A First Course in Mathematical Modeling 5th Edition by Frank Giordano, William Fox, Steven Horton ISBN 1285531760 9781285531762

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Product details:

ISBN 10: 1285531760

ISBN 13: 9781285531762

Author:  Frank Giordano, William P. Fox, Steven Horton 

A First Course in Mathematical Modeling 5th Edition: Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities — whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible — beginning with short projects — this text facilitates your progressive development and confidence in mathematics and modeling.

 

A First Course in Mathematical Modeling 5th Edition Table of contents:

Ch 1: Modeling Change

• Introduction
• 1.1: Modeling Change with Difference Equations
• 1.2: Approximating Change with Difference Equations
• 1.3: Solutions to Dynamical Systems
• 1.4: Systems of Difference Equations

Ch 2: The Modeling Process, Proportionality, and Geometric Similarity

• Introduction
• 2.1: Mathematical Models
• 2.2: Modeling Using Proportionality
• 2.3: Modeling Using Geometric Similarity
• 2.4: Automobile Gasoline Mileage
• 2.5: Body Weight and Height, Strength and Agility

Ch 3: Model Fitting

• Introduction
• 3.1: Fitting Models to Data Graphically
• 3.2: Analytic Methods of Model Fitting
• 3.3: Applying the Least-Squares Criterion
• 3.4: Choosing a Best Model

Ch 4: Experimental Modeling

• Introduction
• 4.1: Harvesting in the Chesapeake Bay and Other One-Term Models
• 4.2: High-Order Polynomial Models
• 4.3: Smoothing: Low-Order Polynomial Models
• 4.4: Cubic Spline Models

Ch 5: Simulation Modeling

• Introduction
• 5.1: Simulating Deterministic Behavior: Area under a Curve
• 5.2: Generating Random Numbers
• 5.3: Simulating Probabilistic Behavior
• 5.4: Inventory Model: Gasoline and Consumer Demand
• 5.5: Queuing Models

Ch 6: Discrete Probabilistic Modeling

• Introduction
• 6.1: Probabilistic Modeling with Discrete Systems
• 6.2: Modeling Component and System Reliability
• 6.3: Linear Regression

Ch 7: Optimization of Discrete Models

• Introduction
• 7.1: An Overview of Optimization Modeling
• 7.2: Linear Programming I: Geometric Solutions
• 7.3: Linear Programming II: Algebraic Solutions
• 7.4: Linear Programming III: The Simplex Method
• 7.5: Linear Programming IV: Sensitivity Analysis
• 7.6: Numerical Search Methods

Ch 8: Modeling Using Graph Theory

• Introduction
• 8.1: Graphs as Models
• 8.2: Describing Graphs
• 8.3: Graph Models
• 8.4: Using Graph Models to Solve Problems
• 8.5: Connections to Mathematical Programming

Ch 9: Modeling with Decision Theory

• Introduction
• 9.1: Probability and Expected Value
• 9.2: Decision Trees
• 9.3: Sequential Decisions and Conditional Probabilities
• 9.4: Decisions Using Alternative Criteria

Ch 10: Game Theory

• Introduction
• 10.1: Game Theory: Total Conflict
• 10.2: Total Conflict as a Linear Program Model: Pure and Mixed Strategies
• 10.3: Decision Theory Revisited: Games against Nature
• 10.4: Alternative Methods for Determining Pure Strategy Solutions
• 10.5: Alternative Shortcut Solution Methods for the 2 x 2 Total Conflict Game
• 10.6: Partial Conflict Games: The Classical Two-Player Games
• 10.7: Illustrative Modeling Examples

Ch 11: Modeling with a Differential Equation

• Introduction
• 11.1: Population Growth
• 11.2: Prescribing Drug Dosage
• 11.3: Braking Distance Revisited
• 11.4: Graphical Solutions of Autonomous Differential Equations
• 11.5: Numerical Approximation Methods
• 11.6: Separation of Variables
• 11.7: Linear Equations

Ch 12: Modeling with Systems of Differential Equations

• Introduction
• 12.1: Graphical Solutions of Autonomous Systems of First-Order Differential Equations
• 12.2: A Competitive Hunter Model
• 12.3: A Predator-Prey Model
• 12.4: Two Military Examples
• 12.5: Euler’s Method for Systems of Differential Equations

Ch 13: Optimization of Continuous Models

• Introduction
• 13.1: An Inventory Problem: Minimizing the Cost of Delivery and Storage
• 13.2: Methods to Optimize Functions of Several Variables
• 13.3: Constrained Continuous Optimization
• 13.4: Managing Renewable Resources: The Fishing Industry

Ch 14: Dimensional Analysis and Similitude

• Introduction
• 14.1: Dimensions as Products
• 14.2: The Process of Dimensional Analysis
• 14.3: A Damped Pendulum
• 14.4: Examples Illustrating Dimensional Analysis
• 14.5: Similitude

Ch 15: Graphs of Functions as Models

• 15.1: An Arms Race
• 15.2: Modeling an Arms Race in Stages
• 15.3: Managing Nonrenewable Resources: The Energy Crisis
• 15.4: Effects of Taxation on the Energy Crisis
• 15.5: A Gasoline Shortage and Taxation

 

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