An introduction to modeling and simulating physical systems with MATLAB, mathematical computing software for engineers and scientists. A concise introduction to programming and modeling real world systems with MATLAB, a popular programming language for science and engineering. Unlike competing books which are often too mathematical and theoretical, this book by best-selling author Allen Downey is designed to be practical, with an emphasis on thinking about how to design and use models. The author shows the reader that systems may have many possible models and shows them how to justify modeling decisions, choose appropriate models, validate their choices, and iteratively improve their models. Readers are taught basic programming skills and how to combine them with MATLAB to model and simulate systems like population growth, baseball flight trajectories, bungee jumping, and celestial mechanics. For example, the book explores concepts like the Penny Drop Myth: the claim that a penny dropped from the top of the Empire State Building lands with enough force to injure a person or the sidewalk. The author addresses this myth by developing and implementing three models of the system, including or excluding features like air resistance and spin. Other physical systems include world population growth, infectious disease, the coffee cooling problem, baseball trajectories, bungee jumping, and celestial mechanics. Readers learn to use MATLAB to visualize and summarize their results, as well as how to use their models to predict, explain, and design systems. The book presents applications from a range of areas including demography, thermodynamics, epidemiology, ecology, pharmacokinetics, and mechanics. Numerous exercises, sample code, and MATLAB Live Scripts (notebooks that include code, results, and explanatory text) help the reader develop the knowledge and skills necessary to work comfortably in MATLAB.