高等数学(上)（英文版） mobi 下载 fb2 夸克云 azw3 网盘 pdf pmlz

　　本书是在响应东南大学国际化需求, 根据国家*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, 此为上册, 主要包括极限, 一元函数微积分及其应用和常微分方程四部分。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, 例题习题的选配典型多样, 强调基本运算能力的培养及理论的实际应用。

Chapter 1　Limits

　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　

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