Modeling and Simulation in Python: An Introduction for Scientists and Engineers

Modeling and Simulation Book - Table of Contents

Front Matter

• 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

Chapter 1: Introduction to Modeling

• The Modeling Framework
• Testing the Falling Penny Myth
• Computation in Python
• False Precision
• Computation with Units
• Summary
• Exercises

Chapter 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

Chapter 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

Chapter 4: Parameters and Metrics

• Functions That Return Values
• Loops and Arrays
• Sweeping Parameters
• Incremental Development
• Summary
• Exercises
• Challenge Exercises
• Under the Hood

Chapter 5: Building a Population Model

• Exploring the Data
• Absolute and Relative Errors
• Modeling Population Growth
• Simulating Population Growth
• Summary
• Exercise

Chapter 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

Chapter 7: Limits to Growth

• Quadratic Growth
• Net Growth
• Finding Equilibrium
• Dysfunctions
• Summary
• Exercises

Chapter 8: Projecting into the Future

• Generating Projections
• Comparing Projections
• Summary
• Exercise

Chapter 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

Chapter 10: Case Studies Part I

• Historical World Population
• One Queue or Two?
• Predicting Salmon Populations
• Tree Growth

PART II: FIRST-ORDER SYSTEMS

Chapter 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

Chapter 12: Quantifying Interventions

• The Effects of Immunization
• Choosing Metrics
• Sweeping Immunization
• Summary
• Exercise

Chapter 13: Sweeping Parameters

• Sweeping Beta
• Sweeping Gamma
• Using a SweepFrame
• Summary
• Exercise

Chapter 14: Nondimensionalization

• Beta and Gamma
• Exploring the Results
• Contact Number
• Comparing Analysis and Simulation
• Estimating the Contact Number
• Summary
• Exercises
• Under the Hood

Chapter 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

Chapter 16: Solving the Coffee Problem

• Mixing Liquids
• Mix First or Last?
• Optimal Timing
• The Analytic Solution
• Summary
• Exercises

Chapter 17: Modeling Blood Sugar

• The Minimal Model
• The Glucose Minimal Model
• Getting the Data
• Interpolation
• Summary
• Exercises

Chapter 18: Implementing the Minimal Model

• Implementing the Model
• The Update Function
• Running the Simulation
• Solving Differential Equations
• Summary
• Exercise

Chapter 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

Chapter 20: The Falling Penny Revisited

• Newton's Second Law of Motion
• Dropping Pennies
• Event Functions
• Summary
• Exercise

Chapter 21: Drag

• Calculating Drag Force
• The Params Object
• Simulating the Penny Drop
• Summary
• Exercises

Chapter 22: Two-Dimensional Motion

• Assumptions and Decisions
• Vectors
• Simulating Baseball Flight
• Drag Force
• Adding an Event Function
• Visualizing Trajectories
• Animating the Baseball
• Summary
• Exercises

Chapter 23: Optimization

• The Manny Ramirez Problem
• Finding the Range
• Summary
• Exercise
• Under the Hood

Chapter 24: Rotation

• The Physics of Toilet Paper
• Setting Parameters
• Simulating the System
• Plotting the Results
• The Analytic Solution
• Summary
• Exercise

Chapter 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

Chapter 26: Case Studies Part III

• Bungee Jumping
• Bungee Dunk Revisited
• Orbiting the Sun
• Spider-Man
• Kittens
• Simulating a Yo-Yo
• Congratulations

Back Matter

Appendix: Under the Hood

• How run_solve_ivp Works
• How root_scalar Works
• How maximize_scalar Works

Index

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.