Applications of Calculus

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... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0883850850
• ISBN13: 9780883850855
• Release Date: September 1996
• Publisher: Mathematical Association of America (MAA)
• Length: 273 Pages
• Weight: 1.50 lbs.

Customer Reviews

An excellent set of modeling problems using calculus

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.