ISSN:0020-739X    

DOI:10.1080/0020739980290401

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The problem of polynomial least squares fitting to a set of data leads to a system of linear equations. The solution of such a system is usually considered as something purely technical which lacks interest and is left for students to solve. We consider that the use of orthogonal polynomials here is numerically necessary and provides interesting didactic contributions.

ISSN:0020-739X    

DOI:10.1080/0020739980290402

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The Chebysev‐Matrix method presented by Sezer and Kaynak, and by Sezer and Dogan for the approximate solutions of second‐order differential equations and Fredholm integral equations, respectively, is applied to Fredholm integrodifferential equations of the higher order. Examples are given which illustrate the pertinent features of the method.

ISSN:0020-739X    

DOI:10.1080/0020739980290403

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper describes a visual method for checking homogeneous polynomial inequalities of the typef(a,b, c) >0 whena, b, care the side lengths of a triangleABC.The similarity class ofABCcan be represented by a unique point in a planePof trilinear coordinates and such points fill out a certain triangular diskDinP.Then the functionfdetermines a curve in P. To decide whether the required inequality holds it suffices to check that does not enter the interior ofD.

ISSN:0020-739X    

DOI:10.1080/0020739980290404

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Student intuitive ideas in mechanics, especially concerning the relationship between force and motion, have been the subject of much research. Many students find aspects of the topic of moments of forces to be stumbling blocks, yet there has been little or no research in this area. This paper reports on a small‐scale investigation of student understanding of moments of forces to provide some indication as to the nature of intuitive ideas in this area, and to provide some suggestions as to the appropriate teaching strategy. The results of the investigation suggests three stumbling blocks in the conceptual understanding of moments of forces. The first stumbling block seems to contain problems where the forces applied are still acting vertically, but the points of application of the forces are not at the same horizontal level. The second stumbling block seems to either contain problems where the forces applied are vertical but there is no obvious sense of symmetry, or problems that represent a conceptual link between moments and rotation. The third stumbling block contains questions whereby the student has to recognize the line of action of the appropriate force and take note of the point of application of the force.

ISSN:0020-739X    

DOI:10.1080/0020739980290405

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In the development of innovative programmes to enhance the application skills of students a neglected population tends to be those students who have difficulty in addressing quite basic problems, but whose educational setting is prescribed by school policies such that more innovative teaching and learning environments are not available to them. This research sets out to develop a diagnostic framework that supports teaching and learning in such situations. Based on empirical research studies and on theoretical constructs of human learning a script analysis framework was developed encompassing criteria across categories of planning, monitoring, heuristic strategies, verification, knowledge resources, and beliefs. The framework represents a synthesis and extension of previous work. Two teachers worked with 47 students throughout a year in a senior secondary mathematics course geared to students intending to study mathematics at tertiary level. Data collection was limited to the type of information available to teachers working under restrictive policies—written protocols of student problems solving together with student comments on their own problem solving processes. Characteristic patterns were identified, confirmed, and used to generate a response quality hierachy within the framework. The resulting structure contained 23 cells and fulfils three purposes:

ISSN:0020-739X    

DOI:10.1080/0020739980290406

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A Parseval‐Goldstein‐type theorem involving the ?2‐transform, the error function and the complementary error function is given. Using the theorem, an integral representation for the incomplete gamma function is introduced, and a number of interesting infinite integrals of elementary and special functions are presented. Some illustrative examples are also g ven.

ISSN:0020-739X    

DOI:10.1080/0020739980290407

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A four‐point quadrature rule with degree of p recision five for the numerical approximation of integrals of analytic functions of a complex variable has been constructed. An asymptotic error estimate and an error bound of the rule constructed have been derived.

ISSN:0020-739X    

DOI:10.1080/0020739980290408

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The issue of relevance is always raised when mathematics modules taken within engineering degrees are discussed. This paper considers one of the ways a good level of industrial relevance is attained for a final year mathematics module for electrical engineers. This involves a course work element where a realistic design exercise is undertaken using finite element analysis.

ISSN:0020-739X    

DOI:10.1080/0020739980290409

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In this paper we suggest that those who teach probability calculus and the foundations of mathematical statistics should give attention to the problem described.

ISSN:0020-739X    

DOI:10.1080/0020739980290410

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor