A Concrete Approach to Mathematical Modelling / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $76.70
Usually ships in 1-2 business days
(Save 48%)
Other sellers (Paperback)
  • All (7) from $76.70   
  • New (5) from $110.41   
  • Used (2) from $76.70   

Overview

WILEY-INTERSCIENCE PAPERBACK SERIES

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

" . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic."
London Times Higher Education Supplement

"The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking."
SIAM Review

"Each chapter discusses a wealth of examples ranging from old standards . . . to novelty . . . each model is developed critically, analyzed critically, and assessed critically."
Mathematical Reviews

A Concrete Approach to Mathematical Modelling provides in-depth and systematic coverage of the art and science of mathematical modelling. Dr. Mesterton-Gibbons shows how the modelling process works and includes fascinating examples from virtually every realm of human, machine, natural, and cosmic activity. Various models are found throughout the book, including how to determine how fast cars drive through a tunnel, how many workers industry should employ, the length of a supermarket checkout line, and more. With detailed explanations, exercises, and examples demonstrating real-life applications in diverse fields, this book is the ultimate guide for students and professionals in the social sciences, life sciences, engineering, statistics, economics, politics, business and management sciences, and every other discipline in which mathematical modelling plays a role.

Read More Show Less

Editorial Reviews

Booknews
A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Read More Show Less

Product Details

  • ISBN-13: 9780470171073
  • Publisher: Wiley
  • Publication date: 5/29/2007
  • Edition number: 1
  • Pages: 620
  • Product dimensions: 5.90 (w) x 9.10 (h) x 1.40 (d)

Meet the Author

Mike Mesterton-Gibbons, PhD, is Professor of Mathematics at Florida State University.

