FAEN 102: Calculus I

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