Modeling and Simulation in Python: An Introduction for Scientists and Engineers
Modeling and Simulation in Python teaches readers how to analyze real-world scenarios using the Python programming language, requiring no more than a background in high school math.
Modeling and Simulation in Python is a thorough but easy-to-follow introduction to physical modeling–that is, the art of describing and simulating real-world systems. Readers are guided through modeling things like world population growth, infectious disease, bungee jumping, baseball flight trajectories, celestial mechanics, and more while simultaneously developing a strong understanding of fundamental programming concepts like loops, vectors, and functions.
Clear and concise, with a focus on learning by doing, the author spares the reader abstract, theoretical complexities and gets right to hands-on examples that show how to produce useful models and simulations.
Cover Page PRAISE FOR MODELING AND SIMULATION IN PYTHON Title Page Copyright Page About the Author About the Technical Reviewer BRIEF CONTENTS CONTENTS IN DETAIL ACKNOWLEDGMENTS INTRODUCTION Who Is This Book For? How Much Math and Science Do I Need? How Much Programming Do I Need? Book Overview Teaching Modeling Getting Started Installing Python Running Jupyter Suggestions and Corrections PART I DISCRETE SYSTEMS 1 INTRODUCTION TO MODELING The Modeling Framework Testing the Falling Penny Myth Computation in Python False Precision Computation with Units Summary Exercises 2 MODELING A BIKE SHARE SYSTEM Our Bike Share Model Defining Functions Print Statements if Statements Parameters for Loops TimeSeries Plotting Summary Exercises Under the Hood 3 ITERATIVE MODELING Iterating on Our Bike Share Model Using More Than One State Object Documentation Dealing with Negative Bikes Comparison Operators Introducing Metrics Summary Exercises 4 PARAMETERS AND METRICS Functions That Return Values Loops and Arrays Sweeping Parameters Incremental Development Summary Exercises Challenge Exercises Under the Hood 5 BUILDING A POPULATION MODEL Exploring the Data Absolute and Relative Errors Modeling Population Growth Simulating Population Growth Summary Exercise 6 ITERATING THE POPULATION MODEL System Objects A Proportional Growth Model Factoring Out the Update Function Combining Birth and Death Summary Exercise Under the Hood 7 LIMITS TO GROWTH Quadratic Growth Net Growth Finding Equilibrium Dysfunctions Summary Exercises 8 PROJECTING INTO THE FUTURE Generating Projections Comparing Projections Summary Exercise 9 ANALYSIS AND SYMBOLIC COMPUTATION Difference Equations Differential Equations Analysis and Simulation Analysis with WolframAlpha Analysis with SymPy Differential Equations in SymPy Solving the Quadratic Growth Model Summary Exercises 10 CASE STUDIES PART I Historical World Population One Queue or Two? Predicting Salmon Populations Tree Growth PART II FIRST-ORDER SYSTEMS 11 EPIDEMIOLOGY AND SIR MODELS The Freshman Plague The Kermack-McKendrick Model The KM Equations Implementing the KM Model The Update Function Running the Simulation Collecting the Results Now with a TimeFrame Summary Exercise 12 QUANTIFYING INTERVENTIONS The Effects of Immunization Choosing Metrics Sweeping Immunization Summary Exercise 13 SWEEPING PARAMETERS Sweeping Beta Sweeping Gamma Using a SweepFrame Summary Exercise 14 NONDIMENSIONALIZATION Beta and Gamma Exploring the Results Contact Number Comparing Analysis and Simulation Estimating the Contact Number Summary Exercises Under the Hood 15 THERMAL SYSTEMS The Coffee Cooling Problem Temperature and Heat Heat Transfer Newton’s Law of Cooling Implementing Newtonian Cooling Finding Roots Estimating r Summary Exercises 16 SOLVING THE COFFEE PROBLEM Mixing Liquids Mix First or Last? Optimal Timing The Analytic Solution Summary Exercises 17 MODELING BLOOD SUGAR The Minimal Model The Glucose Minimal Model Getting the Data Interpolation Summary Exercises 18 IMPLEMENTING THE MINIMAL MODEL Implementing the Model The Update Function Running the Simulation Solving Differential Equations Summary Exercise 19 CASE STUDIES PART II Revisiting the Minimal Model The Insulin Minimal Model Low-Pass Filter Thermal Behavior of a Wall HIV PART III SECOND-ORDER SYSTEMS 20 THE FALLING PENNY REVISITED Newton’s Second Law of Motion Dropping Pennies Event Functions Summary Exercise 21 DRAG Calculating Drag Force The Params Object Simulating the Penny Drop Summary Exercises 22 TWO-DIMENSIONAL MOTION Assumptions and Decisions Vectors Simulating Baseball Flight Drag Force Adding an Event Function Visualizing Trajectories Animating the Baseball Summary Exercises 23 OPTIMIZATION The Manny Ramirez Problem Finding the Range Summary Exercise Under the Hood 24 ROTATION The Physics of Toilet Paper Setting Parameters Simulating the System Plotting the Results The Analytic Solution Summary Exercise 25 TORQUE Angular Acceleration Moment of Inertia Teapots and Turntables Two-Phase Simulation Phase 1 Phase 2 Combining the Results Estimating Friction Animating the Turntable Summary Exercise 26 CASE STUDIES PART III Bungee Jumping Bungee Dunk Revisited Orbiting the Sun Spider-Man Kittens Simulating a Yo-Yo Congratulations APPENDIX: UNDER THE HOOD How run_solve_ivp Works How root_scalar Works How maximize_scalar Works INDEX
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