Mathematical Modeling With Excel

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Overview

Mathematical modeling is the use of applying mathematics to real-world problems and investigating important questions about their outcomes. Mathematical Modeling with Excel presents various methods used to build and analyze mathematical models in a format that students can quickly comprehend. Excel is used as a tool to accomplish this goal of building and analyzing the models. Ideal for math and secondary math education majors, this text presents a wide variety of common types of models, as well as some new types, and presents each in a unique, easy-to-understand format. End-of-chapter exercises ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.
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Product Details

  • ISBN-13: 9780763765668
  • Publisher: Jones & Bartlett Learning
  • Publication date: 7/31/2009
  • Edition description: 1E
  • Pages: 286
  • Product dimensions: 7.40 (w) x 9.20 (h) x 0.90 (d)

Table of Contents

Preface vii

1 What is Mathematical Modeling? 1

1.1 Definitions 2

1.2 Purpose 3

1.3 The Process 4

1.4 Assumptions 9

For Further Reading 11

References 11

2 Proportionality and Geometric Similarity 13

2.1 Introduction 14

2.2 Using Data 14

2.3 Modeling with Proportionality 22

2.4 Fitting Straight Lines Analytically 28

2.5 Geometric Similarity 35

For Further Reading 43

References 43

3 Empirical Modeling 45

3.1 Introduction 46

3.2 Linearizable Models 46

3.3 Coefficient of Determination 56

3.4 Polynomials 64

3.5 Multiple Regression 76

3.6 Spline Models 83

For Further Reading 91

References 91

4 Discrete Dynamical Systems 93

4.1 Introduction 94

4.2 Long-Term Behavior and Equilibria 95

4.3 Growth of a Bacteria Population 103

4.4 A Linear Predator--Prey Model 109

4.5 A Nonlinear Predator--Prey Model 113

4.6 Epidemics 118

For Further Reading 124

References 124

5 Differential Equations 125

5.1 Introduction 126

5.2 Euler's Method 127

5.3 Quadratic Population Model 134

5.4 Volterra's Principle 142

5.5 Lanchester Combat Models 148

5.6 Eigenvalues 155

For Further Reading 162

References 163

6 Simulation Modeling 165

6.1 Introduction 166

6.2 Basic Examples 167

6.3 The Birthday Problem 174

6.4 Random Number Generators 179

6.5 Modeling Random Variables 184

6.6 Approximating Density Functions 189

6.7 A Theoretical Queuing Model 195

6.8 A Coffee Shop Queuing Model 199

6.9 A Scheduling Model 206

6.10 An Inventory Model 210

For Further Reading 214

References 215

7 Optimization 217

7.1 Introduction 218

7.2 Linear Programming 219

7.3 The Transportation Problem 223

7.4 The Assignment Problem andBinary Constraints 231

7.5 Solving Linear Programs 238

7.6 The Simple Method 244

7.7 Sensitivity Analysis 249

7.8 The Gradient Method 256

For Further Reading 265

References 265

A Spreadsheet Basics 267

A.1 Basic Terminology 267

A.2 Entering Text, Data, and Formulas 269

A.3 Creating Charts and Graphs 272

A.4 Scroll Bars 276

A.5 Array Formulas 278

B Built-In Functions 279

Index 283

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