Enhanced descriptions from Syndetics:

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.

Table of contents provided by Syndetics

• 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'H(pital'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

Reviews provided by Syndetics

CHOICE Review

This five-volume set provides new materials with which instructors can refresh the teaching of college-level calculus. The independent volumes are composed of contributions from a wide assortment of college mathematics instructors. Volume 1 presents "labs" with which students learn about fundamental topics in calculus through experimentation and discovery. Students are expected to use calculators and computers, but the presentations are independent of specific software and hardware. Volume 2, more text-like, is a collection of problems that develop fundamental skills in calculus. However, in contrast with traditional calculus texts, effort has been taken to eliminate or rephrase problems whose solutions would be trivial using electronic tools. Commentaries and solutions are provided for each problem. Volumes 3-5 contain material that is more supplemental in nature: Volume 3 contains extended applications of calculus that would be useful for course enrichment; Volume 4 contains projects that depend on calculus for their investigation by students; and Volume 5 is a collection of essays on the history of calculus, the learning of calculus, the place of calculus in society, and the nature of mathematics generally. The set, produced through a National Science Foundation grant to the Associated Colleges of the Midwest and the Great Lakes Colleges Association, join in spirit other efforts to improve mathematics instruction, such as the UMAP Modules from the Consortium for Mathematics and Its Applications, Inc. All are most useful as curriculum resource materials in the hands of those teaching calculus. Undergraduate; faculty. W. R. Lee Iowa State University