微积分是高等数学中研究函数的微分、积分以及有关概念和应用的数学分支，它是数学的一个基础学科，是理工科院校一门重要的基础理论课。它推动了其他学科的发展，推动了人类文明与科学技术的发展，它的作用是举足轻重的。微积分（I）是本科生的一门必修课，内容主要包括函数、极限、函数连续性、导数及其应用、积分及其应用、不定型的极限及广义积分。极限是微积分的基本概念，微分和积分是特定过程特定形式的极限。通过全英教学，学生在学会用英语获取数学知识的同时又通过学习数学掌握和运用英语，达到双赢的目的。从而培养具有国际竞争力并适应国家和社会需要的国际化人才。
授课目标：本课程的目的是使学生掌握一元微积分的基本概念，理论及其应用。通过本课程的学习，在理论上，使学生获得一元函数微积分的基本概念、基本理论和基本运算技能；在具体传授知识的过程中，在教学中注意培养学生抽象思维能力、逻辑推理能力、空间想象能力和自学能力，特别是综合运用所学知识去分析问题和解决问题的能力。
Calculus is the branch of mathematics that studies differentiation, integration and related concepts and applications in advanced mathematics. It is a basic subject of mathematics. It is an important basic theory course in universities of science and engineering. It has promoted the development of other disciplines and human civilization and science and technology, and its function is of great importance. Calculus (I) is a compulsory course for undergraduates. The basic requirements of the course include functions, limits, continuity of function, derivatives and their applications, integrals and their applications, the limits of indefinite forms and generalized integrals. The limit is the basic concept of calculus. Differential and integral are the limits of particular forms of a particular process.
Through the teaching of English, students learn to acquire mathematical knowledge in English while mastering and using English in the process of learning mathematics to achieve a win-win goal. Therefore, we can cultivate international talents with international competitiveness and meet the needs of the state and society.
Teaching Objective: The purpose of this course is to enable students to master the basic concepts, theories and operations of one variable calculus. By the study of this course, in theory, students can master the basic definition, basic theory and basic operation skills of one variable calculus. At the same time, we should pay attention to the cultivation of students’ abstract thinking ability, logical reasoning ability, spatial imaginary ability and self-learning ability in the process of imparting knowledge and teaching. In particular, the ability of analyzing and solving problems is trained by using the learned knowledge.
Course Introduction
Chapter 1 Limits
Introduction to Limits
Rigorous Study of Limits
Limit Theorems
Limits Involving Trigonometric Functions
Limits at Infinity, Infinite Limits
Continuity of Functions
Chapter Review
Assignments for Chapter 1
Discussion Topics of Chapter 1
Homework and Answer of Chapter 1
Homework 1
Homework 1
Chapter 2 The Derivative
Two Problems with One Theme
The Derivative
Rules for Finding Derivatives
Derivate of Trigonometric Functions
The Chain Rule
Higher-Order Derivative
Implicit Differentiation
Related Rates
Differentials and Approximations
Chapter Review
Assignments for Chapter 2
Discussion Topics of Chapter 2
Homework and Answer of Chapter 2
Homework 2
Homework 2
Chapter 3 Applications of the Derivative
Maxima and Minima
Monotonicity and Concavity
Local Extrema and Extrema on Open Intervals
Practical Problems
Graphing Functions Using Calculus
The Mean Value Theorem for Derivatives
Solving Equations Numerically
Anti-derivatives
Introduction to Differential Equations
Chapter Review
Assignments for Chapter 3
Discussion Topics of Chapter 3
Homework and Answer of Chapter 3
Test 1
Test 1
Chapter 4 The Definite Integral
Introduction to Area
The Definite Integral
The First Fundamental Theorem of Calculus
The Second Fundamental Theorem of Calculus and the Method of Substitution
The Mean Value Theorem for Integrals and the Use of Symmetry
Numerical Integration
Chapter Review
Assignments for Chapter 4
Discussion Topics of Chapter 4
Homework and Answer of Chapter 4
Homework 4
Homework 4
Chapter 5 Applications of the Integral
The Area of a plane region
Volumes of Solids: Slabs, Disks
Volumes of Solids of Revolution: Shells
Length of a plane curve
Work and Fluid Force
Moments and Center of Mass
Probability and Random Variables
Chapter Review
Assignments for Chapter 5
Discussion Topics of Chapter 5
Homework and Answer of Chapter 5
Homework 5
Homework 5
Chapter 6 Transcendental and Functions
The Natural Logarithm Function
Inverse Functions
The Natural Exponential Function
General Exponential and Logarithm Function
Exponential Growth and Decay
First-Order Linear Differential Equations
Approximations for Differential Equations
The Inverse Trigonometric Functions and Their Derivatives
The Hyperbolic Functions and Their Derivatives
Chapter Review
Chapter 7 Techniques of Integration
Basic Integration Rules
Integration by parts
Some Trigonometric Integrals
Rationalizing Substitutions
Integration of Rational Functions Using Partial Fraction
Strategies for Integration
Chapter Review
Assignments for Chapter 7
Discussion Topics of Chapter 7
Homework and Answer of Chapter 7
Homework 7
Homework 7
Chapter 8 Indeterminate Forms and Improper Integrals
Indeterminate Forms of Type
Other Indeterminate Forms
Improper Integrals: Infinite Limits of Integration
Improper Integrals: Infinite Integrands
Chapter Review
Assignments for Chapter 8
Discussion Topics of Chapter 8
Homework and Answer of Chapter 8
Test 2
Test 2
期末考试
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