Angela B. Shiflet and George W. Shiflet
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Contents
Preface
Chapter 1 Overview
Module 1.1 Overview of Computational Science
Projects
References
Module 1.2 The Modeling Process
Introduction
Model Classifications
Steps of the Modeling Process
Exercises
References
Chapter 2 Fundamental Considerations
Module 2.1 Computational Toolbox—Tools of the Trade: Tutorial 1
Download
Introduction
Module 2.2 Errors
Introduction
Data Errors
Modeling Errors
Implementation Errors
Precision
Round-off Error
Overflow and Underflow
Arithmetic Errors
Error Propagation
Violation of Numeric Properties
Comparison of Floating Point Numbers
Truncation Error
Exercises
Projects
Answers to Quick Review Questions
References
Module 2.3 Rate of Change
Introduction
Velocity
Derivative
Slope of Tangent Line
Differential Equations
Second Derivative
Exercises
Project
Answers to Quick Review Questions
Reference
Module 2.4 Fundamental Concepts of Integral Calculus
Introduction
Total Distance Traveled and Area
Definite Integral
Total Change
Fundamental Theorem of Calculus
Differential Equations Revisited
Exercises
Project
Answers to Quick Review Questions
References
Chapter 3 System Dynamics Problems with Rate Proportional to Amount
Module 3.1 System Dynamics Tool: Tutorial 1
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Introduction
Module 3.2 Unconstrained Growth and Decay
Introduction
Differential Equation
Difference Equation
Simulation Program
Analytical Solution Introduction
Analytical Solution: Explanation with Indefinite Integrals
Analytical Solution: Explanation without Indefinite Integrals
Completion of Analytical Solution
Further Refinement
Unconstrained Decay
Exercises
Projects
Answers to Quick Review Questions
Reference
Module 3.3 Constrained Growth
Introduction
Carrying Capacity
Revised Model
Equilibrium and Stability
Exercises
Projects
Answers to Quick Review Questions
References
Module 3.4 System Dynamics Tool: Tutorial 2
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Introduction
Module 3.5 Drug Dosage
Downloads
Introduction
One-Compartment Model of Single Dose
One-Compartment Model of Repeated Doses
Mathematics of Repeated Doses
Sum of Finite Geometric Series
Two-Compartment Model
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 4 Force and Motion
Module 4.1 Modeling Falling and Skydiving
Downloads
Introduction
Acceleration, Velocity, and Position
Physics Background
Friction During Fall
Modeling a Skydive
Assessment of the Skydive Model
Exercises
Projects
Answers to Quick Review Questions
References
Module 4.2 Modeling Bungee Jumping
Downloads
Introduction
Physics Background
Vertical Springs
Modeling a Bungee Jump
Exercises
Projects
Answers to Quick Review Questions
References
Module 4.3 Tick Tock—The Pendulum Clock
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Introduction
Simple Pendulum
Linear Damping
Pendulum Clock
Exercises
Projects
Answers to Quick Review Questions
References
Module 4.4 Up, Up, and Away—Rocket Motion
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Introduction
Physics Background
System Dynamics Model
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 5 Simulation Techniques
Module 5.1 Computational Toolbox—Tools of the Trade: Tutorial 2
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Introduction
Module 5.2 Euler's Method
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Introduction