Read More Show Less

Table of Contents

An ABC of modelling xix

I The Deterministic View

1 Growth and decay. Dynamical systems 3

1.1 Decay of pollution. Lake purification 5

1.2 Radioactive decay 7

1.3 Plant growth 7

1.4 A simple ecosystem 8

1.5 A second simple ecosystem 11

1.6 Economic growth 13

1.7 Metered growth (or decay) models 21

1.8 Salmon dynamics 23

1.9 A model of U.S. population growth 26

1.10 Chemical dynamics 29

1.11 More chemical dynamics 30

1.12 Rowing dynamics 32

1.13 Traffic dynamics 34

1.14 Dimensionality, scaling, and units 35

Exercises 40

2 Equilibrium 46

2.1 The equilibrium concentration of contaminant in a lake 52

2.2 Rowing in equilibrium 53

2.3 How fast do cars drive through a tunnel? 57

2.4 Salmon equilibrium and limit cycles 58

2.5 How much heat loss can double-glazing prevent? 63

2.6 Why are pipes circular—66

2.7 Equilibrium shifts 71

2.8 How quickly must driver s react to preserve an equilibrium—76

Exercises 83

3 Optimal control and utility 91

3.1 How fast should a bird fly when migrating? 93

3.2 How big a pay increase should a professor receive? 95

3.3 How many worker s should industry employ? 103

3.4 When should a forest be cut? 104

3.5 How dense should traffic be in a tunnel? 109

3.6 How much pesticide should a crop grower use.an d when? 111

3.7 How many boats in a fishing fleet should be operational? 115

Exercises 119

II Validating a Model

4 Validation: accept, improve, or reject 127

4.1 A model of U.S. population growth 127

4.2 Cleaning Lake Ontario 128

4.3 Plant growth 129

4.4 The speed of a boat 130

4.5 The extent of bird migration 132

4.6 The speed of cars in a tunnel 136

4.7 The stability of cars in a tunnel 138

4.8 The forest rotation time 142

4.9 Crop spraying 146

4.10 How right was Poiseuille? 148

4.11 Competing species 151

4.12 Predator-prey oscillations 154

4.13 Sockeye swings, paradigms, and complexity 157

4.14 Optimal fleet size and higher paradigms 159

4.15 On the advantages of flexibility in prescriptive models 161

Exercises 163

III The Probabilistic View

5 Birth and death. Probabilistic dynamics 175

5.1 When will an old man die? The exponential distribution 180

5.2 When will Í men die? A pure death process 183

5.3 Forming a queue. A pure birth process 185

5.4 How busy must a road be to require a pedestrian crossing control? 187

5.5 The rise and fall of the company executive 189

5.6 Discrete models of a day in the life of an elevator 193

5.7 Birds in a cage. A birth and death chain 198

5.8 Trees in a forest. An absorbing birth and death chain 200

Exercises 202

6 Stationary distributions 208

6.1 The certainty of death 210

6.2 Elevator stationarity. The stationary birth and death process 213

6.3 How long is the queue at the checkout? A first look 215

6.4 How long is the queue at the checkout? A second look 217

6.5 How long must someone wait at the checkout? Another view 219

6.6 The structure of the work force 225

6.7 When does a T-junction require a left-turn lane? 227

Exercises 234

7 Optimal decision and reward 237

7.1 How much should a buyer buy? A first look 237

7.2 How many roses for Valentine’s Day? 243

7.3 How much should a buyer buy? A second look 245

7.4 How much should a retailer spend on advertising? 247

7.5 How much should a buyer buy? A third look 253

7.6 Why don’t fast-food restaurants guarantee service times anymore? 258

7.7 When should one barber employ another? Comparing alternatives 263

7.8 On the subjectiveness of decision making 267

Exercises 268

IV The Art of Application

8 Using a model: choice and estimation 275

8.1 Protecting the cargo boat. A message in a bottle 276

8.2 Oil extraction. Choosing an optimal harvesting model 279

8.3 Models within models. Choosing a behavioral response function 281

8.4 Estimating parameters for fitted curves: an error control problem 285

8.5 Assigning probabilities: a brief overview 291

8.6 Empirical probability assignment 293

8.7 Choosing theoretical distribution s and estimating their parameters 304

8.8 Choosing a utility function. Cautious attitudes to risk 316

Exercises 322

9 Building a model: adapting, extending, and combining 327

9.1 How many papers should a news vendor buy? An adaptation 328

9.2 Which trees in a forest should be felled? A combination 329

9.3 Cleaning Lake Ontario. An adaptation 334

9.4 Cleaning Lake Ontario. An extension 337

9.5 Pure diffusion of pollutants. A combination 345

9.6 Modelling a population’s age structure. A first attempt 350

9.7 Modelling a population’s age structure. A second attempt 360

Exercises 373

V Toward More Advance d Model s

10 Further dynamical systems 383

10.1 How does a fetus get glucose from its mother? 383

10.2 A limit-cycle ecosystem model 389

10.3 Does increasing the money supply raise or lower interest rates? 393

10.4 Linearizing time: The semi-Markov process. An extension 398

10.5 A more general semi-Markov process. A further extension 406

10.6 Who wil l govern Britain in the twenty-first century? A combination 409

Exercises 412

11 Further flow and diffusion 416

11.1 Unsteady heat conduction. An adaptation 417

11.2 How does traffic move after the train has gone by? A first look 421

11.3 How does traffic move after the train has gone by? A second look 423

11.4 Avoiding a crash at the other end. A combination 429

11.5 Spreading canal pollution. An adaptation 433

11.6 Flow and diffusion in a tube: a generic model 436

11.7 River cleaning. The Streeter-Phelps model 440

11.8 Why does a stopped organ pipe sound an octave lower than an open one? 446

Exercises 454

12 Further optimization 458

12.1 Finding an optimal policy by dynamic programming 458

12.2 The interviewer’s dilemma. An optimal stopping problem 465

12.3 A faculty hiring model 470

12.4 The motorist’s dilemma. Choosing the optimal parking space 475

12.5 How should a bird select worms? An adaptation 479

12.6 Where should an insect lay eggs? A combination 496

Exercises 507

Epilogue 514

Appendix 1: A review of probability and statistics 516

Appendix 2: Models, sources, and further reading arranged by discipline 531

Solutions to selected exercises 539

References 583

Index 591

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)