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Description: Mathematical modeling is the practice of applying mathematics to real-world problems and investigating important questions about their outcomes. Mathematical Modeling with Excel presents the 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 not traditionally covered. Each is presented 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. With a flexible design and student-friendly writing style, Mathematical Modeling with Excel is the clear choice for engaging readers in important modeling techniques, mathematical concepts and application types.
Key features include:
· A user-friendly writing style makes the text appropriate for a wide range of students.
· Topics are covered in a unique way by beginning each section with a theoretical derivation of a model scenario, then showing step-by-step instructions for implementing and dynamically analyzing the model in Excel.
· Includes an extensive section on simulation models.
· The analytical spreadsheets, built according to instruction, allow students to dynamically change the values of parameters and analyze changes in the behavior of the model.
· Solutions, worksheets and the author-created Excel worksheet “ Linear Programming” are available on the text’s website.
Contents: What is mathematical modeling? • Definitions • Purpose • The Process • Assumptions • For further reading • References • Proportionality and geometric similarity • Introduction • Using Data • Modeling with Proportionality • Fitting Straight Lines Analytically • Geometric Similarity • For further reading • References • Empirical modeling • Introduction • Linearizable models • Coefficient of determination • Polynomials • Multiple regression • Spline models • For further reading • References • Discrete Dynamical Systems • Introduction • Long term Behavior and equilibria • Growth of a bacteria population • A linear predator- Prey model • A non-linear Predator-Prey model • Differential equations • Introduction • Euler’s Method • Quadratic Population Model • Volterra’s Principle • Lancester Combat models • Eigenvalues • For Further reading • References • Simulation modeling • Introduction • Basic examples • The Birthday problem • Random Number Generators • Modeling Random Variables • Approximating Density Functions • A theoretical queuing model • A Coffee shop queuing model • A scheduling model • An inventory model • For further reading • References • Optimization • Introduction • Linear Programming • The transportation problem • The assignment problem and binary constraints • Solving linear programs • The simplex method • Sensitivity analysis • The gradient method • For Further reading • Reference • Spreadsheet basics • Basic terminology • Entering text, Data and Formulas • Creating charts and graphs • Array formulas.ISBN - 9789380108452
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Pages : 300
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