課程資訊

CALCULUS (1)

112-1

MATH4006

201E49810

11

2.0

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, 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. In addition, we will discuss applications in Economics such as Revenue Optimization and Point Elasticity of Demand.

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.

Provisional Schedule :

Week 1 - Functions and their limits
Week 2 - Limits & Continuity
Week 3 - Differentiation 1 : Basics & Techniques
Week 4 - Differentiation 2 : Chain rule & its Applications
Week 5 - Curve sketchings
Week 6 - Mean Value Theorems & L'Hôpital's rule
Week 7 - Applications in Economics
Week 8 - Reviews

Students will be familiar with Calculus as a tool and be able to apply it in various subjects including Economics after finishing this course.

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.

After 4-hour lecture per week, students are expected to spend around 2-3 hours in revising the materials, completing homework/worksheets and exercises on WeBWorK.
Office Hours

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.

NTU Calculus Unified Website: http://www.math.ntu.edu.tw/~mathcal/a/
NTU Calculus Past Exams: http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7

(僅供參考)

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 課程進度
 週次 日期 單元主題 Week 1 9/4-9/8 Week 1 - Functions and their limits HW 1 due Week 2 9/11-9/15 Week 2 - Limits & Continuity Week 3 9/18-9/22 Week 3 - Differentiation 1 : Basics & Techniques WS 1 due Quiz 1 Week 4 9/25-9/29 Week 4 - Differentiation 2 : Chain rule & its Applications Week 5 10/2-10/6 Week 5 - Curve sketchings HW 4 due Week 6 10/9-10/13 Week 6 - Mean Value Theorems & L'Hôpital's rule WS 2 due Quiz 2 Week 7 10/16-10/20 Week 7 - Applications in Economics HW 6 due Week 8 10/23-10/27 Week 8 - Reviews WS 3 due