Even the best and most applications-oriented calculus textbooks, e.g. [I], do not provide any real world applications of L'Hopita11s Rule. In our view, the reason for this state of affairs is that most of the rule's applications occur later in the...
The study of combinations and permutations has fascinated scholars of all disciplines since ancient times. Within the seventeenth and eighteenth centuries, many music theorists used combinational and permutational techniques to arrange notes in to...
This presentation, centered on Fibonacci number theory and its applications. aims at instilling in beginners' minds the best and perhaps the only enduring motive to read mathematics, which is the aesthetic motive, by showing to them an anthology of...
An industry involved in defense systems can produce a detector that behaves as if it were a circle and knows when an object passes through that circle. The engineer who related this development to us indicated that the cost of production for such a...
The Office of Publications of Local College makes the following statement: Although our College is large, its individual departments are small enough to promote close working relationships among the academic staff. Our average department size is only...
In this paper we develop a model for the response of a diabetic patient to medical therapy. The main tools for the model development come from elementary concepts of statistical theory. calculus. and differential equations. Using a simple step function...
From early experiences of dropping sticks into a river and watching their passage downstream, or later it becomes evident that the speed at which the water flows may vary considerably across its width. For a straight stretch of river the flow will...
Following corneal transplants and cataract surgery patients are often left with considerable astigmatism. There are a variety of surgical techniques for correcting this problem. but only recently have mathematical models been dweloped to predict how...
Each year, North Lake College (Irving, Texas) offers a Mini-College at which time seniors from nearby high schools visit the college for part of a day. During their visit, the students select and attend two half-hour Mini- College courses and...
The manner in which Pythagoras calculated the height of Hercules is indeed naive by today's standards, but the model he used was straight-forward. After the model is presented, it may be criticized and revised in accordance with contemporary knowledge....
In recent years there has been renewed interest in finding alternative sources of energy to those provided by fossil fuels and nuclear power. To anyone living near the sea, the interest has centered on the energy in the waves and the tides, but to...
It is a well-known fact that mathematics, particularly in the last century, has shown a definite tendency to separate from the physical world and to create its own subjects of study. This tendency has been reflected intensively in the field of...
In 1968-72 all books published throughout the world began to receive coded ten-digit numerical labels called International Standard Book Numbers (ISBN's). For example, the ISBN of the text Multivariable Mathematics by Williamson and Trotter is...
The moon, viewed from the earth, always presents the same face; but this face is perceived as tilted at different angles to different observers at different times. Given a few (oversimplified) astronomical facts, it becomes a purely mathematical...
Until relatively recently, the development of mathematics was inextricably intertwined with the development of physics, and many fundamental developments in mathematics can be seen as answers to questions arising in physics. This unreasonable...
There is a great deal of excitement in the mathematical air concerning a new algorithm for linear programming. Big city newspapers and national glossy magazines have announced the development by N. Karmarkar of Bell Labs of an algorithm much faster...
The purpose of this paper is to present an application that I have used many times while teaching an introductory course in linear algebra. This application deals with an occupancydistribution problem which is simple to state and easy to understand. I...
This article describes the analytic hierarchy method for personal decision making and discusses the values and pitfalls of using formal methods for personal decisions. The author advocates that formal methods be used as tools for examining and...
When a projectile is shot or a ball is thrown, the simplest mathematical model ignores air resistance and obtains the familiar parabolic path of motion (see [2] for example). When air resistance is taken into account, the motion is more complicated,...
A chord is a straight line whose endpoints are any two points on a circle. What is the probability that a chord of a circle with radius 1 will have a length greater than SQ3? This simple problem can be quite mystifying, not because one cannot find a...