微积分-1

微积分-1课程：前往报名学习

微积分-1视频慕课课程简介：

本课程专为MOOC设计，讲授常规理工科微积分的前半部分(一元微积分)。以中英文对照的方式讲授，并使用以英文为主的教材和学习资料。

前往报名学习

微积分-1课程列表：

Chapter 1 Numbers and Sets 数域与集合 (first part)

-Unit 1 Review of Real Numbers (回顾实数)

--Review of Real Numbers (回顾实数)

--Exercise1-1

-Unit 2 Exponentiations, Logarithms and Sets (指数、对数与集合)

--Exponentiations, Logarithms and Sets (指数、对数与集合)

--Exercise 1-2

-Unit 3 Limit Points, Open and Closed Sets (聚点、开集与闭集)

--Limit Points, Open and Closed Sets (聚点、开集与闭集)

--Exercise-1-3

Chapter 1 Numbers and Sets 数域与集合 (second part)

-Unit 4 Bounds and Completeness (有界性与完备性)

--Bounds and Completeness (有界性与完备性)

--Exercises-1-4

-Unit 5 Complex Number System, Algebraic and Transcendental Numbers (复数、代数数与超越数)

--Complex Number System, Algebraic and Transcendental Numbers (复数、代数数与超越数)

--Exercise-1-5

-章节测验1

--章节测试1

Chapter 2 Sequence 数列 (first part)

-Unit 1 Limit of a Sequence (数列的极限)

--Limit of a Sequence (数列的极限)

--Exercises-2-1

-Unit 2 Theorems on Limits of Sequences (数列极限定理)

--Theorems on Limits of Sequences (数列极限定理)

--Exercises-2-2

-Unit 3 Infinity and Bounded Monotone Sequences (无穷大和单调有界数列)

--Infinity and Bounded Monotone Sequences (无穷大和单调有界数列)

--Exercises-2-3

Chapter 2 Sequence 数列 (second part)

-Unit 4 Limit Superior and Limit Inferior (上极限和下极限)

--Limit Superior and Limit Inferior (上极限和下极限)

--Exercises-2-4

-Unit 5 Nested Intervals Theorem and Cauchy’s Convergence Criterion (区间套定理和柯西收敛准则)

--Nested Intervals Theorem and Cauchy’s Convergence Criterion (区间套定理和柯西收敛准则)

--Exercises-2-5

-章节测验2

--章节测试2

Chapter 3 Functions, Limits and Continuity 函数，极限与连续性(first part)

-Unit 1 Functions and Graphs (函数与图像)

--Functions and Graphs (函数与图像)

--Exercises-3-1

-Unit 2 Algebraic Function,Transcendental Functions and Inverse Trigonometric Functions (代数函数，超越函数与反三

-- Algebraic Function,Transcendental Functions and Inverse Trigonometric Functions(代数函数，超越函数与反三角函数)

--Exercises-3-2

-Unit 3 Hyperbolic Functions and Inverse Hyperbolic Functions (双曲函数与反双曲函数)

--Hyperbolic Functions and Inverse Hyperbolic Functions(双曲函数与反双曲函数)

--Exercises-3-3

-Unit 4 Maximum and Minimum, Increasing and Decreasing (极大值与极小值，单调增与单调减)

--Maximum and Minimum, Increasing and Decreasing (极大值与极小值，单调增与单调减)

--Exercises-3-4

Chapter 3 Functions, Limits and Continuity 函数，极限与连续性(second part)

-Unit 5 Limits of Functions (函数的极限)

--Limits of Functions(函数的极限)

--Exercises-3-5

-Unit 6 Infinity (无穷)

--Infinity (无穷)

--Exercises-3-6

-Unit 7 Theorems on Limits and Special Limits (极限相关定理与特殊极限)

--Theorems on Limits and Special Limits (极限相关定理与特殊极限)

