Applications of calculus

摘要

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.