Reasoning behind Euler's Method
Algorithm for Euler's Method
Error
Exercises
Projects
Answers to Quick Review Questions
References
Module 5.3 Runge-Kutta 2 Method
Introduction
Euler's Estimate as a Predictor
Corrector
Runge Kutta 2 Algorithm
Error
Exercises
Projects
Answers to Quick Review Questions
References
Module 5.4 Runge-Kutta 4 Method
Introduction
First Estimate ∂1 Using Euler's Method
Second Estimate ∂2
Third Estimate ∂3
Fourth Estimate ∂4
Using the Four Estimates
Runge-Kutta 4 Algorithm
Error
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 6 System Dynamics Models with Interactions
Module 6.1 Competition
Download
Community Relations
Competition Introduction
Modeling Competition
Exercises
Projects
Answers to Quick Review Questions
References
Module 6.2 Spread of SARS
Downloads
Introduction
SIR Model
SARS Model
Reproductive Number
Exercises
Projects
Answers to Quick Review Questions
References
Module 6.3 Enzyme Kinetics
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Introduction
Michaelis-Menten Equation
Differential Equations
Model
Exercises
Projects
Answers to Quick Review Questions
References
Module 6.4 Predator-Prey Models
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Introduction
Lotka-Volterra Model
Particular Situations
Exercises
Projects
Answers to Quick Review Questions
References
Module 6.5 Modeling Malaria
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Introduction
Background Information
Analysis of Problem
Formulating a Model: Gather Data
Formulating a Model: Make Simplifying Assumptions
Formulating a Model: Determine Variables and Units
Formulating a Model: Establish Relationships
Formulating a Model: Determine Equations and Functions
Solving the Model
Verifying and Interpreting the Model’s Solution
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 7 Additional Dynamic Systems Projects
Module 7.0 Chapter 7 Overview
Module 7.1 Radioactive Chains—Never the Same Again
Introduction
Modeling the Radioactive Chain
Projects
Answers to Quick Review Questions
Reference
Module 7.2 Turnover and Turmoil—Blood Cell Populations
Introduction
Formation and Destruction of Blood Cells
Basic Model
Model Parameters
Projects
Answers to Quick Review Questions
References
Module 7.3 Deep Trouble—Ideal Gas Laws and Scuba Diving
Pressure
Ideal Gas
Dalton's Law
Boyle's Law
Charles' Law
Henry's Law
Rate of Absorption
Decompression Sickness
Projects
Answers to Quick Review Questions
References
Module 7.4 What Goes Around Comes Around—The Carbon Cycle
Introduction
Flow between Subsystems
Fossil Fuels
Projects
References
Module 7.5 A Heated Debate—Global Warming
Greenhouse Effect
Global Warming
Greenhouse Gases
Consequences
Projects
References
Module 7.6 Cardiovascular System—A Pressure Filled Model
Circulation
Blood Pressure
Heart Rate
Stroke Volume
Venous Return
Systemic Vascular Resistance
Blood Flow
Projects
References
Module 7.7 Electrical Circuits—A Complete Story
Defibrillators
Current and Potential
Resistance
Capacitance
Inductance
Circuit for Defibrillator
Kirchhoff's Voltage Law
Kirchhoff's Current Law
Projects
Answers to Quick Review Questions
References
Module 7.8 Fueling Our Cells—Carbohydrate Metabolism
Glycolysis
Recycling NAD+’s
Aerobic Respiration
Projects
References
Module 7.9 Mercury Pollution—Getting on Our Nerves
Introduction
Projects
References
Module 7.10 Managing to Eat—What’s the Catch?