--Exercises-3-7

Chapter 3 Functions, Limits and Continuity 函数，极限与连续性 (last part)

-Unit 8 Continuities (连续性)

--Continuity (连续性)

--Exercises-3-8

-Unit 9 Theorems on Continuity (关于连续性的定理)

--Theorems on Continuity (关于连续性的定理)

--Exercises-3-9

-Unit 10 Piecewise Continuity, Uniform Continuity, and Discontinuities (分段连续性， 一致连续性与不连续性)

--Piecewise Continuity, Uniform Continuity, and Discontinuities (分段连续性， 一致连续性与不连续性)

--Exercises-3-10

-Unit 11 Infinitesimals and Bounded Quantities (无穷小量与有界量)

--Infinitesimals and Bounded Quantities (无穷小量与有界量)

--Exercises-3-11

-章节测验3

--章节测试 3

Chapter 4 Derivatives 导数 (first part)

-Unit 1 Basics of Derivatives (导数基本定义)

--Basics of Derivatives (导数的基本定义)

--Exercise-4-1

-Unit 2 Differentiability on Intervals, Piecewise Differentiability and Differentials (区间上的可微性，逐段可微性与

--Differentiability on Intervals, Piecewise Differentiability and Differentials (区间上的可微性，逐段可微性与微分)

--Exercise-4-2

-Unit 3 Basic Methods of Differentiation (基本求导方法)

--Basic Methods of Differentiation (基本求导方法)

--Exercise-4-3

Chapter 4 Derivatives 导数 (second part)

-Unit 4 Derivatives of Commonly Used Functions (常见函数求导)

--Derivatives of Commonly Used Functions (常见函数求导)

--Exercise-4-4

-Unit 5 Higher Order Derivatives and Mean Value Theorem (高阶导数与中值定理)

--Higher Order Derivatives and Mean Value Theorem (高阶导数与中值定理)

--Exercise-4-5

-Unit 6 L'Hospital's Rules (洛必达法则)

-- L'Hospital's Rules (洛必达法则)

--Exercise-4-6

Chapter 4 Derivatives 导数 (last part)

-Unit 7 The First and Second Derivative Tests (导数判别法)

--The First and Second Derivative Tests (导数判别法)

-Unit 8 The Taylor Formula (泰勒公式)

--The Taylor Formula (泰勒公式)

--Exercise-4-8

-章节测验 4

--章节测试4

Chapter 5 Integrals 积分(first part)

-Unit 1 Definite Integrals and Numerical Methods (定积分与数值方法)

-- Definite Integrals and Numerical Methods (定积分与数值方法)

- Exercise 5-1

-Unit 2 Properties of the Definite Integrals and the Fundamental Theorem of Calculus (定积分的性质与微积分基本定理)

--Properties of the Definite Integrals and the Fundamental Theorem of Calculus (定积分的性质与微积分基本定理)

--Exercise-5-2

-Unit 3 Integrals of Elementary Functions and Integration by Substitution (初等函数的积分，换元法)

--Integrals of Elementary Functions and Integration by Substitution (初等函数的积分，换元法)

--Exercise-5-3

-Unit 4 Integration by Parts and Special Techniques(分部积分法与特殊技巧)

--Integration by Parts and Special Techniques(分部积分法与特殊技巧)

--Exercise-5-4

Chapter 5 Integrals 积分(second part)

-Unit 5 Integrations of Rational Fractions and Trigonometrical Rational Functions(有理分式函数与三角有理函数的积分)

-- Integrations of Rational Fractions and Trigonometrical Rational Functions(有理分式函数与三角有理函数的积分)

--Exercise-5-5

-Unit 6 Arc Length(弧长)

--Arc Length(弧长)

--Exercise-5-6

-Unit 7 Areas and Volumes(面积与体积)

--Areas and Volumes(面积与体积)

--Exercise-5-7

-章节测验5

--章节测试5

课程讲义

-课程讲义

微积分-1开设学校：清华大学

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