微积分-2

Overview

“微积分-2”讲授微积分的基础知识，主要内容包括：级数，幂级数，傅立叶级数，多元函数微积分，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。
Calculus-2 teaches foundations of calculus. The main contents are: series, power series, Fourier series, multivariable functions and their calculus, and ODEs， etc. The features of this course are:
1) Chinese-English based;
2) Focus on comprehension, applications, and practical stills;
3) Moderate difficulty with a vast range of contents.

Syllabus

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)

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）

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)

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)

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)

Taught by

Zhuo Chen and

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Tags

数学分析II

数学分析II

微积分-1

工科数学分析（二）

微积分——多元函数与重积分

微积分（下）

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