Calculus I

AY2018/2019 Semester 1

This core mathematical course aims to provide an introduction to the fundamental mathematical concepts (functions, limits, continuity, derivatives and integrals). Computation of derivatives (sum, product, and quotient formulas, chain rule, and implicit differentiation), and application of derivatives to optimization problems and related rates of change problems will also be discussed. This course lays the foundation for more advanced studies in mathematics, physics, engineering, and other related subjects. List of key topics taught 1. Functions 2. Limit and limit laws 3. Continuity 4. Derivatives and derivative function 5. Differentiation formulas 6. Trigonometric derivatives and chain rules 7. Implicit differentiation 8. Linear approximation and extreme values 9. Mean value theorem 10. Limit and infinity 11. Curve sketching 12. Optimization and Newton?s method 13. Antiderivatives