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1.
Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives. 相似文献
2.
The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
Taek‐Joong Kim Baoan Li May‐Britt Hgg 《Journal of Polymer Science.Polymer Physics》2004,42(23):4326-4336
Fixed‐site–carrier membranes were prepared for the facilitated transport of CO2 by casting polyvinylamine (PVAm) on various supports, such as poly(ether sulfone) (PES), polyacrylonitrile (PAN), cellulose acetate (CA), and polysulfone (PSO). The cast PVAm on the support was crosslinked by various methods with glutaraldehyde, hydrochloric acid, sulfuric acid, and ammonium fluoride. Among the membranes tested, the PVAm cast on polysulfone and crosslinked by ammonium fluoride showed the highest selectivity of CO2 over CH4 (>1000). The permeance of CO2 was then measured to be 0.014 m3 (STP)/(m2 bar h) for a 20 μm thick membrane. The effect of the molecular weight of PVAm and feed pressure on the permeance was also investigated. The selectivity increased remarkably with increasing molecular weight and decreased slightly with increased pressure in the range of 1 to 4 bar. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4326–4336, 2004 相似文献
4.
Ramzi May 《Comptes Rendus Mathematique》2003,336(9):731-734
Let be a maximal solution of the Navier–Stokes equations. We prove that u is C∞ on and there exists a constant , which depends only on n, such that if is finite then, for all we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
5.
6.
Elie Leopold 《Numerical Algorithms》2007,44(4):347-366
In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of
all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials
are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given
a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations
are given. 相似文献
7.
We investigate function spaces of generalised smoothness of Besov and Triebel–Lizorkin type. Equivalent quasi-norms in terms
of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is proved.
Mathematics Subject Classification (2000) 46E35 相似文献
8.
9.
The Canadian Light Source (CLS) is constructing two beamlines for Infrared Spectroscopy using synchrotron radiation (IRSR). One will supply mid-Infrared (2–25 μ) light to a Fourier Transform Infrared (FTIR) spectrometer and microscope for biological applications. The second will have a high resolution FTIR spectrometer for gas-phase and surface spectroscopy in the far-Infrared (beyond 25 μ). The Infrared beamlines will use dipole bending magnet radiation from a special bend magnet port design which provides a 50 mrad square acceptance. Issues with the first mirror and photon mask design, as well as the beamline layout and features are discussed. 相似文献
10.
Kochocki JA Allison WW Alner GJ Ambats I Ayres DS Balka LJ Barr GD Barrett WL Benjamin D Border P Brooks CB Cobb JH Cockerill DJ Coover K Courant H Dahlin B DasGupta U Dawson JW Edwards VW Fields TH Kirby-Gallagher LM Garcia-Garcia C Giles RH Goodman MC Heller K Heppelman S Hill N Hoftiezer JH Jankowski DJ Johns K Joyce T Kafka T Litchfield PJ Lopez FV Lowe M Mann WA Marshak ML May EN McMaster L Milburn RH Miller W Napier A Oliver WP Pearce GF Perkins DH Peterson EA Price LE Roback D Rosen DB 《Physical review D: Particles and fields》1990,42(9):2967-2973