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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, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling.
- A new chapter on Modeling with Decision Theory including Probability and Expected Value, Decision Trees, and Conditional Probabilities.
- A new chapter on Game Theory including sections on Illustrative Modeling Examples and Total Conflict as a Linear Program Model: Pure and Mixed Strategies.
- New and revised problems, examples, and projects.
- Chapters on Dimensional Analysis and Similitude and Graphs of Functions as Models have been removed from the text, and are available on the companion website for instructors who still want to include this material in their course.
- Tying in a variety of current tools, technology labs and technology worked examples are available on the web for many technologies, including Excel, Maple, and Mathematica.
- Offering new chapters on Modeling with Decision Theory and Game Theory.
- The fifth edition is packed with scenarios and illustrative examples, enabling students to see theories and models in action.
- Exercises and projects give students hands-on experience putting what they have learned into relevant practice.
- UMAP Models are included on the website for easy reference and review.
- Problems from the COMAP Mathematical Contest in Modeling also are included on the website, giving students experience clarifying, analyzing, and proposing solutions to the same open-ended problems on the rigorous MCM.
2. The Modeling Process, Proportionality, and Geometric Similarity.
3. Model Fitting.
4. Experimental Modeling.
5. Simulation Modeling.
6. Discrete Probabilistic Modeling.
7. Optimization of Discrete Models.
8. Modeling with Graph Theory.
9. Modeling with Decision Theory.
10. Game Theory.
11. Modeling with a Differential Equation.
12. Modeling with Systems of Differential Equations.
13. Optimization of Continuous Modeling.
14. Dimensional Analysis and Similitude.
15. Graphs of Functions as Models.
Appendix A: Problems from the Mathematics Contest in Modeling, 1985-2007.
Appendix B: An Elevator Simulation Model.
Appendix C: The Revised Simplex Method.
Appendix D. Brief Review of Integration Techniques.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Insturctor's Solutions Manual
This manual contains complete, worked solutions to all problems in the text.
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. www.cengage.com/solutionbuilder.