Mathematical Modeling with Maple (1ST)

Mathematical Modeling with Maple (1ST)

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  • 製本 Hardcover:ハードカバー版/ページ数 578 p.
  • 言語 ENG,ENG
  • 商品コード 9780495109419
  • DDC分類 511.8

Full Description


With an innovative approach that leverages the power of the Maple computer algebra system as an analytical tool, MATHEMATICAL MODELING WITH MAPLE offers an effective introduction to mathematical modeling of compelling real world applications. Intended for students with a background in calculus, the text shows how to formulate, build, solve, analyze, and critique models of applications in math, engineering, computer science, business, and the physical and life sciences. The book utilizes Maple for computations, plotting results graphically, and dynamically analyzing results within the modeling process. Easy-to-follow software instructions are provided, and Maple syntax in the book is also offered online as Maple workbooks allowing students to quickly and interactively work problems as they read. MATHEMATICAL MODELING WITH MAPLE helps students develop their analytical skills while harnessing the power of cutting-edge modern technology, allowing them to become competent, confident problem solvers for the 21st century.

Table of Contents

Chapter 1 Introduction to Maple                    1  (16)
1.1 The Structure of Maple 2 (1)
1.2 A General Introduction to Maple 3 (6)
1.3 Maple Quick Review 9 (6)
1.4 Maple Training 15 (2)
Chapter 2 Introduction, Overview, and the 17 (11)
Process of Mathematical Modeling
Introduction 17 (1)
2.1 The Modeling Process 18 (5)
2.2 Illustrated Examples 23 (5)
The Size of Prehistoric Creatures 23 (1)
Prescribed Drug Dosage 24 (1)
Determining Heart Weight 24 (1)
The Bridge Too Far 25 (1)
Oil-Rig Placement 25 (1)
Military to the Rescue 26 (2)
Chapter 3 Discrete Dynamical Models 28 (50)
Maple Commands for Discrete Dynamical Systems 29 (1)
3.1 Modeling Discrete Change 30 (17)
Tower of Hanoi 34 (1)
Drug Dosage Problem 35 (3)
Time Value of Money 38 (2)
Simple Mortgage 40 (2)
The Spotted Owl 42 (5)
3.2 Equilibrium Values and Long-Term Behavior 47 (9)
3.3 Modeling Nonlinear Discrete Dynamical 56 (5)
Systems
Growth of a Yeast Culture 56 (2)
Spread of a Contagious Disease 58 (3)
3.4 Systems of Discrete Dynamical Systems 61 (5)
Merchants Located Downtown and in Malls 61 (2)
Competitive-Hunter Models 63 (1)
Fast-Food Tendencies 64 (2)
3.5 Modeling of Predator-Prey Model, SIR 66 (12)
Model, and Military Models
A Predator-Prey Model: Foxes and Rabbits 66 (4)
Discrete SIR Models of Epidemics 70 (4)
Modeling Military Insurgencies 74 (4)
Chapter 4 Model Fitting 78 (13)
Introduction 78 (1)
4.1 The Different Curve-Fitting Criterion 79 (6)
A Least-Squares Fit of Bass Fishing Derby 82 (3)
Data
4.2 Plotting the Residuals for a 85 (3)
Least-Squares Fit
Bass Fish 86 (1)
Population Example 87 (1)
4.3 Bounding the Chebyshev's Criterion 88 (3)
Chapter 5 Modeling with Proportionality and 91 (29)
Geometric Similarity
5.1 Proportionality 91 (11)
Kepler's Law as a Proportionality Model 93 (4)
Bass Fish Derby 97 (4)
Scaled Engineering Design 101(1)
5.2 Geometric Similarity 102(18)
Heart Weight 104(3)
Crew Races 107(4)
Modeling the Terror Bird 111(9)
Chapter 6 Empirical Model Construction 120(37)
6.1 Simple One-Term Models 122(10)
Bass Fishing Derby 123(2)
Terror Bird Revisited 125(2)
Cost of a Postage Stamp 127(5)
6.2 Fitting an N-1 Order Polynomial to N Data 132(6)
