8) This describes the essential skills and knowledge and their level, required for this unit. Evidence shall show that knowledge has been acquired of safe working practices and undertaking computations in an energy sector environment. All knowledge and skills detailed in this unit should be contextualised to current industry practices and technologies. KS01-EE150A Energy sector applied mathematical concepts Evidence shall show an understanding concepts of engineering mathematics with calculus to an extent indicated by the following aspects: T1 Mathematical linear measurement in engineering situations encompassing: Precision and error in mathematical computations and Displaying mathematical outcomes in the correct format using the appropriate significant figures and in scientific notation Perimeters of plane figures, polygons and the perimeter of shapes involving arcs Pythagoras’ theorem to engineering situations T2 Mathematical spatial measurement in engineering situations encompassing: Areas of combined shapes Volume and surface areas of solids T3 Right triangle trigonometry in engineering problem solving encompassing: Problems using the six trigonometrical ratios Problems involving compass bearings and angles of elevation/depression Trigonometrical concepts in problems involving inclined planes, vectors and forces and electrical sinusoidal waveforms T4 Sine and cosine rules in practical applications encompassing: Sine rule to solve unknown dimensions/angles in triangles Cosine rule to solve unknown dimensions/angles in triangles T5 Mathematical concepts in basic surveying and computation of areas encompassing: Mathematical concepts for radial and triangulation surveys Simpson’s Rule in engineering applications T6 Basic algebra in engineering calculations encompassing: Basic operations involving substitutions, additions, removal of brackets, multiplication and divisions Solving linear equations Transportation in non-linear equations T7 Linear graphical techniques in engineering problem solving encompassing: Graphing linear functions Deriving equations from graphs and tables Solving simulations equations algebraically and graphically The best line of fit graphically and determine equation T8 Mathematical computations involving polynomials encompassing: Adding, subtracting and multiplying polynomials Factorising trinomials Solving quadratic equation T9 Mathematical computations involving quadratic graphs encompassing: Graphs of quadratic functions Maxima and minima Graphical solutions of quadratic equations Properties of a parabola Applications of parabolas in engineering applications T10 Trigonometry and graphical techniques in engineering outcomes encompassing: Graphs of trigonometric functions e.g.: V=Vmsin,I=Imcos Addition of equations such as: vsin + usin( +) graphically Simpson’s Rule to determine the average and root mean square values of a sinusoidal waveform T11 Statistical data presentation encompassing: Appropriate presentation of frequency tables, histograms, polygons, stem and leaf plots Advantages of different visual presentations T12 Appropriate sampling techniques for gathering data encompassing: Design of surveys and census Sample data using correct technique T13 Use of the measures of central tendency encompassing: Estimation of percentiles and deciles from cumulative frequency polygons (ogives) Interpreting data from tables and graphs including interpolation and extrapolation Analysing misleading graphs T14 Measures of dispersion in statistical presentations encompassing: Box-and-whisker graphs Measures of dispersion using variance and standard deviation Standardised scores including Z-scores T15 Correlation and regression techniques encompassing: Interpreting scatter plots Correlation coefficients Calculate the regression equation and use for prediction purposes T16 Elementary probability theory encompassing: Probabilities in everyday situations Counting techniques: factorials; permutations; combinations T17 Paschal’s Triangle and the Normal Curve encompassing: Paschal’s triangle Characteristics of the normal curve Standard Deviation and applications to everyday occurrences Probabilities using the normal curve T18 Differential Calculus encompassing: Basic concepts - definition of the derivative of a function as the slope of a tangent line (the gradient of a curve); limits; basic examples from 1st principles; Notation and Results of derivative of k.f(ax + b) where f(x)=x to the power of n, sin x, cos x, tan x, e to the power of x, ln x. Rules - derivative of sum and difference; product rule; quotient rule; chain rule (function of a function), limited to two rules for any given function. The 2nd derivative Application - equations of tangents and normals; stationary points; turning points; and curve sketching; rates of change; rectilinear motion Verbally formulated problems involving related rates and maxima: minima T19 Integral Calculus encompassing: Integration as the inverse operation to differentiation - results of the integral of k.f(ax + b) where f(x) = x to the power of n, sin x, cos x, sec squared x, e to the power of x The method of substitution The definite integral Applications - areas between curves; rectilinear motion including displacement from acceleration and distance travelled; voltage and current relationship in capacitors and inductors and the like T20 Differential Equations encompassing: First order and separable linear equations |