Description
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.教学资源:教师手册、Online Chapters、Student Tools。
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Chapter
1.3 Solutions to Dynamical Systems
1.4 Systems of Difference Equations
2 The Modeling Process,Proportionality,and Geometric Similarity
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
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
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
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
6 Discrete Probabilistic Modeling
6.1 Probabilistic Modeling with Discrete Systems
6.2 Modeling Component and System Reliability
7 Optimization of Discrete Models
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
8 Modeling Using Graph Theory
8.4 Using Graph Models to Solve Problems
8.5 Connections to Mathematical Programming
9 Modeling with Decision Theory
9.1 Probability and Expected Value
9.3 Sequential Decisions and Conditional Probabilities
9.4 Decisions Using Alternative Criteria
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 2×2 Total Conflict Game
10.6 Partial Conflict Games:The Classical Two-Person Game
10.7 Illustrative Modeling Examples
11 Modeling with a Differential Equation
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
12 Modeling with Systems of Differential Equations
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
13 Optimization of Continuous Models
13.1 An Inventory Problem:Minimizing the Cost of Delivery and Storage
13.2 Methods to Optimize Function of Several Variables
13.3 Constrained Continuous Optimization
13.4 Managing Renewable Resources:The Fishing Industry
APPENDIX Problems from the Mathematics Contest in Modeling,1985-2012
Answers to Selected Problems