Applications of Calculus (MAA Notes Series #29: Resources for Calculus), Vol. 3 Book

Introduction: Resources for Calculus
Preface: Using these Modules

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

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 columns of objects in three and higher dimensions.

Calculus II
11. Reliability and the Cost of Guarantees: Probability integrals predict how long equipment will last
12. Queuing Systems: Differential equations and limits analyze waiting lines
13. Moving a Planar Robot Arm: Derivatives guide a robot arm along a curve
14. Designer 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 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