Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

The author states that this book was written for anyone who wants to know what calculus is all about, and that those with knowledge of some algebra and geometry should be able to understand it. That calculus should be called "slope finding" is discussed, and this term is used extensively. The book is divided into three chapters: (1) the…

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

This module is part of a series designed to be used by life science students for instruction in the application of physical theory to ecosystem operation. Most modules contain computer programs which are built around a particular application of a physical process. This module is used to introduce the biology student to differential calculus, a…

These materials were designed to be used by life science students for instruction in the application of physical theory to ecosystem operation. Most modules contain computer programs which are built around a particular application of a physical process. The module is directed toward intermediate undergraduate students of the ecological sciences…

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

This textbook was designed for a first course in differential and integral calculus, and is directed toward students in engineering, the sciences, mathematics, and computer science. Its major goal is to bring students to a level of technical competence and intuitive understanding of calculus that is adequate for applying the subject to real world…

The first three units in this set of mathematical applications cover applications of calculus to economics. Under the title, The Distribution of Resources, are the following: 60-The Lorenz Curve; 61-The Equal Share Coefficient; and 62-The GINI Index. Each of these units contains a set of exercises, a model exam, and answers to both the exercises…

One module is presented in units 203, 204, and 205, as a guide for students, and presents a general strategy for solving integrals effectively. With this material is a solutions manual to exercises. This document set also includes a unit featuring applications of calculus to geography: 206-Mercator's World Map and the Calculus. Unit 207-Management…

Three of the modules deal with applications of calculus to other mathematics. These are: 240-Pi is Irrational; 241-The Wallis Approximation of Pi; and 242-Buffon's Needle Experiment. The first of these units focuses on a proof of the irrational nature of pi, and provides exercises and answers. The second module of this group reviews the history of…

Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…

The first four units cover aspects of medical applications of calculus: 71-Measuring Cardiac Output; 72-Prescribing Safe and Effective Dosage; 73-Epidemics; and 74-Tracer Methods in Permiability. All units include a set of exercises and answers to at least some of the problems. Unit 72 also contains a model exam and answers to this exam. The fifth…

Many of the suggestions that calculus instructors have published as articles from 1908 through 1973 are included in this book of readings. The main criterion for selecting an item was whether it would be helpful to teachers and students; therefore, those which dealt exclusively with curricular structure were not included. The selected articles are…

This document looks at specific applications of calculus to engineering. It is noted that for an automobile traveling at constant speed, the mathematical relationship between the directional heading and the angular deflection of the steering wheel can be calculated with respect to time. An analysis is presented which derives the relationship from…