Introduction
Gordon-Schaefer Fishery Production Function
Projects
Answers to Quick Review Questions
References
Chapter 8 Data-Driven Models
Module 8.1 Computational Toolbox—Tools of the Trade: Tutorial 3
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Introduction
Module 8.2 Function Tutorial
Download
Introduction
Linear Function
Quadratic Function
Polynomial Functions
Square Root Function
Exponential Function
Logarithmic Functions
Logistic Function
Trigonometric Functions
Module 8.3 Empirical Models
Downloads
Introduction
Linear Empirical Model
Predictions
Linear Regression
Nonlinear One-Term Model
Solving for y in a One-Term Model
Multiterm Models
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 9 Monte Carlo Simulations
Module 9.1 Computational Toolbox—Tools of the Trade: Tutorial 4
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Introduction
Module 9.2 Simulations
Introduction
Element of Chance
Disadvantages
Genesis of Monte Carlo Simulations
Multiplicative Linear Congruential Method
Different Ranges of Random Numbers
Exercises
Projects
Answers to Quick Review Questions
References
Module 9.3 Area Through Monte Carlo Simulation
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Introduction
Throwing Darts for Area
Measure of Quality
Algorithm
Implementation
Exercises
Projects
Answers to Quick Review Questions
Reference
Module 9.4 Random Numbers from Various Distributions
Downloads
Introduction
Statistical Distributions
Discrete Distributions
Normal Distributions
Exponential Distributions
Rejection Method
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 10 Random Walk Simulations
Module 10.1 Computational Toolbox—Tools of the Trade: Tutorial 5
Download
Introduction
Module 10.2 Random Walk
Downloads
Introduction
Algorithm for Random Walk
Animate Path
Average Distance Covered
Relationship between Number of Steps and Distance Covered
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 11 Diffusion
Module 11.1 Computational Toolbox—Tools of the Trade: Tutorial 6
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Introduction
Module 11.2 Spreading of Fire
Downloads
Introduction
Initializing the System
Updating Rules
Periodic Boundary Conditions
Applying a Function to Each Grid Point
Simulation Program
Display Simulation
Exercises
Projects
Answers to Quick Review Questions
References
Module 11.3 Movement of Ants
Downloads
Introduction
Analysis of Problem
Formulating a Model: Gather Data
Formulating a Model: Make Simplifying Assumptions
Formulating a Model: Determine Variables
Formulating a Model: Establish Relationships and Submodels
Formulating a Model: Determine Functions—Sensing
Formulating a Model: Determine Functions—Walking without Concern for Collision
Formulating a Model: Determine Functions—Walking with Concern for Collision
Solving the Model—A Simulation
Verifying and Interpreting the Model's Solution—Visualizing the Simulation
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 12 High-Performance Computing
Module 12.1 Concurrent Processing
Introduction
Analogy
Types of Processing
Multiprocessor
Classification of Computer Architectures
Metrics
Exercises
Project
Answers to Quick Review Questions
References
Module 12.2 Parallel Algorithms
Introduction
Embarrassingly Parallel Algorithm: Adding Two Vectors
Data Partitioning: Adding Numbers
Divide and Conquer: Adding Numbers
Parallel Random Number Generator
Sequential Algorithm for N-Body Problem
Barnes-Hut Algorithm for N-Body Problem
Exercises
Projects
Answers to Quick Review Questions
References
Chapter 13 Additional Cellular Automata Projects
Module 13.0 Chapter 13 Overview
Module 13.1 Polymers—Strings of Pearls
Introduction
Simulations
Projects
References
Module 13.2 Solidification—Let’s Make It Crystal Clear!
Introduction
Projects
References
Module13.3 Foraging—Finding a Way to Eat
Introduction
Simulations
Projects
References
Module 13.4 Pit Vipers—Hot Bodies, Dead Meat
Introduction
Simulations of Heat Diffusion
Projects
References
Module 13.5 Mushroom Fairy Rings—Just Going in Circles
Introduction
What Are Fungi?
What Do Fungi Look Like?
How Do Fungi “Feed Themselves”?
How Do Fungi Reproduce?
How Do Fungi Grow?
The Problem
How Do Fairy Rings Get Started?
Updating Rules
Display the Simulation
Projects
References
Module 13.6 Spread of Disease—"Gesundheit!"
Introduction
Exercise
Projects
Module 13.7 HIV—The Enemy Within
The Developing Epidemic
Attack on the Immune System
Plan of Attack
Simulation of the Attack
Projects
References
Module 13.8 Predator-Prey—"Catch Me If You Can"
Introduction
Projects
References
Module 13.9 Clouds—Bringing It All Together
Introduction
Projects
References
Module 13.10 Fish Schooling—Hanging Together, Not Separately
Introduction
Simulations
Projects
References
Appendices
Glossary
Answers to Selected Exercises