摘要:

Several classes of ordinary differential equations which have polynomial solutions are studied. In particular, generalizations of the Hermite, Laguerre, Legendre, and Chebyshev equations are given for which such solutions exist. These solutions turn out to be generalizations of well‐known polynomials and enjoy similar properties.

ISSN:0020-739X    

DOI:10.1080/0020739890200101

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The paper deals with the findings of a comprehensive questionnaire designed to diagnose study problems confronting students at the Alvan Ikoku College of Education, Owerri. Factors affecting students in their study are found to be poor study habits, lack of organized tutorials, absence of academic advice, insufficient handouts and non‐availability of prescribed textbooks. Recommendations are made on ways to minimize students' study problems.

ISSN:0020-739X    

DOI:10.1080/0020739890200102

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A wonderful problem in chemical kinetics is routinely ignored in physical chemistry courses because it deals with population and ecology rather than chemistry. In this paper, this Volterra‐Lotke problem is discussed in detail, with enough mathematical details filled in to provide a reasonable basis for including this marvellous example in standard courses.

ISSN:0020-739X    

DOI:10.1080/0020739890200103

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

As the impact of computers and computational mathematics on school syllabuses grows it becomes increasingly desirable to say something about the errors which arise in the process of a piece of mathematical computing. Within this note some of the familiar ideas of rounding and truncation error are discussed as well as some of the less‐frequently mentioned aspects related directly to the floating point arithmetic used within a computer.

ISSN:0020-739X    

DOI:10.1080/0020739890200104

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The Discrete Maximum Principle of Control Theory is applied to five problems in Ballistic Missile Defense (BMD). Four of the problems deal with optimal interceptor allocations to attacking missiles, and one deals with optimal budget allocations to a layered defence system. It is shown that modelling of discrete processes of a sequential nature can be conveniently executed using Control Theory methods, resulting in computer‐adaptable algorithms or closed form solutions. It is apparent from these illustrations that it is relatively easy to amend the resulting models to incorporate additional features.

ISSN:0020-739X    

DOI:10.1080/0020739890200105

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This example attempts to show to both teachers and users of mathematics how, as a result of studying a practical problem, two areas of applied mathematics which are usually unrelated are nicely combined to produce a solution of the problem. Further, it is suggested that the derived solution is probably easier to handle than one obtained by other more conventional methods. The two areas which are related are differential equations and recurrence relations. Even so, it is interesting and useful from the teaching point of view to compare and contrast the three methods outlined in the paper.

ISSN:0020-739X    

DOI:10.1080/0020739890200106

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The virial method is utilized to derive an energy principle appropriate to the irrotational motion of a gas bubble in an inviscid incompressible fluid of infinite extent under the action of surface tension forces.

ISSN:0020-739X    

DOI:10.1080/0020739890200107

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper studies the relationship between selected teaching practices and student achievement in mathematics of form III students in Nigeria. Twenty‐three classes were observed, at least once. An achievement test in mathematics was used to gather data on student learning. The process variables question and probe were positively related to achievement while lecture was negatively related to achievement.

ISSN:0020-739X    

DOI:10.1080/0020739890200108

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The classic inequalities are brought together and presented in comprehensive fashion. This is followed by a harangue on pedagogic matters.

ISSN:0020-739X    

DOI:10.1080/0020739890200109

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper indicates some of the difficulties involved in devising ‘assignments' or ‘extended pieces of work’ in readiness for use in the new GCSE mathematics syllabuses. A number of teacher‐produced assignments were subjected to an evaluation using teacher‐perceptions of their intended curriculum focus. The results indicate that group‐produced assignments are to be preferred over individually produced assignments when curriculum focus is an important criterion of acceptability.

ISSN:0020-739X    

DOI:10.1080/0020739890200110

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor