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东南大学大学数学教研室 编
出版社: 东南大学出版社 ISBN:9787564151737 版次:1 商品编码:11555086 包装:平装 丛书名: 高等院校双语教学规划教材 外文名称:Advanced Mathematics(1) 开本:16开 出版时间:2014-09-01 用纸:胶版纸 页数:252 字数:319000 正文语种:中文,英文
《高等数学(上 英文版)/高等院校双语教学规划教材》分为上、下两册,内容包括极限、一元函数微分学、一元函数积分学、常微分方程、级数、向鼍代数与空间解析几何、多元函数微分学、多元函数积分学、向量场的积分、复变函数等十个章节。
《高等数学(上 英文版)/高等院校双语教学规划教材》可作为高等理工科院校非数学类专业本科生学习高等数学的英文教材。也可供其他专业选用和社会读者阅读。
1.1 The Concept of Limits and its Properties
1.1.1 Limits of Sequence
1.1.2 Limits of Functions
1.1.3 Properties of Limits
Exercise 1.1
1.2 Limits Theorem
1.2.1 Rules for Finding Limits
1.2.2 The Sandwich Theorem
1.2.3 Monotonic Sequence Theorem
1.2.4 The Cauchy Criterion
Exercise 1.2
1.3 Two Important Special Limits
Exercise 1.3
1.4 Infinitesimal and Infinite
1.4.1 Infinitesimal
1.4.2 Infinite
Exercise 1.4
1.5 Continuous Function
1.5.1 Continuity
1.5.2 Discontinuity
Exercise 1.5
1.6 Theorems about Continuous Function on a Closed Interval
Exercise 1.6
Review and Exercise
Chapter 2 Differentiation
2.1 The Derivative
Exercise 2.1
2.2 Rules for Fingding the Derivative
2.2.1 Derivative of Arithmetic Combination
2.2.2 The Derivative Rule for Inverses
2.2.3 Derivative of Composition
2.2.4 Implicit Differentiation
2.2.5 Parametric Differentiation
2.2.6 Related Rates of Change
Exercise 2.2
2.3 Higher-Order Derivatives
Exercise 2.3
2.4 Differentials
Exercise 2.4
2.5 The Mean Value Theorem
Exercise 2.5
2.6 L'Hospital's Rule
Exercise 2.6
2.7 Taylor's Theorem
Exercise 2.7
2.8 Applications of Derivatives
2.8.1 Monotonicity
2.8.2 Local Extreme Values
2.8.3 Extreme Values
2.8.4 Concavity
2.8.5 Graphing Functions
Exercise 2.8
Review and Exercise
Chapter 3 The Integration
3.1 The Definite Integral
3.1.1 Two Examples
3.1.2 The Definition of Definite Integral
3.1.3 Properties of Definite Integrals
Exercise 3.1
3.2 The Indefinite Integral
Exercise 3.2
3.3 The Fundamental Theorem
3.3.1 First Fundamental Theorem
3.3.2 Second Fundamental Theorem
Exercise 3.3
3.4 Techniques of Indefinite Integration
3.4.1 Substitution in Indefinite Integrals
3.4.2 Indefinite Integration by Parts
3.4.3 Indefinite Integration of Rational Functions by
Partial Fractions
Exercise 3.4
3.5 Techniques of Definite Integration
3.5.1 Substitution in Definite Integrals
3.5.2 Definite Integration by Parts
Exercise 3.5
3.6 Applications of Definite Integrals
3.6.1 Lengths of Plane Curves
3.6.2 Area between Two Curves
3.6.3 Volumes of Solids
3.6.4 Areas of Surface of Revolution
3.6.5 Moments and Center of Mass
3.6.6 Work and Fluid Force
Exercise 3.6
3.7 Improper Integrals
3.7.1 Improper Integrals.Infinite Limits of Integration
3.7.2 Improper Integrals: Infinite Integrands
Exercise 3.7
Review and Exercise
Chapter 4 Differential Equations
4.1 The Concept of Differential Equations
Exercise 4.1
4.2 Differential Equations of the First Order
4.2.1 Equations with Variable Separable
4.2.2 Homogeneous Equation
Exercise 4.2
4.3 First-order Linear Differential Equations
Exercise 4.3
4.4 Equations Reducible to First Order
4.4.1 Equations of the Form y(n)=f(x)
4.4,2 Equations of the Form y =y (x,y )
4.4.3 Equations of the Form y=f(y,y')
Exercise 4.4
4.5 Linear Differential Equations
4.5.1 Basic Theory of Linear Differential Equations
4.5.2 Homogeneous Linear Differential Equations of the
Second Order with Constant Coefficients
4.5.3 Nonhomogeneous Linear Differential Equations of the
Second Order with Constant Coefficients
4.5.4 Euler Differential Equation
Exercise 4.5
4.6 Systems of Linear Differential Equations
with Constant Coefficients
Exercise 4.6
4.7 Applications
Exercise 4.7
Review and Exercise
本书对基本概念的叙述清晰准确,对基本理论的论述简明易懂。在内容处理上依据国内工科类本科数学基础课程教学基本要求,按照现行的国内微积分教材体系结构进行编排,比国外同类教材简洁,理论性更强。同时,本书还兼顾美国教材重视应用、便于自学的特点,例题和习题的选配典型多样,增加了应用内容与相关的实际问题,强调对基本运算能力及理论的实际应用能力的培养。
本教材的内容是工科学生必备大学数学知识,利用英文编写更有利于学生提高与国际同行专家交流的能力。本书可作为高等理工科院校非数学类专业本科生学习高等数学课程的英文教材,也可供其他专业选用和社会读者阅读。
本书上册共四章,其中第一、二章由陈文彦编写,第三章由范赞编写,第四章由马红铝编写,最后由陈文彦统稿。
本书在编写的过程中得到了东南大学教务处的大力支持,数学系的王栓宏教授、卢剑权教授对本教材的编写提出了许多有益的建议,在此一并对他们表示感谢。本书中缺点和错误在所难免,欢迎读者批评指正。
编者
2014年5月
高等数学(上 英文版)/高等院校双语教学规划教材 [Advanced Mathematics(1)] 电子书 下载 mobi epub pdf txt
高等数学(上 英文版)/高等院校双语教学规划教材 [Advanced Mathematics(1)]-so88
高等数学(上 英文版)/高等院校双语教学规划教材 [Advanced Mathematics(1)] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
东南大学大学数学教研室 编
出版社: 东南大学出版社 ISBN:9787564151737 版次:1 商品编码:11555086 包装:平装 丛书名: 高等院校双语教学规划教材 外文名称:Advanced Mathematics(1) 开本:16开 出版时间:2014-09-01 用纸:胶版纸 页数:252 字数:319000 正文语种:中文,英文
内容简介
《高等数学(上 英文版)/高等院校双语教学规划教材》是为响应东南大学国际化需要,根据国家教育部非数学专业数学基础课教学指导分委员会制定的工科类本科数学基础课程教学基本要求,并结合东南大学数学系多年教学改革实践经验编写的全英文教材。《高等数学(上 英文版)/高等院校双语教学规划教材》分为上、下两册,内容包括极限、一元函数微分学、一元函数积分学、常微分方程、级数、向鼍代数与空间解析几何、多元函数微分学、多元函数积分学、向量场的积分、复变函数等十个章节。
《高等数学(上 英文版)/高等院校双语教学规划教材》可作为高等理工科院校非数学类专业本科生学习高等数学的英文教材。也可供其他专业选用和社会读者阅读。
内页插图
目录
Chapter 1 Limits1.1 The Concept of Limits and its Properties
1.1.1 Limits of Sequence
1.1.2 Limits of Functions
1.1.3 Properties of Limits
Exercise 1.1
1.2 Limits Theorem
1.2.1 Rules for Finding Limits
1.2.2 The Sandwich Theorem
1.2.3 Monotonic Sequence Theorem
1.2.4 The Cauchy Criterion
Exercise 1.2
1.3 Two Important Special Limits
Exercise 1.3
1.4 Infinitesimal and Infinite
1.4.1 Infinitesimal
1.4.2 Infinite
Exercise 1.4
1.5 Continuous Function
1.5.1 Continuity
1.5.2 Discontinuity
Exercise 1.5
1.6 Theorems about Continuous Function on a Closed Interval
Exercise 1.6
Review and Exercise
Chapter 2 Differentiation
2.1 The Derivative
Exercise 2.1
2.2 Rules for Fingding the Derivative
2.2.1 Derivative of Arithmetic Combination
2.2.2 The Derivative Rule for Inverses
2.2.3 Derivative of Composition
2.2.4 Implicit Differentiation
2.2.5 Parametric Differentiation
2.2.6 Related Rates of Change
Exercise 2.2
2.3 Higher-Order Derivatives
Exercise 2.3
2.4 Differentials
Exercise 2.4
2.5 The Mean Value Theorem
Exercise 2.5
2.6 L'Hospital's Rule
Exercise 2.6
2.7 Taylor's Theorem
Exercise 2.7
2.8 Applications of Derivatives
2.8.1 Monotonicity
2.8.2 Local Extreme Values
2.8.3 Extreme Values
2.8.4 Concavity
2.8.5 Graphing Functions
Exercise 2.8
Review and Exercise
Chapter 3 The Integration
3.1 The Definite Integral
3.1.1 Two Examples
3.1.2 The Definition of Definite Integral
3.1.3 Properties of Definite Integrals
Exercise 3.1
3.2 The Indefinite Integral
Exercise 3.2
3.3 The Fundamental Theorem
3.3.1 First Fundamental Theorem
3.3.2 Second Fundamental Theorem
Exercise 3.3
3.4 Techniques of Indefinite Integration
3.4.1 Substitution in Indefinite Integrals
3.4.2 Indefinite Integration by Parts
3.4.3 Indefinite Integration of Rational Functions by
Partial Fractions
Exercise 3.4
3.5 Techniques of Definite Integration
3.5.1 Substitution in Definite Integrals
3.5.2 Definite Integration by Parts
Exercise 3.5
3.6 Applications of Definite Integrals
3.6.1 Lengths of Plane Curves
3.6.2 Area between Two Curves
3.6.3 Volumes of Solids
3.6.4 Areas of Surface of Revolution
3.6.5 Moments and Center of Mass
3.6.6 Work and Fluid Force
Exercise 3.6
3.7 Improper Integrals
3.7.1 Improper Integrals.Infinite Limits of Integration
3.7.2 Improper Integrals: Infinite Integrands
Exercise 3.7
Review and Exercise
Chapter 4 Differential Equations
4.1 The Concept of Differential Equations
Exercise 4.1
4.2 Differential Equations of the First Order
4.2.1 Equations with Variable Separable
4.2.2 Homogeneous Equation
Exercise 4.2
4.3 First-order Linear Differential Equations
Exercise 4.3
4.4 Equations Reducible to First Order
4.4.1 Equations of the Form y(n)=f(x)
4.4,2 Equations of the Form y =y (x,y )
4.4.3 Equations of the Form y=f(y,y')
Exercise 4.4
4.5 Linear Differential Equations
4.5.1 Basic Theory of Linear Differential Equations
4.5.2 Homogeneous Linear Differential Equations of the
Second Order with Constant Coefficients
4.5.3 Nonhomogeneous Linear Differential Equations of the
Second Order with Constant Coefficients
4.5.4 Euler Differential Equation
Exercise 4.5
4.6 Systems of Linear Differential Equations
with Constant Coefficients
Exercise 4.6
4.7 Applications
Exercise 4.7
Review and Exercise
前言/序言
本书是为响应东南大学国际化需要,根据国家教育部非数学专业数学基础课教学指导分委员会制定的工科类本科数学基础课程教学基本要求,并结合东南大学数学系多年教学改革实践经验编写的全英文教材。全书分为上、下两册,内容包括极限、一元函数微分学、一元函数积分学、常微分方程、级数、向量代数与空间解析几何、多元函数微分学、多元函数积分学、向量场的积分、复变函数等十个章节。本书对基本概念的叙述清晰准确,对基本理论的论述简明易懂。在内容处理上依据国内工科类本科数学基础课程教学基本要求,按照现行的国内微积分教材体系结构进行编排,比国外同类教材简洁,理论性更强。同时,本书还兼顾美国教材重视应用、便于自学的特点,例题和习题的选配典型多样,增加了应用内容与相关的实际问题,强调对基本运算能力及理论的实际应用能力的培养。
本教材的内容是工科学生必备大学数学知识,利用英文编写更有利于学生提高与国际同行专家交流的能力。本书可作为高等理工科院校非数学类专业本科生学习高等数学课程的英文教材,也可供其他专业选用和社会读者阅读。
本书上册共四章,其中第一、二章由陈文彦编写,第三章由范赞编写,第四章由马红铝编写,最后由陈文彦统稿。
本书在编写的过程中得到了东南大学教务处的大力支持,数学系的王栓宏教授、卢剑权教授对本教材的编写提出了许多有益的建议,在此一并对他们表示感谢。本书中缺点和错误在所难免,欢迎读者批评指正。
编者
2014年5月
高等数学(上 英文版)/高等院校双语教学规划教材 [Advanced Mathematics(1)] 电子书 下载 mobi epub pdf txt
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