摘要:

Expanding a given number to a continued fraction may help in getting a better understanding of that number's meaning. Some examples, using a simple BASIC program, demonstrate this idea, as well as its limitations.

ISSN:0020-739X    

DOI:10.1080/0020739890200111

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A project, funded by the UGC as part of the programme for providing computing facilities for teaching in universities, is being conducted at the University of Kent at Canterbury [1]. This has led to the development of CAL material to supplement lecture courses on numerical analysis. The paper describes the details of four packages covering the topics of nonlinear equations, interpolation and nonlinear unconstrained optimization (single and multivari‐able functions) which have been developed for use in the teaching of the mathematics degree programmes.

ISSN:0020-739X    

DOI:10.1080/0020739890200112

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A unified derivation of the equations of Gauss, Weingarten, and of the affinity transformation is presented in non‐Riemannian geometry. These concepts from differential geometry are obtained here directly from the propagation derivative of the two‐point parallel propagator tensor. In order to measure the deviation of a surface from its tangent plane, the propagation derivative is written in terms of the projection, onto the surface, of the in‐space covariant derivative of the parallel propagator. Consequently, an expression is obtained which involves the unit vector normal to the surface rather than the unit vector tangent to a curve embedded in the surface. The desired concepts are, then, derived directly from this expression in a coherent manner.

ISSN:0020-739X    

DOI:10.1080/0020739890200113

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The objectives of this paper are two‐fold: (1) to show that a proper appreciation of the roles that syntax and semantics play in the solution of equations can not only simplify the solution but also lead to greater generality, and (2) to demonstrate the utility of recursion as a practical tool in analysis.

ISSN:0020-739X    

DOI:10.1080/0020739890200114

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Teaching is greatly about helping students to learn—by, for instance, sparking curiosity, fuelling imagination, and demonstrating relevance. We present material on number systems for catching and sustaining the attention of older pupils. This consists of a survey of the current legacies from various systems used historically, and some examples of how an understanding of number systems can aid in problem solving. The article offers a general appreciation of number‐systems, and concludes by introducing some basic results from number theory.

ISSN:0020-739X    

DOI:10.1080/0020739890200115

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

By suitably generalizing a lemma of R. K. Stump, the authors obtain discs in which convex linear combinations of n convex functions of order a are starlike and convex. This is a generalization of a result of H. Silverman and E. Silvia.

ISSN:0020-739X    

DOI:10.1080/0020739890200116

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A method of estimation of the coefficients of a linear regression model is described as invariant if the basic regression results obtained by the method are unaltered by a location/scale transformation of the data matrix. A necessary and sufficient condition for a method to be invariant is presented. Finally specific methods of estimation are examined for invariance.

ISSN:0020-739X    

DOI:10.1080/0020739890200117

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The objectives of this study were to identify exemplary school programmes with well‐developed independent study programmes in mathematics and to isolate the key ingredients of such programmes. The first objective involved analysing data from 509 schools. Four stringent criteria were applied to isolate the top 2% of the schools and these were labelled exemplary schools. Each of the exemplary schools had developed viable independent research programmes in mathematics. The key ingredients that were isolated included the following: dynamic research‐oriented mathematics teachers, establishing problem‐centred courses which used no text or tests, securing administrative support, active student recruiting, and making contact with nearby universities. None of the schools had above average facilities or extensive computer resources.

ISSN:0020-739X    

DOI:10.1080/0020739890200118

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A mathematically simple example of the partition coefficient computation from first (statistical mechanical) principles is given. The physical system represented approximates the partition of iodine between water and carbon tetrachloride phases. The example shows clearly how the chemical potential operates to determine concentrations in phase.

ISSN:0020-739X    

DOI:10.1080/0020739890200119

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor