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More About This Textbook
Overview
"This is an important book with a wonderful collection of examples, models, and references."—Robert M. Panoff, Shodor Education Foundation
"This is a very good introduction to the field of computational science. It provides several good applications to illustrate the general nature of computational science, developing background material on a justintime basis."—Peter Turner, Clarkson University
Editorial Reviews
MAA Reviews
The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application. . . . [This book] has been carefully written with students clearly in mind.— Bill Satzer
Physics Today
Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding.— Wouter van Jollingen
UMAP Journal
I think this text is a masterpiece. I know of nothing comparable. I give it five stars.— JamesM. Cargal
Zentralblatt MATH Database
[A] flexible, readable textbook that assumes only a background in high school algebra . . . . It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.Zentralblatt MATH
[A] flexible, readable textbook that assumes only a background in high school algebra . . . . It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.
MAA Reviews  Bill Satzer
The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application. . . . [This book] has been carefully written with students clearly in mind.Physics Today  Wouter van Jollingen
Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding.UMAP Journal  James M. Cargal
I think this text is a masterpiece. I know of nothing comparable. I give it five stars.UMAP Journal  JamesM. Cargal
I think this text is a masterpiece. I know of nothing comparable. I give it five stars.From the Publisher
"The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application. . . . [This book] has been carefully written with students clearly in mind."—Bill Satzer, MAA Reviews"Introduction to Computational Science is useful for students and others who want to obtain some of the basic skills of the field. Its impressive collection of projects allows readers to quickly enjoy the power of modern computing as an essential tool in building scientific understanding."—Wouter van Jollingen, Physics Today
"I think this text is a masterpiece. I know of nothing comparable. I give it five stars."—JamesM. Cargal, UMAP Journal
Product Details
Related Subjects
Meet the Author
Angela B. Shiflet is Larry Hearn McCalla Professor of Mathematics and Computer Science and Chair of the Computer Science Department at Wofford College in Spartanburg, South Carolina. George W. Shiflet is Larry Hearn McCalla Professor of Biology and Chair of the Biology Department at Wofford College.
Read an Excerpt
Introduction to Computational Science
Modeling and Simulation for the SciencesBy Angela B. Shiflet George W. Shiflet
Princeton University Press
Copyright © 2006 Princeton University PressAll right reserved.
ISBN: 0691125651
Chapter One
MODULE 1.1Overview of Computational Science
Many significant applied and basic research questions in science today are interdisciplinary in nature, involving physical and/or biological sciences, mathematics, and computer science. For example, Nature reported that John Krebs, chief executive of Britain's Natural Environment Research Council, considers that the environment "requires a 'new breed' of scientist, and new ways of problem solving that cut across traditional disciplines" and that Britain expects a shortage of "environmental scientists with mathematical, computational and statistical skills." (Masood 1998)
The Human Genome Project "has created the need for new kinds of scientific specialists who can be creative at the interface of biology and other disciplines, such as computer science, engineering, mathematics, physics, chemistry, and the social sciences. As the popularity of genomic research increases, the demand for these specialists greatly exceeds the supply.... There is an urgent need to train more scientists in interdisciplinary areas that can contribute to genomics," according to Francis Collins in anarticle in Science (Collins et al. 1998).
Computational science is a fastgrowing interdisciplinary field that is at the intersection of the sciences, computer science, and mathematics. There is a critical need for scientists who have a strong background in computational science. Much scientific investigation now involves computing as well as theory and experiment. Computing can often stimulate the insight and understanding that theory and experiment alone cannot achieve.
This field of computational science combines computer simulation, scientific visualization, mathematical modeling, computer programming and data structures, networking, database design, symbolic computation, and high performance computing with various scientific disciplines. Computer simulation and modeling offer valuable approaches to problems in many areas, as the following examples indicate.
1. Scientists at Los Alamos National Laboratory and the University of Minnesota wrote, "mathematical modeling has impacted our understanding of HIV pathogenesis. Before modeling was brought to bear in a serious manner, AIDS was thought to be a slow disease in which treatment could be delayed until symptoms appeared, and patients were not monitored very aggressively. In the large, multicenter AIDS cohort studies aimed at monitoring the natural history of the disease, blood typically was drawn every six months. There was a poor understanding of the biological processes that were responsible for the observed levels of virus in the blood and the rapidity at which the virus became drug resistant. Modeling, coupled with advances in technology, has changed all of this." Dynamic modeling not only has revealed important features of HIV pathogenesis but has advanced the drug treatment regime for AIDS patients (Perelson and Nelson 1999).
2. Boeing Airline engineers completely designed The Boeing 777 jetliner using threedimensional computer graphics. "Preassembly" of the airplane on the computer at every stage of the design process eliminated the necessity of a costly, fullscale mockup and reduced error, adjustments, and revisions by 50 percent (Boeing). The pilots that fly these and other large airplanes train on sophisticated, computer flight simulators, which enable the pilots to practice dealing with dangerous situations, such as engine fire and wind shear.
3. From the 1960s, numerical weather prediction has revolutionized forecasting. "Since then, forecasting has improved sidebyside with the evolution of computing technology, and advances in computing continue to drive better forecasting as weather researchers develop improved numerical models" (Pittsburgh Supercomputing Center 2001).
4. Researchers at the University of Washington's School of Fisheries are employing mathematical modeling to examine the impact on fish survival of the removal of four dams on the lower Snake River. Another team at the University of Tennessee? Institute for Environmental Modeling is using computational ecology to study complex options for ecological management of the Everglades. Louis Gross, Director of the Institute, says that "computational technology, coupled with mathematics and ecology, will play an everincreasing role in generating vital information society needs to make tough decisions about its surroundings" (Helly et al.).
5. A group of engineers and computer scientists at Carnegie Mellon University and seismologists from the University of Southern California and the National University of Mexico is building threedimensional computer simulations of ground motion during earthquakes to predict how areas, such as the Greater Los Angeles Basin, will behave during such a disaster. Using powerful parallelprocessing computer systems, one simulation indicated a complex pattern of basin ground motion with some sites experiencing nine times greater motion than others. With such information, scientists can predict the damage in an area (Pittsburgh Supercomputing Center 1997). Seattle, Washington is another area prone to earthquakes. The National Tsunami Hazard Mitigation Program has an extensive simulation modeling effort to assess the hazards of tsunami threats after earthquakes in the Puget Sound region so that officials can plan and mitigate their dangers (Koshimura and Mofjeld 2001). With computational models, others have studied the economic impact of disruption to the water supply caused by an earthquake in the Portland, Oregon region and appropriate responses to minimize the consequences (Rose and Liao).
Such collaboration among scientists, mathematicians, engineers, and computer scientists is indicative of much computational science research and practice. The fruits of these researchers' models and simulations are a deeper understanding of complex systems, a better foundation for important decisions, and a revolution in scientific advances that are helping people all over the world.
Projects
1. Investigate three applications of computational science involving different scientific areas and write at least a paragraph on each. List references.
2. Investigate an application of computational science and write a threepage, typed, doublespaced paper on the topic. List references.
(Continues...)
Table of Contents
Preface xix
CHAPTER 1: OVERVIEW
Module 1.1 Overview of Computational Science 3
Projects 5
References 5
Module 1.2 The Modeling Process 6
Introduction 6
Model Classifications 7
Steps of the Modeling Process 8
Exercises 11
References 11
CHAPTER 2: FUNDAMENTAL CONSIDERATIONS
Module 2.1 Computational Toolbox—Tools of the Trade: Tutorial 1 15
Download 15
Introduction 16
Module 2.2 Errors 17
Introduction 17
Data Errors 17
Modeling Errors 17
Implementation Errors 18
Precision 18
Absolute and Relative Errors 19
Roundoff Error 21
Overflow and Underflow 22
Arithmetic Errors 23
Error Propagation 24
Violation of Numeric Properties 27
Comparison of Floating Point Numbers 27
Truncation Error 29
