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.
Author(s): Brian Albright; William P. Fox
Series: Textbooks in Mathematics
Publisher: CRC Press
Year: 2020
Language: English
Pages: x+360
Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
1. What is Mathematical Modeling?
1.1 Definitions
1.2 Purpose
1.3 The Process
1.4 Assumptions
2. Proportionality and Geometric Similarity
2.1 Introduction
2.2 Using Data
2.3 Modeling with Proportionality
2.4 Fitting Straight Lines Analytically
2.5 Geometric Similarity
2.6 Linearizable Models
2.7 Coefficient of Determination
3. Linear Algebra
3.1 Linear Algebra Basics
3.2 Modeling with Systems of Equations
3.3 Polynomials
3.4 Multiple Regression
3.5 Spline Models
4. Discrete Dynamical Systems
4.1 Introduction
4.2 Long–Term Behavior and Equilibria
4.3 Discrete Logistic Equation
4.4 A Linear Predator–Prey Model
4.5 A Nonlinear Predator–Prey Model
4.6 Epidemics
5. Differential Equations
5.1 Introduction
5.2 Euler’s Method
5.3 Mixing Problems
5.4 Systems of Differential Equations
5.5 Quadratic Population Model
5.6 Volterra’s Principle
5.7 Lanchester Combat Models
5.8 Runge-Kutta Methods
6. Simulations
6.1 Introduction
6.2 Basic Examples
6.3 Three Famous Problems
6.4 The Poker Problem
6.5 Random Number Generators
6.6 Modeling Random Variables
6.7 A Theoretical Queuing Model
6.8 A Scheduling Model
6.9 An Inventory Model
7. Linear Optimization
7.1 Introduction
7.2 Linear Programming
7.3 The Transportation Problem
7.4 The Assignment Problem and Binary Constraints
7.5 Solving Linear Programs
7.6 The Simplex Method
7.7 Sensitivity Analysis
8. Nonlinear Optimization
8.1 Introduction
8.2 Newton’s Method
8.3 The Golden Section Method
8.4 The One-Dimensional Gradient Method
8.5 Two-Dimensional Gradient Method
8.6 Lagrange Multipliers
8.7 Branch and Bound
8.8 The Traveling Salesman Problem
Appendix A: Spreadsheet Basics
A.1 Basic Terminology
A.2 Entering Text, Data, and Formulas
A.2.1 Understanding Cell References
A.2.2 Formatting Cells
A.3 Creating Charts and Graphs
A.3.1 Adding Data to a Chart
A.3.2 Graphing Functions
A.4 Scroll Bars
A.5 Array Formulas
Index
