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微积分-1

Tsinghua University via XuetangX

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Overview

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“微积分-1”讲授微积分的基础知识，主要内容包括：数集，数列与极限，函数极限，导数与积分，简单微分方程等。授课对象主要是理学、工学本科低年级大学生。本课程的特点是：1）中英文对照，英文为主；2）侧重理解, 应用和计算技能的训练；3）难度适中，面广实用。

Syllabus

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

Unit 1 Review of Real Numbers (回顾实数)
Unit 2 Exponentiations, Logarithms and Sets (指数、对数与集合)
Unit 3 Limit Points, Open and Closed Sets (聚点、开集与闭集)

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

Unit 4 Bounds and Completeness (有界性与完备性)
Unit 5 Complex Number System, Algebraic and Transcendental Numbers (复数、代数数与超越数)
章节测验1

Chapter 2 Sequence 数列 (first part)

Unit 1 Limit of a Sequence (数列的极限)
Unit 2 Theorems on Limits of Sequences (数列极限定理)
Unit 3 Infinity and Bounded Monotone Sequences (无穷大和单调有界数列)

Chapter 2 Sequence 数列 (second part)

Unit 4 Limit Superior and Limit Inferior (上极限和下极限)
Unit 5 Nested Intervals Theorem and Cauchy’s Convergence Criterion (区间套定理和柯西收敛准则)
章节测验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)
Unit 2 Algebraic Function,Transcendental Functions and Inverse Trigonometric Functions (代数函数，超越函数与反三
Unit 3 Hyperbolic Functions and Inverse Hyperbolic Functions (双曲函数与反双曲函数)
Unit 4 Maximum and Minimum, Increasing and Decreasing (极大值与极小值，单调增与单调减)

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)
Unit 6 Infinity (无穷)
Unit 7 Theorems on Limits and Special Limits (极限相关定理与特殊极限)

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

Unit 8 Continuities (连续性)
Unit 9 Theorems on Continuity (关于连续性的定理)
Unit 10 Piecewise Continuity, Uniform Continuity, and Discontinuities (分段连续性，一致连续性与不连续性)
Unit 11 Infinitesimals and Bounded Quantities (无穷小量与有界量)
章节测验3

Chapter 4 Derivatives 导数 (first part)

Unit 1 Basics of Derivatives (导数基本定义)
Unit 2 Differentiability on Intervals, Piecewise Differentiability and Differentials (区间上的可微性，逐段可微性与
Unit 3 Basic Methods of Differentiation (基本求导方法)

Chapter 4 Derivatives 导数 (second part)

Unit 4 Derivatives of Commonly Used Functions (常见函数求导)
Unit 5 Higher Order Derivatives and Mean Value Theorem (高阶导数与中值定理)
Unit 6 L'Hospital's Rules (洛必达法则)

Chapter 4 Derivatives 导数 (last part)

Unit 7 The First and Second Derivative Tests (导数判别法)
Unit 8 The Taylor Formula (泰勒公式)
章节测验 4

Chapter 5 Integrals 积分(first part)

Unit 1 Definite Integrals and Numerical Methods (定积分与数值方法)
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)
Unit 3 Integrals of Elementary Functions and Integration by Substitution (初等函数的积分，换元法)
Unit 4 Integration by Parts and Special Techniques(分部积分法与特殊技巧)

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)
Unit 6 Arc Length(弧长)
Unit 7 Areas and Volumes(面积与体积)
章节测验5

课程讲义

Taught by

Zhuo Chen and

Tags

china

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