scholarly journals Multimedia Approach in Teaching Mathematics – Examples of Interactive Lessons from Mathematical Analysis and Geometry

10.5772/36989 ◽  
2012 ◽  
Author(s):  
Marina Milovanovi ◽  
urica Takai ◽  
Aleksandar Milaji
Keyword(s):  
Mathematical Analysis ◽  
Teaching Mathematics ◽  
Interactive Lessons

Didactic features of the organization of computer means of teaching students of mathematical specialties

2020 ◽  
Vol 1 (1) ◽  
pp. 34-41
Author(s):  
N. V. Brovka
Keyword(s):  
Uniform Convergence ◽  
Computer Science ◽  
Mathematical Analysis ◽  
Theory And Practice ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Visual Modeling ◽  
Mathematical Objects ◽  
Cognitive Visualization ◽  
Practice Of Teaching

The article is devoted to the description of didactic approaches that allow to integrate the theory and practice of teaching students of mathematical specialties by updating informative intra- and interdisciplinary connections of mathematical disciplines and informatics.Methods for implementing cognitive visualization taking into account the specifics of mathematics and computer science are given. The interpretation of interdisciplinary connections (as a category of teaching didactics) and visual modeling in relation to teaching mathematics are also clarified.The article describes a variant of the organization of content in the computer means of teaching (CMT) students of the classical university in mathematical analysis. The content of this course in one or another volume is a mandatory component of mathematical training in universities, it is consistently associated with the content of the course of school mathematics and is widely used in applied problems.On the basis of the analysis of semantics and logic of construction of formulations of those properties which are repeated in relation to various mathematical objects, the variant of content didactic clustering at which such concepts as “convergence”, “uniform convergence”, “differentiability”, etc., act as patterns in the organization of the maintenance of computer means of training is presented.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

Moving Forward Four Words at a Time: Effects of a Supplemental Preschool Vocabulary Intervention

2020 ◽  
Vol 51 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Lindsey A. Peters-Sanders ◽  
Elizabeth S. Kelley ◽  
Christa Haring Biel ◽  
Keri Madsen ◽  
Xigrid Soto ◽  
...  
Keyword(s):  
Group Intervention ◽  
Single Case ◽  
Single Case Design ◽  
Vocabulary Intervention ◽  
Iterative Development ◽  
At Risk Children ◽  
Before And After ◽  
Child Friendly ◽  
Interactive Lessons ◽  
Case Design

Purpose This study evaluated the effects of an automated, small-group intervention designed to teach preschoolers challenging vocabulary words. Previous studies have provided evidence of efficacy. In this study, we evaluated the effects of the program after doubling the number of words taught from 2 to 4 words per book. Method Seventeen preschool children listened to 1 prerecorded book per week for 9 weeks. Each storybook had embedded, interactive lessons for 4 target vocabulary words. Each lesson provided repeated exposures to words and their definitions, child-friendly contexts, and multiple opportunities for children to respond verbally to instructional prompts. Participants were asked to define the weekly targeted vocabulary before and after intervention. A repeated acquisition single-case design was used to examine the effects of the books and embedded lessons on learning of target vocabulary words. Results Treatment effects were observed for all children across many of the books. Learning of at least 2 points (i.e., 1 word) was replicated for 74.5% of 149 books tested across the 17 participants. On average, children learned to define 47% of the target vocabulary words (17 out of 36). Conclusions Results support including 4 challenging words per book, as children learned substantially more words when 4 words were taught, in comparison to previous studies. Within an iterative development process, results of the current study take us 1 step closer to creating an optimal vocabulary intervention that supports the language development of at-risk children.

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

A Simple Model for Cornering and Belt-edge Separation in Radial Tires

1986 ◽  
Vol 14 (1) ◽  
pp. 3-32 ◽  
Author(s):  
P. Popper ◽  
C. Miller ◽  
D. L. Filkin ◽  
W. J. Schaffers
Keyword(s):  
Simple Model ◽  
Transverse Shear ◽  
Mathematical Analysis ◽  
Pure Bending ◽  
Radial Tire ◽  
Optimum Angle ◽  
Shear Strains ◽  
Interlaminar Shear ◽  
Edge Separation ◽  
Shear Bending

Abstract A mathematical analysis of radial tire cornering was performed to predict tire deflections and belt-edge separation strains. The model includes the effects of pure bending, transverse shear bending, lateral restraint of the carcass on the belt, and shear displacements between belt and carcass. It also provides a description of the key mechanisms that act during cornering. The inputs include belt and carcass cord properties, cord angle, pressure, rubber properties, and cornering force. Outputs include cornering deflections and interlaminar shear strains. Key relations found between tire parameters and responses were the optimum angle for minimum cornering deflections and its dependence on cord modulus, and the effect of cord angle and modulus on interlaminar shear strains.

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