Points
An (N-1)-Degree Polynomial 133(2)
Fitting a Fifth-Order Polynomial Using 135(3)
Least Squares
6.3 Polynomial Smoothing 138(5)
Simple Squared Data 139(1)
Vehicular Stopping Distance 140(3)
6.4 The Cubic-Spline Model 143(14)
Obtaining Linear and Cubic Splines 143(1)
Fruit Fly Population 143(2)
Vehicle Stopping Distance 145(1)
Determining the Cost of Postage Stamps 146(11)
Using Cubic Splines
Chapter 7 Modeling with Linear Programming 157(49)
Introduction 157(2)
7.1 Formulating Linear Programming Problems 159(6)
Production Mix of New Drinks 159(1)
Financial Planning 160(2)
Blending Problem and Formulation 162(1)
Production Planning Problem 163(2)
7.2 Graphical Simplex for Linear Programming 165(8)
Problems with Two Variables
Memory Chips for CPUs 165(2)
Finding the Feasible Region 167(2)
Minimization Problem 169(1)
Unbounded Feasible Region 170(3)
7.3 Graphical Sensitivity Analysis 173(4)
Manufacturing Problem Sensitivity Analysis 176(1)
7.4 The Simplex Method 177(18)
Maximization Problem with Simplex 185(3)
Wooden Soldier Revisited 188(7)
7.5 Linear Programming in Maple 195(3)
Maximizing a Linear Programming Problem in 196(1)
Maple
Method 2 in Maple with Maximization Problem 196(2)
from Example 1
7.6 Sensitivity Analysis in Maple 198(3)
7.7 Modeling of Ranking Units Using Data 201(5)
Envelopment Analysis
Ranking Banks 202(1)
Ranking Banks with LP 203(3)
Chapter 8 Modeling with Single-Variable 206(31)
Unconstrained Optimization
Introduction 206(1)
8.1 Single-Variable Basic Theory 206(4)
8.2 Models with Basic Applications of Max-Min 210(5)
Theory
Chemical Sales 210(1)
Inventory Model: Manufacturing and Storage 211(1)
Producing the SP6 Computer 212(3)
8.3 Applied Single-Variable Optimization 215(6)
Models
An Inventory Problem: Revisit Minimizing 215(62)
the Cost of Delivery and Storage
Oil-Rig Location Problem 277
8.4 Single-Variable Search Techniques with 221(16)
Maple
Minimizing a Step Function 222(1)
Dichotomous Search to Find a Minimum 223(3)
Using Golden Section Search to Maximize a 226(1)
Function That Does Not Have a Derivative
Maximizing a Transcendental Function with 226(3)
Golden Section Search
Maximizing a Function That Does Not Have a 229(1)
Derivative with Fibonacci Search
Maximizing a Transcendental Function with 229(2)
Fibonacci Search
Newton's Method to Minimize f(x)=x2+2x 231(1)
Maximize f(x)=-2x3+10x-10 231(1)
Bisection Method to Minimize the Function 232(5)
f(x)
Chapter 9 Models Using Unconstrained 237(38)
Optimization: Maximization and Minimization
with Several Variables
Introduction 237(1)
9.1 Basic Theory 238(1)
9.2 The Hessian Matrix 239(9)
Finding the Hessian for f(x1,x2)=x2,+3x22 240(1)
Finding the Hessian for 240(1)
f(x1,x2)=-x1,-3x22+3x1*x2
Finding the Principal Minors of a 3x3 240(1)
Hessian Matrix
Determinants of Principal Minors 241(1)
A Convex Function 242(1)
A Concave Function 243(1)
Neither a Convex nor a Concave Function 243(3)
A Negative Definite Hessian Matrix 246(1)
A Positive Semidefinite Hessian Matrix 246(1)
Maple Checking "Definiteness" 247(1)
9.3 Unconstrained Optimization 248(11)
Finding and Classifying Stationary Points 248(1)
Finding and Classifying All Extreme Points 249(3)
Finding Stationary Points for 252(1)
f(x,y)-2xy+4x+6y-2x2-2y2
Least-Squares Model 253(2)
Finding the Island 255(4)
9.4 Multivariable Numerical Search Methods 259(16)
Maximization with Gradient Search 260(2)
Maximizing the Function 262(2)
f(x1,x2)=55x,-4x2,+135x2-15x22-100
