamical systems with examples, including one-dimensional growth models, periodic solutions, and visualization techniques.
Chapter 2 “Mechanical and Electromechanical Systems” Covers modeling of mechanical systems (single and multi-degree), rotational systems, electrical circuits, and electromechanical devices like DC motors.
Chapter 3 “Thermal and Fluid Systems” Discusses heat transfer, fluid dynamics, and linearization of nonlinear systems, with applications to thermal and fluid engineering problems.
Chapter 4 “The Laplace Transform” Introduces the Laplace transform and its inverse, applying them to solve linear differential equations and discussing key properties and transform pairs.
Chapter 5 “The Transfer Function and Time Responses of Dynamical Systems” Explains transfer functions, impulse and step responses for first-, second-, and higher-order systems, including stability tests and special cases.
Chapter 6 “Frequency Response, Resonances, and Beats in Dynamical Systems” Analyzes frequency response, resonance, lightly damped systems, and beating phenomena, including filter concepts and sinusoidal steady-state analysis.
Chapter 7 “Control Systems: Basic Definitions and Concepts” Introduces control systems and block diagrams in both the time and the Laplace domains, develops proportional, feedforward, and proportional-integral control, and compares open- and closed-loop designs, highlighting the advantages of feedback.
Chapter 8 “Control Systems Design” Presents PID controllers and their practical modifications, design methods for first- and second-order systems based on transient specifications, root locus analysis and design, and the mechanisms by which saturation, rate limits, and unmodeled dynamics can destabilize a feedback loop.
Download
Version 1.0, September 22, 2026. This is the first version of these lecture notes made publicly available; it is free to download.
Complete book in slide/landscape format (recommended): [PDF]
Complete book in upright/textbook format: [PDF file]
Archive of the figures, in PDF format: [tgz]
Bibliography, in BibTeX format: [bib]
Future versions will correct errors and add content. This page always carries the current version, so please link here rather than to a copy.
@Book{lectures-dynamical-systems,
author = {F. Bullo},
title = {Lectures on Dynamical Systems},
year = 2026,
edition = {Version 1.0},
url = {https://fbullo.github.io/lds}
}
Copyright information
Copyright © Francesco Bullo 2023-2026. These lecture notes are made available free of charge for personal, educational, and other non-commercial use. You are welcome to download them and to print a copy for your own use. You may not sell them, use them for commercial purposes, or redistribute them in any medium or format. Please link to this page instead, so that readers always reach the current version.
Unless otherwise noted, all figures in the book are my own work; they are available in the archive above and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). A small number of figures are the work of others and are not covered by that license; they are not included in the archive. Each is identified in its caption, together with its source and, where applicable, the license under which it is reproduced. Those images remain the property of their respective copyright holders and are reproduced in a work distributed free of charge for teaching purposes, as fair use. If you hold the rights to one of them and would prefer that it not appear, please write to me and I will remove it from the next version.
History
Fall 2023: first time I taught the course
Fall 2024: second time I taught the course
June 8, 2025: third revision
Oct 1, 2025: first edition online
Sep 22, 2026: version 1.0, first public release
Feedback
I am thankful for any feedback information, including suggestions, evaluations, error descriptions, or comments about teaching or research uses. Please email bullo at ucsb.edu