Higher harmonic large-amplitude fourier transformed alternating current voltammetry : analytical attributes derived from studies of the oxidation of ferrocenemethanol and uric acid at a glassy carbon electrode

An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s−1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e− rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast.

Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.