基本介紹
- 中文名：微積分1(Calculus I)（全英）
- 提供院校：華南理工大學
- 類別：慕課
- 授課老師：鄧雪、楊啟貴、梁勇、劉小蘭、高文華
課程大綱,參考教材,
課程大綱
Course Introduction
Chapter 1 Limits
1.1 Introduction to Limits
1.2 Rigorous Study of Limits
1.3 Limit Theorems
1.4 Limits Involving Trigonometric Functions
1.5 Limits at Infinity, Infinite Limits
1.6 Continuity of Functions
1.7 Chapter Review
Supplementary Material for Chapter One
Homework for Chapter One
Answer to Chapter One
Chapter 1 Limits
Chapter 2 The Derivative
2.1 Two Problems with One Theme
2.2 The Derivative
2.3 Rules for Finding Derivatives
2.4 Derivate of Trigonometric Functions
2.5 The Chain Rule
2.6 Higher-Order Derivative
2.7 Implicit Differentiation
2.8 Related Rates
2.9 Differentials and Approximations
2.10 Chapter Review
Homework for Chapter Two
Answer to Chapter Two
Chapter 2 The Derivative
Chapter 3 Applications of the Derivative
3.1 Maxima and Minima
3.2 Monotonicity and Concavity
3.3 Local Extrema and Extrema on Open Intervals
3.4 Practical Problems
3.5 Graphing Functions Using Calculus
3.6 The Mean Value Theorem for Derivatives
3.7 Solving Equations Numerically
3.8 Anti-derivatives
3.9 Introduction to Differential Equations
3.10 Chapter Review
Supplementary Material for Chapter Three
Homework for Chapter Three
Answer to Chapter Three
Test 1
Chapter 4 The Definite Integral
4.1 Introduction to Area
4.2 The Definite Integral
4.3 The First Fundamental Theorem of Calculus
4.4 The Second Fundamental Theorem of Calculus and the Method of Substitution
4.5 The Mean Value Theorem for Integrals and the Use of Symmetry
4.6 Numerical Integration
4.7 Chapter Review
Homework for Chapter Four
Answer to Chapter Four
Chapter 4 The Definite Integral
Chapter 5 Applications of the Integral
5.1 The Area of a plane region
5.2 Volumes of Solids: Slabs, Disks
5.3 Volumes of Solids of Revolution: Shells
5.4 Length of a plane curve
5.5 Work and Fluid Force
5.6 Moments and Center of Mass
5.7 Probability and Random Variables
5.8 Chapter Review
Homework for Chapter Five
Answer to Chapter Five
Chapter 5 Applications of the Integral
Chapter 6 Transcendental and Functions
6.1 The Natural Logarithm Function
6.2 Inverse Functions
6.3 The Natural Exponential Function
6.4 General Exponential and Logarithm Function
6.5 Exponential Growth and Decay
6.6 First-Order Linear Differential Equations
6.7 Approximations for Differential Equations
6.8 The Inverse Trigonometric Functions and Their Derivatives
6.9 The Hyperbolic Functions and Their Derivatives
6.10 Chapter Review
Chapter 7 Techniques of Integration
7.1 Basic Integration Rules
7.2 Integration by parts
7.3 Some Trigonometric Integrals
7.4 Rationalizing Substitutions
7.5 Integration of Rational Functions Using Partial Fraction
7.6 Strategies for Integration
7.7 Chapter Review
Homework for Chapter Seven
Answer to Chapter Seven
Chapter 7 Techniques of Integration
Chapter 8 Indeterminate Forms and Improper Integrals
8.1 Indeterminate Forms of Type
8.2 Other Indeterminate Forms
8.3 Improper Integrals: Infinite Limits of Integration
8.4 Improper Integrals: Infinite Integrands
8.5 Chapter Review
Supplementary Material for Chapter Eight
Homework for Chapter Eight
Answer to Chapter Eight
Test 2
參考教材
配套課本 ：微積分=calculus,（美/第九版）沃伯格（Varberg, D），柏塞爾（Purcell, E.J.），里格登（Rigdon,S.E.）著, 北京：機械工業出版社，2009.8.
Matching textbook：Calculus, Ninth Edition (Varberg, D., Purcell, E.J., Rigdon, S.E.). Beijing: Mechanical Industry Publisher, 2009.8.
Reference materials ：Advanced Mathematics (I and II), Department of Mathematics, Tongji University. Shanghai: Tongji University Publisher, 2006.7.
