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

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