摘要:

By means of a number of examples relating to solid state and optoelectronic devices, we investigate the sorts of mathematical problems which arise in the new ‘microphysical technologies’.

ISSN:0020-739X    

DOI:10.1080/0020739860170101

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739860170102

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Linear systems of ordinary differential equations are a basic topic in the mathematical background of an engineer. In this paper we present an interactive program about planar linear systems, which runs on a personal computer. In particular, the concepts of phase space and stability of equilibrium are emphasized.

ISSN:0020-739X    

DOI:10.1080/0020739860170103

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739860170104

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Differential notation is shown to be interpretable in several ways as notation for derivatives of outputs. Customary operations with differentials in scientific applications are mathematically justified.

ISSN:0020-739X    

DOI:10.1080/0020739860170105

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Practical mathematical modelling can lead to mathematical problems of intrinsic interest. In this paper, earlier results of K. A. and C. J. Jukes, arising from a study of practical rules of thumb for generating recipe quantities for various shaped cake tins, are extended to regular n‐gons.

ISSN:0020-739X    

DOI:10.1080/0020739860170106

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The Heaviside expansion theorem is widely known and used in circuit theory. It is, in fact, a mathematical result with a long history. Its discovery forms a chapter in the history of differential equations and it was arrived at independently at least three times before Heaviside first announced it. It may be regarded as being implicit in the work of Euler, Lagrange and Cauchy, but it is also given almost directly by Cauchy, Lobatto and Boole, although Heaviside's later discovery was most probably independent.

ISSN:0020-739X    

DOI:10.1080/0020739860170107

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In the classical literature, various delicate conditions are imposed on a set so that it is qualified to be calledmeasurableand on a function, so that it is qualified to be calledintegrable.However, very often the essential ideas involved in measure and integration are hidden by the complexities of these conditions. In this article an effort is made to stress the basic notions involved in measure and integration while keeping the necessary definitions as simple as possible.

ISSN:0020-739X    

DOI:10.1080/0020739860170108

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This article suggests ways in which commercial and statistical packages may be used to illustrate simple ideas in economics and statistics and provide both an introduction to micro‐computing and an aid to tedious calculation in standard statistical techniques.

ISSN:0020-739X    

DOI:10.1080/0020739860170109

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Teaching the rate of change over an interval as a property of various functions separates it from the study of the limit. It is suggested that the rate of change be taught in high school as part of the study of functions during pre‐calculus studies. Whenever a new function is introduced, its rate of change over a given interval will be computed and interpreted. Introduction of the rate of change into the pre‐calculus curriculum paves the way for proving theorems about the derivatives of the sum and product of two functions. An algebraic and a numerical approach to the computation of the rate of change are presented. The numerical approach is simple and easy to implement on a microcomputer. A computer program in BASIC which plots any given function, its rate of change function over an interval, and the rate of change at any given point, is provided.

ISSN:0020-739X    

DOI:10.1080/0020739860170110

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor