摘要:

The error associated with Simpson's 1/3rd rule is derived in a simple alternative way.

ISSN:0020-739X    

DOI:10.1080/002073900287318

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/00207390050032243

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Many texts in 'advanced calculus' present Darboux's Theorem (also known as the Intermediate Value Theorem for Derivatives) and the well-known example f(x) = { x2sin1/x, x = 0 /0, x = 0 of a function with discontinuous derivative at the origin. But these texts typically fail to discuss the relationship between Darboux's result and the type of discontinuity a given derivative must have at such a point. It is no accident, for example, that the discontinuity of f'(x) = { 2xsin 1/x - cos 1/x, x = 0 /0, x = 0 at the origin is such that limx-0f'(x) does not exist. In this paper, we precisely identify such discontinuities. The arguments stay within the realm of elementary classical analysis and are thus accessible to students encountering a first proof course in the subject.

ISSN:0020-739X    

DOI:10.1080/00207390050032252

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

A simple procedure is highlighted for generating Covariance matrices.

ISSN:0020-739X    

DOI:10.1080/00207390050032261

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

A unified elementary approach is used to prove the arithmetic-geometric mean inequality, Cauchy's inequality and Triangle inequality.

ISSN:0020-739X    

DOI:10.1080/00207390050032270

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We recall the basic facts connected with the barycentre of a system of weighted points in an affine (or an Euclidean) space. Then we present some applications from classical geometry, modern applied mathematics, economics, etc.

ISSN:0020-739X    

DOI:10.1080/00207390050032289

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this note the author suggests a heuristic formula for the derivative of functions of the form f(x)g(x). This formula provides an alternative way to find derivatives of functions of such a form. It has been successfully taught to a number of first semester calculus classes. The author invites calculus instructors to use this formula in their classes.

ISSN:0020-739X    

DOI:10.1080/00207390050032298

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The note deals with the problem of finding analytic solutions to first-order nonlinear differential equations. A new approach, created by L. Roman-Miller and jointly presented by both authors, to finding an integrating factor enables the determination of exact solutions in a large number of previously unsolved cases. The method is illustrated by some observations on the van der Pol equation, which can be reduced to a first-order equation by means of a standard substitution.

ISSN:0020-739X    

DOI:10.1080/00207390050032306

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor