This unit considers the application of calculus in determining price discrimination and consumer surplus in a competitive market. Producer surplus and two-tier price discrimination are also developed in problems. It is noted that calculus cannot usually provide numerical answers for practical economic problems. The importance of calculus…

This is the instructor's guide to a text designed for the contemporary business student who frequently questions the need for studying mathematics. The text material is presented in a "building-block" fashion, with skills learned in earlier chapters organized to provide a smooth transition into more difficult topics. This guide consists…

College teachers attending an NSF-sponsored summer workshop (1974) produced a series of films showing computer displays of mathematical problems and phenomena. These instructional materials are organized into four units: (1) functions and graphs; (2) analysis; (3) probability, statistics, and simulation; and (4) mathematical models. They are keyed…

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Sophomore and junior students in the College of Engineering at Cornell University have been taught engineering mathematics using new computer software that performs exact symbolic algebraic and calculus operations. Describes this software, the computer-based mathematics laboratory, changes in the teaching/learning environment, and short- and…

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…

Investigated students' (N=110) understanding of elementary calculus using clinical interview method. Analysis of responses to tasks concerning differentiation and rate of change led to detailed data concerning degree of understanding attained and common errors/misconceptions. Implications for mathematics instruction are discussed. (This is a…

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Presented is a Poisson derivation using explicitly stated assumptions and exact functional equations. The assumptions are homogeneity, independence, and negligibility. Included are the derivations and proofs using L'Hopital's rule for each assumption. (KR)

Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)

Illustrates three examples usually delayed until sufficient terminology, concepts, and methods have been developed unless using calculators or computers. The three examples are on exponential growth, triangle construction, and end behavior of certain function. Discusses the advantages of technology-enhanced mathematics teaching. (YP)

Describes how to develop students' communication skills, regular study habits, basic mathematics skills, and a talent for logical thinking in a calculus class. Eight references are listed. (YP)

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

With reference to a self-paced calculus course, the following aspects are reviewed: the structure and the mechanisms, the grading and credit arrangements, the essentials of proper record keeping, the restrictions and prerequisites for enrollment, the cost and the effectiveness, and the potential for application to other mathematics courses. (JJK)

The purpose of this paper is to show, by computer examples, that very different results can be obtained by rearranging selected conditionally convergent series. Computer programs allow the students to select the real number to which they wish the rearrangement to converge. Two computer programs are appended. (KR)