《微积分1（Calculus I）（全英）》PPT课件 华南理工大学 邓雪

 
课件内容： 
Course Introduction 
Course Introduction 
Chapter 1 Limits 
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 
Discussion Topics of Chapter 1 
1.1 Introduction to Limits 
1.2 Rigorous Study of Limits 
1.3 Limit Theorems 
1.4 Limits Involving Trigonometric Functions 
Assignment 1 for Chapter 1 
Assignment 2 for Chapter 1 
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 
Discussion Topics of Chapter 2 
Assignment 2 for Chapter 2 
Chapter 2 The Derivative 
Assignment 1 for Chapter 2 
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 
Discussion Topics of Chapter 3 
Assignment 1 for Chapter 3 
Assignment 2 for Chapter 3 
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 
Discussion Topics of Chapter 4 
Chapter 4 The Definite Integral 
Assignment 1 for Chapter 4 
Assignment 2 for Chapter 4 
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 
Discussion Topics of Chapter 5 
Chapter 5 Applications of the Integral 
Assignment 1 for Chapter 5 
Assignment 2 for Chapter 5 
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 
Discussion Topics of Chapter 7 
Chapter 7 Techniques of Integration 
Assignment 1 for Chapter 7 
Assignment 2 for Chapter 7 
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 
Discussion Topics of Chapter 8 
Assignment 1 for Chapter 8 
Assignment 2 for Chapter 8 
Test 2 
Exercises 
Limit of sequence and limit of function 
Continuity, differentiation and derivative 
Derivative 
Indefinite integral Ι 
Indefinite integral II 
Indefinite integral III 
Definite integral 
Supplement