微积分-2（2016春）

微积分-2（2016春）

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  • 从21 二月 2016开始

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课程详情

教学大纲

Chapter 1 Improper Integrals 广义积分 (first part)
Introduction (课程介绍)
Unit 1 Definition of Improper Integrals (广义积分的定义)(section 1)
Unit 1 Definition of Improper Integrals (广义积分的定义)(section 2)
Unit 2 Examples of Improper Integrals (广义积分的例子)
Chapter 1 Improper Integrals 广义积分 (second part)
Unit 3 Tests of Convergence(收敛性判别)(section 1)
Unit 3 Tests of Convergence(收敛性判别)(section 2)
Unit 4 Absolute Convergence and Conditional Convergence (绝对收敛和条件收敛)
章节测验1
Chapter 2 Infinite Series 无穷级数(first part)
Unit 1 Infinite Series and Their Convergence（无穷级数及其收敛性）
Unit 2 Absolute Convergence and Conditional Convergence （绝对收敛与条件收敛）
Unit 3 More Tests for Convergence (更多的收敛性判别法)（section 1）
Unit 3 More Tests for Convergence (更多的收敛性判别法)（section 2）
Unit 3 More Tests for Convergence (更多的收敛性判别法)（section 3）
Chapter 2 Infinite Series 无穷级数 (second part)
Unit 4 Sequences and Series of Founctions(函数项数列与函数项级数)（section 1）
Unit 4 Sequences and Series of Founctions(函数项数列与函数项级数)（section 2）
Unit 5 Uniform Convergence(一致收敛性)（section 1）
Unit 5 Uniform Convergence(一致收敛性)（section 2）
章节测验 2
Chapter 3 Power Series and Fourier Series 幂级数和Fourier级数 (first part)
Unit 1 Power Series (幂级数)(section 1)
Unit 1 Power Series (幂级数）(section 2)
Unit 2 Expansion of Functions in Power Series (函数的幂级数展开)
Unit 3 Fourier Expansion (Fourier级数展开) (section 1)
Unit 3 Fourier Expansion (Fourier级数展开) (section 2)
Chapter 3 Power Series and Fourier Series 幂级数和Fourier级数 (second part)
Unit 4 Convergence of Fourier Series(Fourier 级数的收敛性)(section 1)
Unit 4 Convergence of Fourier Series(Fourier 级数的收敛性)(section 2)
Unit 5 Other Forms of Fourier Series(其他形式的Fourier级数)
章节测验 3
Chapter 4 Differentiations of Multivariable Functions 多元函数微分学 (first part)
Unit 1 Euclidean Space (欧几里德空间) (section 1)
Unit 1 Euclidean Space (欧几里德空间) (section 2)
Unit 1 Euclidean Space (欧几里德空间) (section 3)
Unit 2 Curves and Surfaces (曲线与曲面) (section 1)
Unit 2 Curves and Surfaces (曲线与曲面) (section 2)
Unit 2 Curves and Surfaces (曲线与曲面) (section 3)
Unit 3 Point-Set Topology of E3 (E3中的点集拓扑) (section 1)
Unit 3 Point-Set Topology of E3 (E3中的点集拓扑) (section 2)
Unit 3 Point-Set Topology of E3 (E3中的点集拓扑) (section 3)
Chapter 4 Differentiations of Multivariable Functions 多元函数微分学 (second part)
Unit 4 Completeness and Connectness (完备性与连通性) (section 1)
Unit 4 Completeness and Connectness (完备性与连通性) (section 2)
Unit 5 Continuous Multivariable Functions (连续多元函数) (section 1)
Unit 5 Continuous Multivariable Functions (连续多元函数) (section 2)
Unit 5 Continuous Multivariable Functions (连续多元函数) (section 3)
Chapter 4 Differentiations of Multivariable Functions 多元函数微分学 (third part)
Unit 6 Partial Derivatives and Differentiability (偏导数与可微性) (section 1)
Unit 6 Partial Derivatives and Differentiability (偏导数与可微性) (section 2)
Unit 6 Partial Derivatives and Differentiability (偏导数与可微性) (section 3)
Unit 7 Jacobian Matrix and Directional Derivatives (雅克比矩阵与方向导数) (section 1)
Unit 7 Jacobian Matrix and Directional Derivatives (雅克比矩阵与方向导数) (section 2)
Unit 7 Jacobian Matrix and Directional Derivatives (雅克比矩阵与方向导数) (section 3)
Unit 7 Jacobian Matrix and Directional Derivatives (雅克比矩阵与方向导数) (section 4)
Chapter 4 Differentiations of Multivariable Functions 多元函数微分学 (fourth part)
Unit 8 Taylor's Theorem (泰勒定理) (section 1)
Unit 8 Taylor's Theorem (泰勒定理) (section 2)
Unit 8 Taylor's Theorem (泰勒定理) (section 3)
Unit 9 Applications of Gradients (梯度的应用) (section 1)
Unit 9 Applications of Gradients (梯度的应用) (section 2)
章节测验4
Chapter 5 Multiple Integrals 重积分 (first part)
Unit 1 Multiple Integrals (重积分) (section 1)
Unit 1 Multiple Integrals (重积分) (section 2)
Unit 1 Multiple Integrals (重积分) (section 3)
Unit 2 Triple Integrals (三重积分) (section 1)
Unit 2 Triple Integrals (三重积分) (section 2)
Unit 2 Triple Integrals (三重积分) (section 3)
Unit 3 Line Integrals (曲线积分) (section 1)
Unit 3 Line Integrals (曲线积分) (section 2)
Chapter 5 Multiple Integrals 重积分 (second part)
Unit 4 Surface Integrals (I) (第一型曲面积分) (section 1)
Unit 4 Surface Integrals (I) (第一型曲面积分) (section 2)
Unit 4 Surface Integrals (I) (第一型曲面积分) (section 3)
Unit 5 Surface Integrals (II) (第二型曲面积分) (section 1)
Unit 5 Surface Integrals (II) (第二型曲面积分) (section 2)
Unit 5 Surface Integrals (II) (第二型曲面积分) (section 3)
Chapter 5 Multiple Integrals 重积分 (last part)
Unit 6 Some Theorems of Line and Surface Integrals (曲线与曲面积分的几个定理) (section 1)
Unit 6 Some Theorems of Line and Surface Integrals (曲线与曲面积分的几个定理) (section 2)
Unit 6 Some Theorems of Line and Surface Integrals (曲线与曲面积分的几个定理) (section 3)
Unit 6 Some Theorems of Line and Surface Integrals (曲线与曲面积分的几个定理) (section 4)
Unit 7 Field Theory (场论) (section 1)
Unit 7 Field Theory (场论) (section 2)
Unit 7 Field Theory (场论) (section 3)
Unit 7 Field Theory (场论) (section 4)
章节测验5

先决条件

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讲师

  • 陈酌

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慕华（北京）网络技术有限公司旗下的学堂在线是免费公开的MOOC（大规模开放在线课程）平台，是教育部在线教育研究中心的研究交流和成果应用平台，致力于通过来自国内外一流名校开设的免费网络学习课程，为公众提供系统的高等教育，让每一个中国人都有机会享受优质教育资源。通过和清华大学在线教育研究中心、以及国内外知名大学的紧密合作，学堂在线将不断增加课程的种类和丰富程度。

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