微积分-1（2016春）

微积分-1（2016春）

Course
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Chinese
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  • From www.xuetangx.com
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  • Introductive Level
  • Starts on February 21, 2016

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Course details

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，超越函数与反三角函数)
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，逐段可微性与微分)
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

Prerequisite

None.

Instructors

  • 陈酌

Platform

Founded by Tsinghua University in October 2013, XuetangX is the world’s first Chinese MOOC platform and serves as the research and application platform for the Ministry of Education (MOE) Research Center for Online Education. XuetangX has been awarded as one of the national first batch of demonstration base projects for innovation and entrepreneurship. Besides, XuetangX also works with the International Center for Engineering Education (ICEE) under the auspices of UNESCO and supports its online portion. By the end of June 2018, with a total of 25 million enrollments and more than 1,500 online courses from 13 disciplined fields, XuetangX has accumulated over 12 million registered users, covering 209 countries and regions.

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