Program Overview

CALCULUS (1)

Course Description

Calculus 1 (微積分1) Differentiation on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem 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 sessions in which students are able to improve their skills in handling calculations and explore applications of Calculus under the guidance of teaching assistants.

Course Objective

Upon completing the course, students are expected to be able to:

• Understand the notion of the limits of a function and compute them.
• Use limits to describe properties of a function, including continuity and asymptotic behaviors.
• Define the derivative of a function, understand its geometric meaning, and determine the differentiability of a function.
• Use chain rule to differentiate composed functions, implicit functions and inverse functions.
• Employ differentiation to determine the local and global extreme values of functions.
• Apply Mean Value Theorem to derive properties of a function from its derivatives such as monotonicity and concavity.
• Apply the L'Hôspital's rule to compute limits of more sophisticated functions.

Course Requirement

Before taking this course, students should be skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test which is designed for NTU freshmen. Students are expected to attend and participate actively in lectures as well as discussion sessions.

Grading

• 50%: Exam
• 20%: Quizzes
• 12%: Worksheets
• 8%: WeBWorK
• 10%: Homework and others

Course Schedule

The course schedule includes the following topics:

• Week 1: The Tangent and Velocity Problems, The Limit of a Function, Calculating Limits Using the Limit Laws
• Week 2: Continuity, Limits at Infinity; Horizontal Asymptotes, Derivatives and Rates of Change, The Derivative as a Function
• Week 3: Derivatives of Polynomials and Exponential Functions, The Product and Quotient Rules, Derivatives of Trigonometric Functions, The Chain Rule
• Week 4: Implicit Differentiation, Derivatives of Logarithmic and Inverse Trigonometric Functions
• Week 5: Exponential Growth and Decay (Continuously Compounded Interest), Linear Approximations and Differentials, Maximum and Minimum Values
• Week 6: The Mean Value Theorem, What Derivatives Tell Us about the Shape of a Graph, Indeterminate Forms and l'Hospital's Rule
• Week 7: Summary of Curve Sketching, Optimization Problems
• Week 8-9: Final exam preparation

Additional Information

• The course is conducted in English.
• Intensive courses.
• No Specialization Program.
• English is the language of instruction.
• The course is part of the NTU COOL program.
• Core Capabilities and Curriculum Planning are emphasized.
• Notes: The course is conducted in English. Intensive courses.