Review of the prerequisites such as limits of sequences and functions, continuity, uniform continuity and differentiability. Successive differentiation, Leibniz’s theorem (without proof), Taylor's & Maclaurin's expansions of single variable, Indeterminate forms.
Partial differentiation and its applications
Partial and total differential coefficient, Euler’s theorem, Transformations, Geometrical interpretation of partial derivatives, Tangent plane and Normal line, Jacobians, Taylor’s expansion for two variables, Errors and approximations,Maxima and Minima of functions of two variables,Lagrange method of undetermined multipliers to determine stationary values.
Reduction Formulae: Reduction formulae of the type ò sinn xdx,ò cosn x dx, ò sinmxcosnxdx ,ò tannxdxandò cotnxdx.Beta&Gammafunction,Error function, Elliptic integrals. Application of integration- Length of a curve, for Cartesian, parametric & polarform.
Double integral, change of order of integration, transformation of variables by Jacobian only for double integration, change into polar co-ordinates in double integrals only ,Triple integral
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