This course will be conducted in English.

Calculus was independently founded by Isaac Newton and Gottfried Leibniz to describe and study the change of functions with respect to their variables. This subject has found applications and become fundamental in fields such as physics, chemistry, and engineering. In the first module of this Calculus series (MATH4006-4009), we will introduce differentiation of functions in one real variable.

Specifically, we will define the derivative of a function, derive basic rules and techniques of differentiation, analyze extrema of a function, discuss the statement and applications of the Mean Value Theorem(s), and sketch the graph of a function.

Key definitions are discussed, and important theorems are derived in lectures to help students develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated to promote an organic interaction between the theory of Calculus and students’ own fields of study.

This course also provides TA classes, where students can enhance their proficiency in handling Calculus calculations under the guidance of our teaching assistants.

Provisional Schedule :

Week 1 Functions and Their Limits
Week 2 Continuity
Week 3 Differentiation (I) : Definition and Technique
Week 4 Differentiation (II) : Chain Rule and Implicit
Week 5 Mean Value Theorem and L’Hospital’s Rule
Week 6 Curve Sketching
Week 7 Optimisation Problems
Week 8 Exam Week