課程概述

In this course, we will continue our journey in Calculus and turn our attention to the theory of integration (à la Riemann). We shall begin with the definition and techniques of integration, derive the Fundamental Theorem of Calculus that provides an important link between integration and differentiation, compute areas and volumes of some 2D/3D objects, discuss applications to analytic (plane) geometry and solve certain first order differential equations.

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 TA classes in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

課程目標

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. Calculus 1-2-3-4 provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.

課程要求

High school mathematics (trigonometry), Calculus 1.

成績評量方式

1. Final Exam: 50%. 
2. Quizzes: 20%. Two quizzes of 30-40mins
3. Assessment: 30%. This includes the following items : Worksheets, Homework, WeBWork, etc.

參考書目

Textbook: Stewart, Clegg, Watson, CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition (Note that this is a new edition)
This course will be supplemented by instructor's lecture notes.