Limits and Continuity of a function of a single variable. Differentiation: Rules of differentiation,
chain rule and parametric differentiation, differentiation of trigonometric functions and their
inverses, exponential and logarithmic functions, higher order derivatives, Leibnitz’s rule.
Differentiability: Rolle’s Theorem, mean-value theorem, approximate methods of solving
equations (graphical and Newton-Raphson methods). Integration and its applications: Area under
curve, volumes of solids of revolution. Numerical integration: Trapezium and Simpson’s rules.
Vector function of a single variable: Differentiation and integration of vector functions, kinematics
of a single particle in motion. Newton’s laws of motion, motion in a straight line and in a plane,
projectiles and circular motion, work, energy and power; impulse and momentum, moment of a
force, couple, conditions for equilibrium of rigid bodies