Differentiation and Integration, or, collectively, Calculus, on functions of a single variable together with their profound applications in various subject areas are introduced in this course. On differentiation, it includes the definitions of limits and continuity, techniques of differentiation, strategies in solving extreme-value problem and so on; on integration, it includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, finding areas and volumes, solving elementary differential equations and more.

Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.