Applications of Calculus (Classroom Resource Materials)
By: Philip D. Straffin (editor)Paperback
1 - 2 weeks availability
Students see how calculus can explain the structure of a rainbow, guide a robot arm, or analyze the spread of AIDS. Each module starts with a concrete problem and moves on to provide a solution. The discussions are detailed, realistic, and pay careful attention to the process of mathematical modeling. Exercises, solutions, and references are provided.
Part I. Calculus: I: Derivatives: 1. Arbitrating disputes: maximizing quadratic polynomials finds a fair solution to a labor dispute; 2. Fitting lines to data: minimizing quadratic polynomials finds the regression line to a data set; 3. Somewhere within the rainbow: minimizing trigonometric functions explains properties of the rainbow; 4. Three optimization problems in computing: maximizing functions shows how to store and transmit data most efficiently; 5. Newton's method and fractal patterns: Newton's method generates fractal designs in the complex plane; Part II. Calculus I: Differential Equations and Integrals: 6. How old is the Earth? The exponential decay of rubidium is used to date very old rocks; 7. Falling raindrops: four differential equation models describe how a raindrop falls; 8. Measuring voting power: Integrals of polynomials give a measure of voting power; 9. How to tune a radio: trigonometric integrals explain tuning a radio; 10. Volumes and hypervolumes: integrals calculate the volumes of objects in three and higher dimensions; Part III. Calculus II: 11. Reliability and the cost of guarantees: probability integrals predict how long equipment will last; 12. Queueing systems: differential equations and limits analyze waiting lines; 13. Moving a planar robot arm: derivatives guide a robot arm along a curve; 14. Design curves: parametric curves are used in computer-aided design of automobiles; 15. Modeling the AIDS epidemic: differential equations model the spread of AIDS; 16. Speedy sorting: integrals, limits, and L'Hopital's rule compare the speed of sorting algorithms; Part IV. Calculus of Several Variables: 17. Hydro-turbine optimization: lagrange multipliers allocate water to hydroelectric turbines; 18. Portfolio theory: lagrange multipliers choose a best stock-market portfolio.
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