Browsing by Subject "vectors"

Now showing 1 - 3 of 3
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    Large-scale perturbations on the brane and the isotropy of the cosmological singularity
    (2004) Goheer, Naureen; Dunsby, Peter K S; Coley, Alan; Bruni, Marco
    We present the complete set of propagation and constraint equations for the kinematic and non-local first order quantities which describe general linear inhomogeneous and anisotropic perturbations of a flat FRW braneworld with vanishing cosmological constant and decompose them in the standard way into their scalar, vector and tensor contributions. A detailed analysis of the perturbation dynamics is performed using dimensionless variables that are specially tailored for the different regimes of interest; namely, the low energy GR regime, the high energy regime and the dark energy regime. Tables are presented for the evolution of all the physical quantities, making it easy to do a detailed comparison of the past asymptotic behaviour of the perturbations of these models. We find results that exactly match those obtained in the analysis of the spatially inhomogeneous $G_{2}$ braneworld cosmologies presented recently; i.e., that isotropization towards the ${cal F}_b$ model occurs for $gamma > 4/3$.
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    PHY1012F
    (2013) Leigh, Gregor
    First year physics lectures covering a wide range of topics, namely: Motion; Kinematics; Vectors; and Kinematics in two dimensions. These lecturer slides are aimed at introdcutory courses for Physics at a university level. These lecture slides contain graphs and visualisations of key physics concepts, as well as problem-solving strategies to help students develop their analytical and mathematical skills. These lecture slides can be used by lecturers looking to supplement their lecture materials with external materials or students looking to improve their knowledge through self-study. 5) Dynamics 6) Circular Motion 7) Momentum 8) Energy 9) Work 10) Rotation
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    Simple rule, hidden meaning: the scalar product in engineering mathematics
    (Elephant Delta, 2017-09-13) Craig, Tracy S; Cloete, Trevor J
    Engineering is a highly mathematical field of study with different university courses requiring proficiency at different types of mathematics. Engineering dynamics requires the skilful use of vectors in various ways and proficiency at vector arithmetic, algebra and geometry is of vital importance to incoming students. This paper reports on findings from the administering of a vector proficiency assessment instrument across two semesters of a dynamics course. Findings suggest that problems requiring use of the scalar product embedded within a context are of the highest difficulty level. We argue that the geometric role of the scalar product is weakly understood by the majority of students, leading to poor performance at any problem requiring more than a basic calculation. We suggest that lecturers of engineering mathematics foreground the geometric role and that lecturers of engineering courses be aware of the level of challenge manifest in these problems.