摘要:

Under the auspices of the National Development Programme in Computer‐Assisted Learning, a C.A.L. course entitled ‘ Fundamentals of Fluid Mechanics and Heat Transfer ‘ has been given at Imperial College London to final‐year B.Sc. students in Mechanical Engineering in the session 1974/75 and 1975/76. The course consisted of 20 lectures and an equal number of periods devoted to the solution and discussion of a carefully‐selected set of illustrative problems which the students tackled with the aid of computer programmes specially developed for the purpose. In this paper, the authors present (a) a brief description of the course, with special emphasis on the role played by the computational component, (b) an outline of the methods used to assess the students’ understanding of the material taught and (c) a description of the methods, both subjective and objective, used to evaluate the success of the course.

ISSN:0020-739X    

DOI:10.1080/0020739770080101

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This article attempts to answer the following questions about a course commonly known as ‘ Mathematics for Liberal Arts Students ‘, based on the author's thought and experience gathered from teaching such a course: (1) Why should there be such a course? (2) What do we want to get across? (3) What can we talk about in the course?

ISSN:0020-739X    

DOI:10.1080/0020739770080102

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In this paper the author examines the potential intuitive use of the most widely known kinds of diagrams, the Euler and Venn Diagrams, and distinguishes between these two.

ISSN:0020-739X    

DOI:10.1080/0020739770080103

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A convenient method is presented for the reduction of coefficients in zero‐one linear inequalities. By using the Boolean resolvent of the original inequality a first ordering of the coefficients is achieved. This first ordering is used as a basis for an algorithmic approach to forming an inequality equivalent to the original inequality.

ISSN:0020-739X    

DOI:10.1080/0020739770080104

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The present paper deals with the study of sub‐tabulation for tracking high speed bodies. This is essentially an application of non‐linear interpolation and the’ throwback ‘ technique is applied to reduce the higher‐order difference terms of a suitable interpolating polynomial to those of lower order, while maintaining, however, the same order of accuracy in the numerical calculations. Given the values of the function at equal intervals (say, 1 min intervals) an eighth‐order difference polynomial is postulated and by the ‘ throwback ‘ technique it is reduced to a fifth‐order difference polynomial. Then, using a fifth‐order reduced difference table, the successive values of the sub‐tabulated function (i.e. the values of the function at 1 sec sub‐intervals) are calculated by the Newtonian method.

ISSN:0020-739X    

DOI:10.1080/0020739770080105

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

When given a transformation in two dimensions from a Cartesian coordinate system to a more general system, it is easy to determine the line element for the new coordinates. The reverse process is not so easy and indeed it is not always possible given a line element to find a transformation which will reduce it to a Pythagorean form.

ISSN:0020-739X    

DOI:10.1080/0020739770080106

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This paper attempts to obviate certain difficulties met by students on mathematics honours degree and other courses when studying extrema of functions of two or more variables.

ISSN:0020-739X    

DOI:10.1080/0020739770080107

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The purpose of this article is to describe an alternative approach into the basic concepts of measures of central location and dispersion as used in the context of descriptive statistics. The treatment, designed to provide a more stimulating introduction than the traditional intuitive based discussion, is structured so as to generate a more sensitive insight into the origin, nature and limitations of these measures as used in summarizing a set of variate results. It also indicates how an alternative algebraic form of the (data) variance, so essential for computational efficiency, may be generated without undue tedious algebraic analysis. The presentation is primarily intended for those who, though not being experienced in the teaching of statistics, wish to include some basic ideas of descriptive techniques within, and in a manner consistent with a mathematical course.

ISSN:0020-739X    

DOI:10.1080/0020739770080108

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Bounds on harmonic functions between interior points and the boundaries of unit spheres in various dimensions are obtained when the values at the interior points and the maximum absolute values of the harmonic functions on the boundaries are given. Only elementary results such as Poisson integral representations, the Harnack inequalities, and Fourier expansions are used in the proofs. These Schwarz lemma analogues can be presented when harmonic functions are studied in courses on complex analysis or partial differential equations.

ISSN:0020-739X    

DOI:10.1080/0020739770080109

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

It is argued that the existence of the probabilistic abacus can be an incentive to teach probability in a way that blunts the students’ critical sense, by giving them the habit of accepting hypotheses without seriously questioning their validity. This is first illustrated on two examples and then commented on from a more general point of view. The conclusion is that the choice of a flow‐graph must be preceded by the analysis of a tree and its probability function.

ISSN:0020-739X    

DOI:10.1080/0020739770080110

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor