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Applications of Calculus (Classroom Resource Materials)

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While the teaching of calculus is largely composed of presenting and solving basic and illustrative problems, that approach can tend to leave the students with a limited impression of how valuable it is. At least once in the two course calculus series, the students should be given a more complex problem that is based on a scenario that appears in the world. This book is a collection of outstanding elements of that class of problem.
The problems are:

*) Arbitrating disputes - maximizing quadratic polynomials finds a fair solution to a labor dispute
*) Fitting lines to data - minimizing quadratic polynomials finds the regression line to a data set
*) Somewhere within the rainbow - minimizing trigonometric functions explains the properties of a rainbow
*) Three optimization problems in computing - maximizing functions shows how to store and transmit data most efficiently
*) Newton's method and fractal patterns - Newton's method generates fractal patterns in the complex plane
*) How old is the Earth? - the exponential decay of rubidium is used to date very old rocks
*) Falling raindrops - four differential equation models describe how a raindrop falls
*) Measuring voting power - integrals of polynomials give a measure of voting power
*) How to tune a radio - trigonometric integrals explain tuning a radio
*) Volumes and hypercubes - integrals calculate the volumes of objects in three and higher dimensions
*) Reliability and the cost of guarantees - probability integrals predict how long equipment will last
*) Queueing systems - differential equations and limits analyze waiting lines
*) Designer curves - parametric curves are used in computer aided design of automobiles
*) Modeling the AIDS epidemic - differential equations model the spread of AIDS
*) Speedy sorting - integrals, limits and L'Hopital's rule compare the speed of sorting algorithms
*) Hydro-turbine optimization - Lagrange multipliers allocate water to hydroelectric turbines
*) Portfolio theory - Lagrange multipliers choose a best stock-market portfolio

This set of modules would also be suitable for a special topics course in mathematical modeling using calculus. They are all well written, well explained and solutions to the exercises are included.