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Math 1304 Calculus I

Math 1304 Calculus I. 1.2 Mathematical Models. Mathematical Models. What is modeling? Why model? How are models made? Risks of Modeling Single vs. multiple parameters. What is a Mathematical Model?.

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Math 1304 Calculus I

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  1. Math 1304 Calculus I 1.2 Mathematical Models

  2. Mathematical Models • What is modeling? • Why model? • How are models made? • Risks of Modeling • Single vs. multiple parameters

  3. What is a Mathematical Model? • Definition: A mathematical model is a mathematical description, often by means of a function or equation, of a real-world phenomenon. • Goal: To understand and predict behavior of real-world systems.

  4. Why Model? • Determine feasibility of building real-world systems • Determine how to build real-world systems • Reduce cost of building and operating real-world systems • Improve performance of real-world systems

  5. How to Model? • Given a real-world situation • Identify and name independent and dependent variables • Make assumptions about how variables are related • Collect data • Use physical laws or best practice rules • Draw mathematical conclusions • Interpret as real-world predictions • Test against real-world • Revise mathematical model as needed

  6. Modeling Process Real-world situation Mathematical Model Real-world prediction Mathematical Conclusions

  7. Types functions used in models • Linear • Polynomial • Power • Rational • Algebraic • Trigonometric • Exponential • Logarithmic • Special functions - beyond scope of this course

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