Exercises 31
Projects 32
Answers to Quick Review Questions 34
References 35
Module 2.3 Rate of Change 36
Introduction 36
Vel o c ity 36
Derivative 41
Slope of Tangent Line 42
Differential Equations 47
Second Derivative 48
Exercises 49
Project 51
Answers to Quick Review Questions 51
Reference 52
Module 2.4 Fundamental Concepts of Integral Calculus 53
Introduction 53
Total Distance Traveled and Area 53
Definite Integral 60
Total Change 61
Fundamental Theorem of Calculus 62
Differential Equations Revisited 64
Exercises 64
Project 66
Answers to Quick Review Questions 66
References 67
CHAPTER 3: SYSTEM DYNAMICS PROBLEMS WITH RATE PROPORTIONAL TO AMOUNT
Module 3.1 System Dynamics Tool: Tutorial 1 71
Download 71
Introduction 71
Module 3.2 Unconstrained Growth and Decay 73
Introduction 73
Differential Equation 73
Difference Equation 74
Simulation Program 78
Analytical Solution Introduction 79
Analytical Solution: Explanation with Indefinite Integrals 79
Analytical Solution: Explanation without Indefinite Integrals 80
Completion of Analytical Solution 80
Further Refinement 82
Unconstrained Decay 82
Exercises 84
Projects 85
Answers to Quick Review Questions 86
Reference 86
Module 3.3 Constrained Growth 87
Introduction 87
Carrying Capacity 87
Revised Model 89
Equilibrium and Stability 91
Exercises 92
Projects 93
Answers to Quick Review Questions 95
References 96
Module 3.4 System Dynamics Tool: Tutorial 2 97
Download 97
Introduction 97
Module 3.5 Drug Dosage 98
Downloads 98
Introduction 98
OneCompartment Model of Single Dose 99
OneCompartment Model of Repeated Doses 101
Mathematics of Repeated Doses 103
Sum of Finite Geometric Series 106
TwoCompartment Model 106
Exercises 107
Projects 108
Answers to Quick Review Questions 109
References 110
CHAPTER 4: FORCE AND MOTION
Module 4.1 Modeling Falling and Skydiving 113
Downloads 113
Introduction 113
Acceleration, Velocity, and Position 114
Physics Background 117
Friction During Fall 120
Modeling a Skydive 122
Assessment of the Skydive Model 124
Exercises 125
Projects 125
Answers to Quick Review Questions 127
References 128
Module 4.2 Modeling Bungee Jumping 129
Downloads 129
Introduction 129
Physics Background 130
Vertical Springs 132
Modeling a Bungee Jump 135
Exercises 137
Projects 137
Answers to Quick Review Questions 138
References 139
Module 4.3 Tick Tock—The Pendulum Clock 140
Download 140
Introduction 140
Simple Pendulum 141
Linear Damping 144
Pendulum Clock 144
Exercises 145
Projects 146
Answers to Quick Review Questions 147
References 147
Module 4.4 Up, Up, and Away—Rocket Motion 149
Download 149
Introduction 149
Physics Background 150
System Dynamics Model 152
Exercises 154
Projects 155
Answers to Quick Review Questions 157
References 157
CHAPTER 5: SIMULATION TECHNIQUES
Module 5.1 Computational Toolbox—Tools of the Trade: Tutorial 2 161
Download 161
Introduction 161
Module 5.2 Euler's Method 162
Download 162
Introduction 162
Reasoning behind Euler's Method 162
Algorithm for Euler's Method 164
Error 165
Exercises 167
Projects 167
Answers to Quick Review Questions 168
References 169
Module 5.3 RungeKutta 2 Method 170
Introduction 170
Euler's Estimate as a Predictor 170
Corrector 170
RungeKutta 2 Algorithm 173
Error 174
Exercises 175
Projects 175
Answers to Quick Review Questions 175
References 175
Module 5.4 RungeKutta 4 Method 176
Introduction 176
First Estimate Using Euler's Method 176
Second Estimate 177
Third Estimate 179
Fourth Estimate 181
Using the Four Estimates 183
RungeKutta 4 Algorithm 184
Error 185
Exercises 186
Projects 186
Answers to Quick Review Questions 186
References 187
CHAPTER 6: SYSTEM DYNAMICS MODELS WITH INTERACTIONS
Module 6.1 Competition 191
Download 191
Community Relations 191
Competition Introduction 191
Modeling Competition 192
Exercises 195
Projects 195
Answers to Quick Review Questions 197
References 197
Module 6.2 Spread of SARS 198
Downloads 198
Introduction 198
SIR Model 199
SARS Model 202
Reproductive Number 207
Exercises 208
Projects 208
Answers to Quick Review Questions 210
References 211
Module 6.3 Enzyme Kinetics 213
Download 213
Introduction 213
MichaelisMenten Equation 214
Differential Equations 217
Model 218
Exercises 219
Projects 221
Answers to Quick Review Questions 222
References 223
Module 6.4 PredatorPrey Model 224
Download 224
Introduction 224
LotkaVolterra Model 225
Particular Situations 227
Exercises 230
Projects 231
Answers to Quick Review Questions 235
References 235
Module 6.5 Modeling Malaria 237
Download 237
Introduction 237
Background Information 238
Analysis of Problem 238
Formulating a Model: Gather Data 239
Formulating a Model: Make Simplifying Assumptions 240
Formulating a Model: Determine Variables and Units 241
Formulating a Model: Establish Relationships 242
Formulating a Model: Determine Equations and Functions 243
Solving the Model 244
Verifying and Interpreting the Model's Solution 247
Exercises 249
Projects 249
Answers to Quick Review Questions 251
References 251
CHAPTER 7: ADDITIONAL DYNAMIC SYSTEMS PROJECTS
Overview 253
Module 7.1 Radioactive Chains—Never the Same Again 255
Introduction 255
Modeling the Radioactive Chain 255
Projects 257
Answers to Quick Review Question 258
Reference 258
Module 7.2 Turnover and Turmoil—Blood Cell Populations 259
Introduction 259
Formation and Destruction of Blood Cells 259
Basic Model 260
Model Parameters 260
Projects 262
Answers to Quick Review Questions 263
References 264
Module 7.3 Deep Trouble—Ideal Gas Laws and Scuba Diving 265
Pressure 265
Ideal Gas 266
Dalton's Law 266
Boyle's Law 267
Charles'Law 268
Henry's Law 269
Rate of Absorption 270
Decompression Sickness 271
Projects 271
Answers to Quick Review Questions 272
References 273
Module 7.4 What Goes Around Comes Around—The Carbon Cycle 274
Introduction 274
Flow between Subsystems 274
Fossil Fuels 275
Projects 276
References 276
Module 7.5 A Heated Debate—Global Warming 278
Greenhouse Effect 278
Global Warming 279
Greenhouse Gases 279
Consequences 279
Projects 280
References 281
Module 7.6 Cardiovascular System—A PressureFilled Model 283
Circulation 283
Blood Pressure 284
Heart Rate 284
Stroke Volume 285
Venous Return 285
Systemic Vascular Resistance 285
Blood Flow 285
Projects 286
References 287
Module 7.7 Electrical Circuits—A Complete Story 288
Defibrillators 288
Current and Potential 288
Resistance 290
Capacitance 291
Inductance 292
Circuit for Defibrillator 292
Kirchhoff's Voltage Law 293
Kirchhoff's Current Law 295
Projects 296
Answers to Quick Review Questions 297
References 297
Module 7.8 Fueling Our Cells—Carbohydrate Metabolism 299
Glycolysis 299
Recycling NAD's 300
Aerobic Respiration 301
Projects 301
References 302
Module 7.9 Mercury Pollution—Getting on Our Nerves 303
Introduction 303
Projects 304
References 307
Module 7.10 Managing to Eat—What's the Catch? 308
Introduction 308
Economics Background 309
GordonSchaefer Fishery Production Function 314
Projects 314
Answers to Quick Review Questions 316
References 316
CHAPTER 8: DATADRIVEN MODELS
Module 8.1 Computational Toolbox—Tools of the Trade: Tutorial 3 321
Download 321
Introduction 321
Module 8.2 Function Tutorial 322
Download 322
Introduction 322
Linear Function 323
Quadratic Function 324
Polynomial Function 325
Square Root Function 326
Exponential Function 327
Logarithmic Functions 328
Logistic Function 330
Trigonometric Functions 331
Module 8.3 Empirical Models 335
Downloads 335
Introduction 336
Linear Empirical Model 336
Predictions 338
Linear Regression 339
Nonlinear OneTerm Model 340
Solving for y in a OneTerm Model 346
Multiterm Models 349
Exercises 351
Projects 351
Answers to Quick Review Questions 351
References 352
CHAPTER 9: MONTE CARLO SIMULATIONS
Module 9.1 Computational Toolbox—Tools of the Trade: Tutorial 4 357
Download 357
Introduction 357
Module 9.2 Simulations 358
Introduction 358
Element of Chance 359
Disadvantages 359
Genesis of Monte Carlo Simulations 359
Multiplicative Linear Congruential Method 360
Different Ranges of Random Numbers 361
Exercises 364
Projects 365
Answers to Quick Review Questions 366
References 366
Module 9.3 Area Through Monte Carlo Simulation 367
Download 367
Introduction 367
Throwing Darts for Area 368
Measure of Quality 370
Algorithm 371
Implementation 371
Exercises 371
Projects 372
Answers to Quick Review Questions 373
Reference 373
Module 9.4 Random Numbers from Various Distributions 374
Downloads 374
Introduction 374
Statistical Distributions 374
Discrete Distributions 377
Normal Distributions 380
Exponential Distributions 382
Rejection Method 384
Exercises 385
Projects 387
Answers to Quick Review Questions 387
References 388
CHAPTER 10: RANDOM WALK SIMULATIONS
Module 10.1 Computational Toolbox—Tools of the Trade: Tutorial 5 391
Download 391
Introduction 391
Module 10.2 Random Walk 392
Downloads 392
Introduction 392
Algorithm for Random Walk 393
Animate Path 395
Average Distance Covered 398
Relationship between Number of Steps and Distance Covered 400
Exercises 400
Projects 401
Answers to Quick Review Questions 402
References 402
CHAPTER 11: DIFFUSION
Module 11.1 Computational Toolbox—Tools of the Trade: Tutorial 6 405
Download 405
Introduction 405
Module 11.2 Spreading of Fire 406
Downloads 406
Introduction 406
Initializing the System 407
Updating Rules 408
Periodic Boundary Conditions 411
Applying a Function to Each Grid Point 414
Simulation Program 416
Display Simulation 417
Exercises 417
Projects 419
Answers to Quick Review Questions 420
References 420
Module 11.3 Movement of Ants 422
Downloads 422
Introduction 422
Analysis of Problem 423
Formulating a Model: Gather Data 423
Formulating a Model: Make Simplifying Assumptions 424
Formulating a Model: Determine Variables 424
Formulating a Model: Establish Relationships and Submodels 424
Formulating a Model: Determine Functions—Sensing 425
Formulating a Model: Determine Functions—Walking without Concern for Collision 425
Formulating a Model: Determine Functions—Walking with Concern for Collision 426
Solving the Model—A Simulation 428
Verifying and Interpreting the Model's Solution—Visualizing the Simulation 429
Exercises 429
Projects 431
Answers to Quick Review Questions 434
References 434
CHAPTER 12: HIGH PERFORMANCE COMPUTING
Module 12.1 Concurrent Processing 437
Introduction 437
Analogy 439
Types of Processing 440
Multiprocessor 441
Classification of Computer Architectures 443
Metrics 443
Exercises 446
Project 446
Answers to Quick Review Questions 446
References 447
Module 12.2 Parallel Algorithms 448
Introduction 448
Embarrassingly Parallel Algorithm: Adding Two Vectors 448
Data Partitioning: Adding Numbers 449
Divide and Conquer: Adding Numbers 452
Parallel Random Number Generator 455
Sequential Algorithm for N Body Problem 457
BarnesHut Algorithm for N Body Problem 462
Exercises 465
Projects 467
Answers to Quick Review Questions 468
References 470
CHAPTER 13: ADDITIONAL CELLULAR AUTOMATA PROJECTS
Overview 471
Module 13.1 Polymers—Strings of Pearls 473
Introduction 473
Simulations 475
Projects 476
References 477
Module 13.2 Solidification—Let's Make It Crystal Clear! 479
Introduction 479
Projects 480
References 482
Module 13.3 Foraging—Finding a Way to Eat 483
Introduction 483
Simulations 484
Projects 485
References 488
Module 13.4 Pit Vipers—Hot Bodies, Dead Meat 489
Introduction 489
Simulations of Heat Diffusion 489
Projects 490
References 491
Module 13.5 Mushroom Fairy Rings—Just Going in Circles 492
Introduction 492
What Are Fungi? 493
What Do Fungi Look Like? 493
How Do Fungi "Feed Themselves"? 494
How Do Fungi Reproduce? 494
How Do Fungi Grow? 494
The Problem 494
How Do Fairy Rings Get Started? 495
Initializing the System 495
Updating Rules 497
Displaying the Simulation 498
Projects 498
References 499
Module 13.6 Spread of Disease—"Gesundheit!"501
Introduction 501
Exercise 501
Projects 501
Module 13.7 HIV—The Enemy Within 504
The Developing Epidemic 504
Attack on the Immune System 505
Plan of Attack 506
Simulation of the Attack 507
Projects 507
References 508
Module 13.8 PredatorPrey—"Catch Me If You Can "510
Introduction 510
Projects 510
References 514
Module 13.9 Clouds—Bringing It All Together 516
Introduction 516
Projects 517
References 520
Module 13.10 Fish Schooling—Hanging Together, not Separately 521
Introduction 521
Simulations 522
Projects 522
References 523
Glossary of Terms 525
Answers to Selected Exercises 543
Index 547