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Suggests that the cross product of two vectors can be more easily and accurately explained by starting from the perspective of dyadics because then the concept of vector multiplication has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. (AIM)

Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (MDH)

Several examples of solid figures that calculus students can use to exercise their skills at estimating volume are presented. Although these figures are bounded by surfaces that are portions of regular cylinders, it is interesting to note that their volumes can be expressed as rational numbers. (JJK)

Presented are student activities that involve two standard problems from geometry and calculus--the volume of a box and the bank shot on a pool table. Problem solving is emphasized as a method of inquiry and application with descriptions of the results using graphical, numerical, and physical models. (JJK)

Describes an Apple computer program (listing available from author) which simulates Fraunhofer and Fresnel diffraction using vector addition techniques (vector chaining) and allows user to experiment with different shaped multiple apertures. Graphics output include vector resultants, phase difference, diffraction patterns, and the Cornu spiral (geometric representation of Fresnel integral). (JM)

A handbook for teachers of calculus and analytic geometry is described. Five categories of materials are included, with illustrative examples and a lesson plan. (MNS)

Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

Graphing techniques are used to demonstrate the inverse function theorem and that the graph of the inverse function can be obtained by flipping the graph about the line y=x. (MP)

The lesson described combines mathematics, science, and literature, and is easily adaptable for use with classes in basic mathematics, geometry, analytic geometry, or calculus. (MP)

In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplication operations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally, the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonian conics are given. Additionally, examples were given and drawings were made to make the resulting characterizations and theorems more memorable. [ABSTRACT FROM AUTHOR]

In this paper, we aim to contribute to the planning and implementation of education in higher mathematics education for students from non-mathematics study programs, specifically focusing on multivariable calculus, i.e., multiple integrals. Indeed, the outcomes of various empirical studies indicate that students from non-mathematical faculties struggle to grasp and comprehend multiple integrals and multivariable functions in general. The research presented in this paper aims to ascertain whether there is a significant correlation between students' achievements in multiple integrals and their achievements in applying knowledge and skills from analytical geometry (to define sets of points in the plane and space, determined by lines, curves, planes and surfaces). Additionally, the study investigates whether this correlation potentially varies based on the various instructional teaching approaches. The presented empirical research was conducted at the Faculty of Engineering, University of Kragujevac, with 72 second-year students, divided into two groups. The results indicate that the given linear correlation is statistically significant and positive. Moreover, the differences in correlation coefficients calculated for two groups of students who acquired knowledge in multiple integrals through different instructional approaches are not statistically significant. These findings underscore the need to devote substantial attention to the teaching of multiple integrals, especially in devising methods that enable students to visualize specific mathematical concepts in both plane and space. Additionally, a precise definition of integration domains, and an accurate specification of variable bounds, should be emphasized in the multiple integrals teaching and learning process. [ABSTRACT FROM AUTHOR]

We calculate accurate potential energy curves for HeO-, NeO-, and ArO-, including the full counterpoise correction and allowing for spin–orbit effects. Comparison with previous curves is presented, where these are available. The three curves, 2Σ1/2+, 2Π1/2, and 2Π3/2, are used to derive spectroscopic constants and to calculate the transport coefficients for O- moving in a bath of the respective rare gas. Conclusions are made based on a comparison with the available data. [ABSTRACT FROM AUTHOR]

Highlights • The effect of surface radiations on Casson-dusty particulate suspension past a vertical wavy cone is presented. • Stefan-Boltzmann law is employed in the boundary conditions to express the contribution of surface radiative heat flux. • The transformed system is integrated numerically by means of an implicit finite difference scheme. • It is found that the dominant impact of wavy cone geometry configurations in terms of amplitude parameter, a , and cone half-angle, ϕ , is to increase the rate of heat transfer. • Large values of Casson rheological parameter β results in strong acceleration, whereas increment in β on temperature profiles. Abstract A boundary layer analysis is presented to analyze the effect of non-linear surface radiation on Casson-dusty particulate suspension flow past a vertical wavy cone. Stefan-Boltzmann law is employed in the boundary conditions to express the contribution of surface radiative heat flux. Appropriate sets of transformations are used to convert the governing equations into non-dimensional, non-conserved form and then numerical scheme is applied to obtain the solutions. Our numerical results are shown graphically under the variation of important non-dimensional parameters. Comparison is also established with the available literature and it is observed that our results are in good agreement. From this study it is noticed that amplitude of the wavy cone, a , and half-angle of the cone, ϕ , increase the rate of heat transfer. Furthermore, large values of Casson rheological parameter β results in considerable enchantment in fluid velocity but an opposite behavior is noticed on temperature profiles. [ABSTRACT FROM AUTHOR]

The related rates falling ladder problem is well-known calculus exercise with a paradoxical twist. We revisit the problem and derive a closed-form solution. We also describe experimental support for the solution and discuss some related paradoxes that may tempt future experimenters. [ABSTRACT FROM AUTHOR]

Robustness with respect to delays is discussed for homogeneous systems with negative degree. It is shown that if homogeneous system with negative degree is globally asymptotically stable at the origin in the delay-free case then the system is globally asymptotically stable with respect to a compact set containing the origin independently of delay. The possibility of applying the result for local analysis of stability for not necessary homogeneous systems is analyzed. The theoretical results are supported by numerical examples. [ABSTRACT FROM AUTHOR]

We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines. [ABSTRACT FROM AUTHOR]

This paper presents the authors' reflections on using integral calculus when preparing the process of locating single ground-based chains of positioning systems in marine navigation. These reflections are purely theoretical and presented research results apply to a hypothetical navigation system that operates based on the ratio of distances, which is regarded as a navigation parameter. [ABSTRACT FROM AUTHOR]

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages and challenges of a pedagogy based on teaching with primary sources. We then present three lower-division case studies based on our classroom experience of teaching discrete mathematics courses with student projects based on primary sources, and comment on how these could be adapted for use with other lower-division audiences. [ABSTRACT FROM AUTHOR]

For students with little experience in mathematical thinking and conceptualization, writing-to-learn activities (WTL) can be particularly effective in promoting discovery and understanding. For community college students embarking on a first calculus course in particular, writing activities can help facilitate the transition from an “apply the formula” approach to problem-solving, to a “conceptual understanding of the formula” to initiate mathematical knowledge-building. Community college students face several common challenges in a beginning calculus course, including difficulties using mathematical notation, applying theorems, and understanding the language of proof. Several WTL assignments are discussed, ranging from low-stakes assignments to more formal assignments with a chance for revision, which effectively addressed these difficulties. Samples of students’ work are presented to highlight the learning objectives different writing tasks help attain, student’s understanding of concepts, and the benefits of frequent, low-stakes writing assignments. An analysis of individual students’ work shows that WTL activities not only help students cement mathematical knowledge, deepen understanding, and develop appreciation for the rigor and concision of mathematical language, but also enable them to develop learning habits essential to their success in any field. [ABSTRACT FROM AUTHOR]