Mathematics II

Course Content

Module Content

•  Calculus: Ordinary Differentiation; differentiation: introduction to differentiation – differentiation from first principle, standard derivatives, differentiation of products and quotients, differentiation by substitution, successive differentiation, logarithmic differentiation, parametric functions, apply rules of differentiation in solving various mathematical problems, higher derivations, application of differentiation in :stationary points and solve problems involving stationary points, curve sketching, rates of change, small change or errors. 


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• Integration; define integration, types of integral (indefinite, definite), refer to tables of indefinite integrals of common functions in mathematical tables, methods of integration (substitution, trigonometric substitution, integration of parts, reduction formulae, partial fractions), applications of integration in :area, volume, mean value, first and second moments, centre of mass, room mean square, arc length, time constants, RLE and RCE circuit with E constant, energy of inductor, energy of capacitor. 


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• Differential Equations; first order differential equations; define differential equation, explain how to form first order differential equations, methods of solving differential equations (separating variables, exact, linear, homogenous, integrating factor method), application of first order differential equations in :electric circuits, mechanical engineering, physical sciences.


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•   Second order differential equations; define second order differential equation, explain how to form a second order differential equations for a given system, methods of solving second order differential equations (general methods, homogenous linear equations with constant coefficients, linear differential equations with constant coefficients, operational method, simultaneous differential equations, series), explain application of second order differential equations in: electric circuits RCL.