課程概述

Calculus was independently founded by Issac Newton and Gottfried Leibniz to describe and study the change of functions with respect to their variables. This subject had found applications (and also become fundamental) in physics, chemistry, engineering etc. In the first module of this serial of courses in Calculus (MATH4006-4009), we will introduce differentiation of functions in one (real) variable. To be specific, we will define the derivative of a function, derive basic rules and techniques of differentiation, analyse 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 some important theorems are derived in the lectures with a view to help students to develop their abilities to conduct logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote an 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 will 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, Mathematical Analysis and Differential Equations.

課程要求

The prerequisites are high school mathematics - proficiency in trigonometry (compound angle formulas, radian measures) is expected. Prior experience with calculus is helpful but not essential.

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.