Gradient Search When Calculus Fails 264(2)
Newton's Method to Find a Maximum 266(1)
Maple with Newton's Method 267(1)
Maximize 2x1x2+2x2-ex1-ex2+10 267(8)
Chapter 10 Modeling Optimization with 275(39)
Constraints
10.1 Equality Constraints Method of Lagrange 275(16)
Multipliers
Minimization with Lagrange Multipliers 279(5)
Lagrange Multipliers with Multiple 284(1)
Constraints
Cobb縫ouglas Function 285(2)
Oil Transfer 287(4)
10.2 Inequality Constraints: Kuhn傍ucker 291(23)
Necessary and Sufficient Conditions
Maximizing with Inequality Constraints 294(3)
Two Variable-Two Constraint Linear Problem 297(3)
Two-Variable, Three-Constraints Linear 300(7)
Problem
Geometric Three-Variable Nonlinear 307
Constrained Problem
Revisiting Example 4 304(1)
Minimization with Two Inequality Constraints 305(1)
Maximizing Profit from Perfume Manufacturing 306(2)
Minimum Variance of Expected Investment 308(6)
Returns
Chapter 11 Modeling with Linear Systems of 314(30)
Equations Using Linear Algebra Techniques
Introduction 314(1)
11.1 Introduction to Systems of Equations 314(4)
Solving a System of Equations 317(1)
11.2 Models with Unique Solutions Using 318(13)
Systems of Equations
A Bridge Too Far 318(3)
The Leontief Input飽utput Economic Model as 321(2)
a Linear System of Equations
Least-Squares Models as Systems of Equations 323(2)
Natural Cubic Splines as a System of 325(6)
Equations
11.3 Models with Infinite Solutions Using 331(13)
Systems of Equations
Simple Chemical Balancing: Balancing S6+ 02 333(1)
-> SO2
Balancing a More Complicated Equation 334(2)
Balancing More Complicated 336(1)
Oxidation乏eduction (Redox Reaction)
Equations
Balancing Equations with the Conservation 337(1)
of Mass and Charge: Oxidation乏eduction
Equations, with Systems of Equations
Balancing a Redox Equation 337(2)
Balancing an Oxidation乏eduction Equation 339(2)
Oxidation乏eduction: Balancing CH3CH2OH + 341(3)
Cr2022- + H+   CH3CO2H + Cr3+ + H20
Chapter 12 Modeling First-Order Ordinary 344(41)
Differential Equations (ODEs)
Introduction 344(2)
12.1 Applied First-Order Models 346(4)
Radioactive Decay 346(2)
Newton's Law of Cooling 348(1)
Mixtures 349(1)
Population Models 349(1)
The Spread of a Contagious Disease 350(1)
12.2 Slope Fields and Qualitative Assessments 350(7)
of Autonomous First-Order ODEs
12.3 Analytical Solution to First-Order ODEs 357(9)
Recognizing a Separable ODE 357(1)
Recognizing a Nonseparable ODE 358(1)
A Separable ODE after Manipulation 358(1)
Solving a Separable ODE 358(1)
Radioactive Decay as a Separable ODE 359(1)
Malthusian Population Model 360(1)
Newton's Law of Cooling 360(1)
Chemical Mixtures 361(1)
Refined Population Model 362(1)
Solving a Linear ODE by Using the 363(1)
Integrating Factor
Newton's Law of Cooling 364(1)
Revisit Example 4 Using Maple 364(1)
Refined Population Model Using Maple 365(1)
12.4 Numerical Methods for Solutions to 366(19)
First-Order ODEs
Euler's Method to Solve: dy/dt=.25 y 367(2)
t,y(0)=2
Euler's Method with Maple 369(3)
Solving y' = 0.25ty, y(0) = 2 with Improved 372(1)
Euler's Method
Improved Euler's Method Using Maple 373(3)
Runga-Kutta Method by Hand: y'=0.25ty, 376(9)
y(0)=2
Chapter 13 Modeling with Systems of 385(45)
Differential Equations
13.1 Applied Systems of Differential Equations 386(4)
Economics: Basic Supply-and-Demand Models 386(1)
An Electrical Network 387(1)
Competition between Species 388(1)
Predator-Prey Relationships 388(1)
Diffusion Models 388(1)
Insurgency Models 389(1)
13.2 Phase Portraits and Qualitative 390(3)
Assessment of Autonomous Systems of
First-Order Differential Equations
The Fish Pond 391(2)
13.3 Solving Homogeneous and Nonhomogeneous 393(10)
Systems of ODEs in Maple
Solving Homogeneous Systems 393(2)
Complex Eigenvalues (Eigenvalues of the 395(3)
Form A=aアbi)
Repeated Eigenvalues Solution 398(5)
13.4 Applied Systems of ODEs with Maple 403(6)
Diffusion Example 403(1)
Diffusion through a Double-Walled Membrane 404(2)
Electrical Circuits 406(3)
13.5 Numerical Solutions to Systems of ODE 409(9)
with Maple
Euler's Method 410(1)
Predator-Prey Model 411(7)
13.6 Predator-Prey, SIR, and Combat Models 418(12)
Predator-Prey Revisited 418(3)
Continuous SIR Models of Epidemics 421(2)
Hong Kong Flu 423(3)
Models of Combat: Iwo Jima 426(4)
Chapter 14 Classical Probability and Discrete 430(24)
Probability Modeling
Introduction 430(1)
14.1 Introduction to Classical Probability 431(8)
Fast-Food Selection 432(5)
Lightbulbs 437(1)
Flaws on a Glass Surface 437(1)
A Poisson Process 438(1)
14.2 Reliability Models in Engineering and 439(6)
Science
Systems in a Series Configuration 439(1)
Parallel Systems 440(1)
Series and Parallel Systems Combined 440(1)
Listening Devices for an Undercover 441(1)
Operation as an Active Redundant System
Playing Tetris on Game Boy as a Standby 442(3)
Redundant System
14.3 Overbooking Airlines Model 445(4)
Overbooking Airline Flights 446(3)
14.4 Markov Chains as a DDS 449(5)
Downtown and the Mall Revisited 449(2)
Fast-Food Tendencies 451(3)
Chapter 15 Continuous Probability Models 454(33)
Introduction 454(1)
15.1 Reliability Revisited 455(6)
Battery Reliability 456(1)
Reliability of New Rechargeable Batteries 456(2)
A System Network 458(1)
A Simplified Network 458(3)
15.2 Modeling Using the Normal Distribution 461(3)
15.3 Confidence Intervals and Hypothesis 464(5)
Testing
Hypothesis Testing for a Small Aviation 467(2)
Company's Crews
15.4 Regression: Linear, Transformed, and 469(18)
Nonlinear
Ponderosa Pines 471(2)
Telemetry Model 473(1)
Tire Tread Wear 474(2)
Fitting a Model Form: Z=a 476(3)
Tire Tread Wear Revisited 479(8)
Chapter 16 Simulation Modeling 487(25)
Introduction 487(1)
16.1 Monte Carlo Simulation 488(4)
16.2 Probability and Monte Carlo Simulation 492(4)
Using Deterministic Behavior
A Deterministic Example 492(2)
Area Under a Nonnegative Curve 494(1)
Finding the Volume in the First Octant 495(1)
16.3 Probability and Monte Carlo Simulation 496(7)
Using Probabilistic Behavior
Flip a Fair Coin 497(1)
Roll of a Fair Die 498(5)
16.4 Applied Simulation Models 503(9)
Missile Attack 503(1)
Gasoline-Inventory Simulation 504(8)
Chapter 17 Modeling with Game Theory 512(60)
Introduction 512(1)
Coin Matching 512(1)
17.1 Two-Person Zero-Sum Games 513(13)
Predator-Prey Game 514(3)
Baseball's Hitter-Pitcher Duel 517(2)
Dorfman's Original Example (1951) 519(1)
The 2x3 Games 520(1)
A 3x3 Game in Which Traditional Equalizing 521(2)
Strategies Do Not Work
A 3x3 Game with a Saddle-Point Solution 523(1)
Multiple Saddle Points 523(3)
17.2 The Non-Zero-Sum Game and Optimization 526(4)
Partial Conflict Mixed-Strategy Game 528(1)
Solution
Two-Player Games with More Than Two 529(1)
Strategies Each
17.3 Nash Arbitration and Nonlinear 530(6)
Programming Formulation
Nash Arbitration Example from a 532(2)
Non-Zero-Sum Game
Management-Labor Arbitration 534(2)
17.4 Illustrative Example: The 2007-2008 536(36)
Writers Guild Strike
Answers to Selected Problems 542(30)
Index 572