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 using advanced computational processes to provide solutions to energy sector engineering problems. All knowledge and skills detailed in this unit should be contextualised to current industry practices and technologies. KS01-EE127A Advanced Engineering Maths Evidence shall show an understanding of advanced engineering maths to an extent indicated by the following aspects: T1 Differential Calculus encompassing: basic concepts of differential calculus, limited to 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. applications - 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 T2 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, 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. T3 Linear Algebra encompassing: matrices and inverse matrices; linear mapping, determinants, solution of linear equations. T4 Vectors encompassing: geometrical representation, addition and scalar multiplication, dot and cross products, equations of lines and planes. T5 Variables encompassing: graphs, level curves and surfaces partial derivatives; chain rule; directional derivative; maxima and minima. T6 Sequences and Series encompassing: algebraic and Fourier series, convergence; Taylor’s Theorem power series manipulation. T7 Differential Equations encompassing: first order and separable linear equations second order linear equations. partial differential equations. numerical Techniques. T8 Number encompassing: integer, irrational and complex numbers. number systems. arithmetic operations. accuracy and stability. T9 Statistics encompassing: assembly, representation and analysis of data. fitting distributions to data. non-parametric statistics. tests of significance for means, variances and extreme values. correlation |