 The expected learning outcome is that the students achieve thorough knowledge in fundamental concepts in prime field differentiation and integration of calculus and theory of equations and enhance their analytical skills, develop insight for application in real life situations, use mathematical knowledge for decision making and search for more areas of application.
Successive Differentiation Successive derivatives, standard forms for , , , , log(ax+b), sin(ax+b), cos(ax+b), sin (bx+c), cos (bx+c). Leibnitz’s theorem and related problems. Expansions of Functions Maclaurin’s Theorem (without proof), Standard expansions for sinx, cosx, log (1 x) , and related functions. Some useful Definite Integrals and Reduction Formulae i) Some useful definite integrals and their particular cases. ii) Reduction Formulae Reduction formulae for xdx , xdx , xdx, xdx, x xdx, xdx, xdx, xdx, xdx, xdx Theory of Equations Transformation of equations by reducing the roots, Removal of the second term, Synthetic division method, Cubic and biquadratic equations, Cardano’s method for the solution of cubic equation and Ferrari’s method for the solution of a biquadratic equation.