Culculus

September 2002—January 2003

Professor: Wang Kunyang

Assistants: Ms. Yu Dan and Mr. He Xiaoyuan

Place: Zhuhai Campus of Beijing Normal University

Chapter 2. Limits and Continuity

Lecture 1. Rigorous discussion on limits

Lecture 2. Convergence Criterion and its applications

Lecture 3. Continuity of functions

Lecture 4. Exponential and logarithmic functions

Chapter 3. The Derivative

Lecture 1. Definitions and Techniques of Differentiation

Lecture 2. Derivatives of inverse and composition functions

Chapter 4. The Derivative in Applications

Lecture 1. Mean-Value Theorems (Section 4.8 )

Lecture 2. Local and holistic extrema

Lecture 3. Applied extrema problems (Section 4.6 )

Lecture 4. Newton's Method, L'H^opital's Rule (Section 4.7 and Section 7.7 )

Chapter 5. Integration

Lecture 1. The indefinite integral and antiderivative (Section 5.2, Section 7.3, Section 8.2 )

Lecture 2. The definite integral (Section 5.5 and Section 5.6)

Lecture 3. Evaluating definite integral by substitution and by parts

(Section 5.7 and Section 8.2 )

Chapter 6. Applications of the Integral

Lecture 1. Area and Volume (Section 5.7, Section 6.1 and Section 6.2)

Lecture 2. Length of a plane curve, Area of a surface of revolution

and Applications in Physics (Section 6.4, Section 6.5 and Section 6.6)

Examination