Elementary Mathematics II (Calculus)

At the end of the course, students should be able to: 1. identify the types of rules in differentiation and integration; 2. recognise and understand the meaning of function of a real variable, graphs, limits and continuity; 3. solve function of a real variable, plot relevant graphs, identify limits and idea of continuity; 4. identify the derivative as limit of rate of change; 5. identify techniques of differentiation and perform extreme curve sketching; 6. identify integration as an inverse of differentiation; 7. identify methods of integration and definite integrals; 8. solve some applications of definite integrals in areas and volumes; and 9. perform integration application to areas, volumes.

Functions of a real variable, graphs, limits and idea of continuity. The derivative as limit of rate of change. Techniques of differentiation, maxima and minima. Extreme curve sketching, integration, definite integrals, reduction formulae, application to areas, volumes (including approximate integration: Trapezium and Simpson's rule).