摘要:

In education, representing three‐dimensional objects on a two‐dimensional display surface is a frequent requirement. SIGAD is an interactive system to help students to build drawings, which involve points, segments, vectors, lines and planes. The originality of the system lies in the fact that each figure can be defined by its geometric relations with other figures. The system was designed for the non‐specialist user and the student‐computer dialogue has been chosen to be friendly, efficient and natural.

ISSN:0020-739X    

DOI:10.1080/0020739830140201

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Using the concept of vector‐valued functions describing linear growth, a treatment of homogenous linear systems of difference and differential equations with constant coefficients is presented. This approach allows the derivation of the general solution for a system of differential equations as the continuous analogue of the ‘obvious’ solution of the discrete case. The standard fundamental solutions of pth‐order difference and differential equations are given as special cases of the general solutions.

ISSN:0020-739X    

DOI:10.1080/0020739830140202

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The familiar technique of solution in series converts a linear differential equation into a difference equation. In text‐book examples, the latter is usually a two‐term recurrence relation whose solution presents no difficulty. In general, the extraction of the appropriate solution of the difference equation is a substantial computational problem, and the difference equation is not necessarily simpler to solve than the differential equation. We give an example where the technique is used in reverse, to solve a difference equation by transforming it into a differential equation.

ISSN:0020-739X    

DOI:10.1080/0020739830140203

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The aim of this paper is to present analogous investigations of power functions with natural exponents with respect to convergence and differentiability using the ϵ‐δ‐definitions. These investigations were made possible through the application of various heuristic strategies established by Duncker and Pólya. I have used these strategies in order to point out some useful ideas and procedures and to facilitate the deductive proofs.

ISSN:0020-739X    

DOI:10.1080/0020739830140204

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Operations research (OR) has long suffered from an identity crisis. The problem is particularly acute for black students who are under‐represented in careers requiring a mathematics background. This paper presents a discussion of how simple games have been used to acquaint secondary students in the Atlanta area with operations research.

ISSN:0020-739X    

DOI:10.1080/0020739830140205

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

There is nothing wrong with the mathematical bases of calculus; the sole source of the difficulties encountered in its application to physics is the confusion between physical concepts like ‘variable’ (especially, gradient‐variable) and mathematical concepts like ‘function’ (especially, derivative‐function).

ISSN:0020-739X    

DOI:10.1080/0020739830140206

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

An eighteen‐lecture course on stochastic processes given to final year students of applied mathematics is outlined. The last six or seven lectures of this course are devoted to first‐order stochastic differential equations and a summary of the lecture notes for this part of the course is given including two examples. The difference between Ito and Stratonovich methods of integrating stochastic differential equations is explained in an intuitively appealing (though nonrigorous) way.

ISSN:0020-739X    

DOI:10.1080/0020739830140207

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

HHC (hand‐held calculators) and computers have spread more and more in schools generally, and in secondary schools especially. Their use can be seen as a new item in learning and teaching methods. As with any new item in learning and teaching methods, the use of HHC and computers influences both the way of solving problems and the kind of problems to solve. One of the new kinds of problems to solve is: how often has a given problem different kinds of solutions? Some of these problems and their emanations into mathematical education are dealt with in this paper, assuming the data (e.g., coefficients of an equation or lengths of segments) are chosen from a uniformly distributed continuous population. The main results are

ISSN:0020-739X    

DOI:10.1080/0020739830140208

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A Personalized System of Instruction (PSI), or Keller plan, has been used in teaching engineering mathematics to a group of about 200 third‐year students. The organization of the course is such that only the same number of teacher hours are used as when the course was run by conventional lecture methods.

ISSN:0020-739X    

DOI:10.1080/0020739830140209

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The distributions of the run‐lengths are readily available for independent variables but those of the run‐sums are not. It is therefore desirable to obtain their moments. In this paper the first four moments of the run‐sums are shown to be expressed in terms of the moments of the truncated variable and the probabilities corresponding to the truncation level for independent sequences of random variables. The explicit expressions for the moments of the truncated variable are given for the case of normal, lognormal and gamma distributions. It is shown that the expected values of the positive and negative run‐sums have the same magnitude when the sequence under consideration is truncated at the mean.

ISSN:0020-739X    

DOI:10.1080/0020739830140210

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor