摘要:

When finite difference methods are employed in the numerical solution of partial differential equations, the geometry of the region can make the use of overlapping coordinate grid systems desirable. In such cases, unexpected error can result if linear interpolation is employed to exchange information between the grids. The use of such interpolated quantities in the evaluation of finite difference approximations to the derivatives is examined, and various attendant sources of error are discussed. In illustration, the two‐dimensional Laplacian is calculated using data obtained by bilinear interpolation from a neighbouring grid system; the procedure is seen to give unreliable results.

ISSN:0020-739X    

DOI:10.1080/0020739800110311

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

This paper discusses a method of study which is inefficient but is used by large numbers of students, including many taking university courses in mathematics. The method is described and its effect and origins for a large proportion of the students who use it are examined. The wider relevance of the discussion, for subjects other than mathematics, such as arts subjects, is also examined.

ISSN:0020-739X    

DOI:10.1080/0020739800110312

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739800110313

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Is it possible to humanize the teaching of a subject as cold and abstract as mathematics, a subject which appeals to the intellect, but attaches no value to other human qualities such as emotions and ethical character? This question is answered in the affirmative. After establishing what may be considered the main task of a human education, the author shows, giving concrete suggestionsior the class‐room, how the teaching of mathematics may be adapted in order to play its proper part in fulfilling this task.

ISSN:0020-739X    

DOI:10.1080/0020739800110314

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The various complicating factors associated with string vibrations are discussed briefly. An extensive study of strings with elastic support and resistive medium is made and the Green's functions associated with these string oscillations are obtained. With the aid of associated Green's functions, contributions to the scientific study is predicted.

ISSN:0020-739X    

DOI:10.1080/0020739800110315

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

Third‐World mathematicians seem to agree that their discipline has an important role to play in their respective countries struggle for total development. For reasons specific to countries of the region, the national effort necessary for building mathematics has to be initiated and led by university mathematics institutions in these countries. The paper attempts to find out whether these institutions are adequately equipped to shoulder their immense responsibility. On examining basic structures of a number of university mathematics departments in the region, it is concluded that these structures are seriously deficient; and a brief description of ‘relevant’ structures is given.

ISSN:0020-739X    

DOI:10.1080/0020739800110316

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The Fourier transform and complex variable method is utilized to evaluate the Green's functions of a second order differential equation. The method of solution is exemplified by taking the well‐known Riccati differential equation under the influence of a slowly varying impulse.

ISSN:0020-739X    

DOI:10.1080/0020739800110317

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739800110318

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739800110319

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor