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Introduction to Computational Science: Modeling and Simulation for the Sciences

Textbook

By: Angela B Shiflet and George W Shiflet

576 pages, 198 line illus, 62 tables

Princeton University Press

Hardback | Jun 2006 | #157922 | ISBN: 0691125651
Availability: Usually dispatched within 5 days Details
NHBS Price: £65.00 $82/€77 approx

About this book

Computational science is a quickly emerging field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. However, limited educational materials exist in this field. Introduction to Computational Science fills this void with a flexible, readable textbook that assumes only a background in high school algebra and enables instructors to follow tailored pathways through the material. It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.

The text embraces two major approaches to computational science problems: System dynamics models with their global views of major systems that change with time; and cellular automaton simulations with their local views of how individuals affect individuals. While the text is generic, an extensive author-generated Web-site contains tutorials and files in a variety of software packages to accompany the text.

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


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 Round-off 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 One-Compartment Model of Single Dose 99 One-Compartment Model of Repeated Doses 101 Mathematics of Repeated Doses 103 Sum of Finite Geometric Series 106 Two-Compartment 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 Runge-Kutta 2 Method 170 Introduction 170 Euler's Estimate as a Predictor 170 Corrector 170 Runge-Kutta 2 Algorithm 173 Error 174 Exercises 175 Projects 175 Answers to Quick Review Questions 175 References 175 Module 5.4 Runge-Kutta 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 Runge-Kutta 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 Michaelis-Menten Equation 214 Differential Equations 217 Model 218 Exercises 219 Projects 221 Answers to Quick Review Questions 222 References 223 Module 6.4 Predator-Prey Model 224 Download 224 Introduction 224 Lotka-Volterra 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 Pressure-Filled 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 Gordon-Schaefer Fishery Production Function 314 Projects 314 Answers to Quick Review Questions 316 References 316 CHAPTER 8: DATA-DRIVEN 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 One-Term Model 340 Solving for y in a One-Term 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 Barnes-Hut 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 Predator-Prey--"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

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Biography

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.

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