Week 1-2: Some techniques of integration; by substitution, by parts and partial fraction.
Week 3-4: Differentiation; reduction formula, partial differentiations, applications and classification of
critical points of functions of two variables.
Week 5-6: Lagrangian multipliers, Coordinate systems: change from Cartesian to polar, spherical and
cylindrical coordinate systems.
Week 7-8: Taylor’s and Maclaurin’s series. Differential coefficients of the nth order.
Week 9-10 Leibnitz’s rule; application to the solution of differential equations. Complex numbers;
Hyperbolic functions, De Moivre’s theorem.
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