Students’ conceptual understanding of a function and its derivative in an experimental calculus course

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.     

Novel fixed‐site–carrier polyvinylamine membrane for carbon dioxide capture

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     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.     

Analyse systemati oue d'elements en traces dans l'or metalli oue par activation neutroni oue

Résumé Une méthode d'analyse des impuretés dans l'or métallique par activation neutronique, a été mise au point. Après irradiation de 15 heures dans un flux de 2·10¹⁴ n·cm⁻²·sec⁻¹, l'échantillon d'or est traité en cellule blindée. La matrice est séparée des impuretés à analyser par des méthodes électrolytiques. Les impuretés sont généralement séparées en 3 fractions qui sont mesurées par spectrométrie γ. Le traitement des informations est effectué sur ordinateur IBM 360/91 moyennant un programme écrit au laboratoire. 29 éléments sont détectables par cette méthode.     

Determination quantitative des impuretes des graphites nucleaires par les methodes de radioactivation analyse systematique

Impurities contained in nuclear graphites have been determined so far individually. A method of systematic analysis is described which permits to determine about twenty impurities in one sample, such as the following elements: Ag, Se, Hg, Sb, Cu, Fe, Ga, Co, Cd, Zn, In, Zr, Cr, Sc, Ba, Ca, Na, K, Rb, and Cs. Brief mention is made of methods used for the determination of all rare earth metals, Si, S and P, as well as the elements which can be determined without chemical separation, such as Cl, Mn, V.

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Determination quantitative des impuretes des graphites nucleaires par les methodes de radioactivation analyse systematique

     

7-Benz[c] acridinemethanols as tetracyclic analogs of the 2-phenyl-4-quinolinemethanol antimalarials

A series of new 7-benz[c]acridinemethanols and 5,6-dihydro-7-benz[c]acridinemethanols was prepared as rigid, tetracyclic analogs of the antimalarial 2-phenyl-4-quinolinemethanols. Condensation of 5,7-dichloroisatin with 6-chloro-, 7-chloro-, and 6,7-dichloro-1-tetralone furnished halogenated 5,6-dihydro-7-benz[c]acridinecarboxylic acids, which were transformed into the corresponding acid chlorides, acyl malonates, α-bromomethyl ketones, and epoxides. Fully aromatic members of the series obtained via dehydrogenation of the 5,6-dihydro acids were likewise converted into epoxides via the acylmalonate route. Although all the epoxides studied proved to be exceptionally resistant to ring-opening by di-n-butylamine, probably on account of steric effects, they could be cleaved readily with piperidine or morpholine. Nmr spectra of the resulting amino alcohols suggest that these compounds exist in a single preferred conformation stabilized by internal O-H····N hydrogen bonding, and that free rotation about the side chain C-C bond does not occur at room temperature.