高等数学（上册 英文版）
作者：北京邮电大学高等数学双语教学组 主编
出版时间：2011年版
内容简介
本书是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编写的全英文教材，全书分为上、下两册，此为上册，主要包括函数与极限，一元函数微积分及其应用和无穷级数三部分。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。本书可作为高等理工科院校非数学类专业本科生的教材，也可供其他专业选用和社会读者阅读。
目录
chapter 0 preliminary knowledge
0.1 polar coordinate system
0.1.1 plotting points with polar coordinates
0.1.2 converting between polar and cartesiancoordinates
0.2 complex numbers
0.2.1 the definition of the complex number
0.2.2 the complex plane
0.2.3 absolute value,conjugation and distance
0.2.4 polar form of complex numbers
chapter 1 theoretical basis of calculus
1.1 sets and functions
1.1.1 sets and their operations
1.1.2 mappings and functions
1.1.3 the primary properties of functions
1.1.4 composition of functions
1.1.5 elementary functions and hyperbolic functions
1.1.6 modeling our real world
exercises 1.1
1.2 limits of sequences of numbers
1.2.1 the sequence
1.2.2 convergence of a sequence
1.2.3 calculating limits of sequences
exercises 1.2
1.3 limits of functions
1.3.1 speed and rates of change
1.3.2 the concept of limit of a function
1.3.3 properties and operation rules of functionallimits
1.3.4 two important limits
exercises 1.3
1.4 infinitesimal and infinite quantities
1.4.1 infinitesimal quantities and their order
1.4.2 infinite quantities
exercises 1.4
1.5 continuous functions
1.5.1 continuous function and discontinuous points
1.5.2 operations on continuous functions and the continuityof elementary functions
1.5.3 properties of continuous functions on a closedinterval
exercises 1.5
chapter 2 derivative and differential
2.1 concept of derivatives
2.1.1 introductory examples
2.1.2 definition of derivatives
2.1.3 geometric interpretation of derivative
2.1.4 relationship between derivability andcontinuity
exercises 2.1
2.2 rules of finding derivatives
2.2.1 derivation rules of rational operations
2.2.2 derivative of inverse functions
2.2.3 derivation rules of composite functions
2.2.4 derivation formulas of fundamental elementaryfunctions
exercises 2.2
2.3 higher-order derivatives
exercises 2.3
2.4 derivation of implicit functions and parametricequations,related rates
2.4.1 derivation of implicit functions
2.4.2 derivation of parametric equations
2.4.3 related rates
exercises 2.4
2.5 differential of the function
2.5.1 concept of the differential
2.5.2 geometric meaning of the differential
2.5.3 differential rules of elementary functions
exercises 2.5
2.6 differential in linear approximate computation
exercises 2.6
chapter 3 the mean value theorem and applications ofderivatives
3.1 the mean value theorem
3.1.1 rolle's theorem
3.1.2 lagrange's theorem
3.1.3 cauchy s theorem
exercises 3.1
3.2 l'hospital's rule
exercises 3.2
3.3 taylor's theorem
3.3.1 taylor's theorem
3.3.2 applications of taylor's theorem
exercises 3.3
3.4 monotonicity and convexity of functions
3.4.1 monotonicity of functions
3.4.2 convexity of functions,inflections
exercises 3.4
3.5 local extreme values,global maxima and minima
3.5.1 local extreme values
3.5.2 global maxima and minima
exercises 3.5
3.6 graphing functions using calculus
exercises 3.6
chapter 4 indefinite integrals
4.1 concepts and properties of indefinite integrals
4.1.1 antiderivatives and indefinite integrals
4.1.2 properties of indefinite integrals
exercises 4.1
4.2 integration by substitution
4.2.1 integration by the first substitution
4.2.2 integration by the second substitution
exercises 4.2
4.3 integration by parts
exercises 4.3
4.4 integration of rational fractions
4.4.1 integration of rational fractions
4.4.2 antiderivatives not expressed by elementaryfunctions
exercises 4.4
chapter 5 definite integrals
5.1 concepts and properties of definite integrals
5.1.1 instances of definite integral problems
5.1.2 the definition of definite integral
5.1.3 properties of definite integrals
exercises 5.1
5.2 the fundamental theorems of calculus
exercises 5.2
5.3 integration by substitution and by parts in definiteintegrals
5.3.1 substitution in definite integrals
5.3.2 integration by parts in definite integrals
exercises 5.3
5.4 improper integral
5.4.1 integration on an infinite interval
5.4.2 improper integrals with infinitediscontinuities
exercises 5.4
5.5 applications of definite integrals
5.5.1 method of setting up elements of integration
5.5.2 the area of a plane region
5.5.3 the arc length of a curve
5.5.4 the volume of a solid
5.5.5 applications of definite integral in physics
exercises 5.5
chapter 6 infinite series
6.1 concepts and properties of series with constantterms
6.1.1 examples of the sum of an infinite sequence)
6.1.2 concepts of series with constant terms
6.1.3 properties of series with constant terms
exercises 6.1
6.2 convergence tests for series with constant terms
6.2.1 convergence tests of series with positive terms
6.2.2 convergence tests for alternating series
6.2.3 absolute and conditional convergence
exercises 6.2
6.3 power series
6.3.1 functional series
6.3.2 power series and their convergence
6.3.3 operations of power series
exercises 6.3
6.4 expansion of functions in power series
6.4.1 taylor and maclaurin series
6.4.2 expansion of functions in power series
6.4.3 applications of power series expansion offunctions
exercises 6.4
6.5 fourier series
6.5.1 orthogonality of the system of trigonometricfunctions
6.5.2 fourier series
6.5.3 convergence of fourier series
6.5.4 sine and cosine series
exercises 6.5
6.6 fourier series of other forms
6.6.1 fourier expansions of periodic functions with period2l
6.6.2 complex form of fourier series
exercises 6.6
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