微积分学(CALCULUS with Space Analytic Geometry)

出版时间：2001-8-1  出版社：天津大学出版社  作者：张凤玲,张玉环,姚妙新  页数：253  

前言

科学技术的高速发展，特别是互联网的使用，使得知识信息可以跨越国界，实现全球共享，这就要求作为新科技人才培养基地的高等院校，其课程的内容及形式都应有新的发展。本书是根据国内高等学校对数学教学的要求，并参考国外一些优秀的微积分教程而编写的一本英文高等数学教材。在内容的深度及广度方面，它包括了一元函数微积分学、多元函数微积分学、级数及空间解析几何的有关内容，并给出了相关概念在几何、物理及经济方面的应用实例。本书可以作为高等学校科技英语专业的高等数学课程教科书，也可以作为文科类专业采用英文教学的高等数学课程教材。由于本书包括了微积分的所有基本内容，它也可以作为高等学校工科各专业高年级学生及工程技术人员学习科技英语的一本辅助教材，同时可以作为外国留学生学习中文版高等数学课程相关内容的一本对照参考书。本书由张凤玲、姚妙新主编，由张凤玲、姚妙新、张玉环编写。全书共11章。第1～7章是一元函数微积分的内容，第8章是有关级数的内容，第9章是有关空间解析几何的内容，第10～11章是多元函数微积分的内容。每章后面都配有习题，书后附有答案及部分习题的提示。本书作为天津大学教学改革“九五”重点教材，得到了天津大学教务处、出版社、数学系的大力支持，并在编写排版过程中得到了数学系喻文唤、毛云英、杨正方、杨玉芳老师的帮助，在此表示衷心的感谢。

内容概要

　　《微积分学（英文）》是根据国内高等学校对数学教学的要求，并参考国外一些优秀的微积分教程而编写的一本英文高等数学教材。在内容的深度及广度方面，它包括了一元函数微积分学、多元函数微积分学、级数及空间解析几何的有关内容，并给出了相关概念在几何、物理及经济方面的应用实例。　　《微积分学（英文）》可以作为高等学校科技英语专业的高等数学课程教科书，也可以作为文科类专业采用英文教学的高等数学课程教材。

书籍目录

1 Functions1.1 Sets1.1.1 Definition of Set1.1.2 Operations upon Sets1.1.3 The Set of Real Numbers1.2 Functions1.2.1 Definition1.2.2 Some Properties of Functions1.3 Composite Functions and Inverse Functions1.3.1 Composite Functions1.3.2 Inverse Functions1.4 Elementary Functions1.4.1 Constant functions1.4.2 Power functions1.4.3 Exponential functions1.4.4 Logarithmic functions1.4.5 Trigonometric functions1.4.6 Anti-trigonometric functions1.5 Exercises2 Limits and Continuity2.1 Limits of Sequences2.1.1 Definition2.2 Limits of Functions2.2.1 A Limit of a Function f(x) as x Tends to a Real Number xo2.2.2 Limits Involving Infinity2.3 Techniques for Finding Limits2.4 Continuous Functions2.5 Exercises3 The Derivative3.1 Tangent lines and Rates of Change3.2 Definition of Derivative3.3 Differentiation Formulas3.4 Derivatives of Logarithmic Functions3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Derivatives of Inverse Functions and Implicit Differentiation3.8 Higher Derivative3.9 Differentials and Linear Approximations3.9.1 Differentials3.9.2 Linear Approximations3.10 Exercises4 Applications of Derivative4.1 The Mean Value Theorem4.2 Indeterminate Forms and L'HOSPITAL'S Rule4.2.1 The Forms4.2.2 The Forms4.3 Monotonic Functions4.4 Concavity and Points of Inflection4.5 Extrema of Functions4.6 Applications to Economics4.7 Exercises5 Indefinite Integrals5.1 Antiderivatives and the Indefinite Integral5.2 Substitution Rules5.3 Integration by Parts5.4 ExercisesDefinite Integrals6.1 Area and the Definite Integral6.2 Properties of the Definite Integral6.3 The Fundamental Theorem of Calculus6.4 Techniques of Integration6.4.1 Formula for integration by substitution6.4.2 Formula for integration by parts6.5 Improper Integrals6.5.1 Type 1: Infinite Intervals6.5.2 Type 2: Discontinuous Integrand6.6 Exercises7 Applications of Definite Integrals7.1 Area between Curves7.2 Volume7.3 Arc Length7.4 Area of a Surface of Revolution7.5 Work7.6 Applications in Business and Economics7.6.1 Continuous Income Stream7.6.2 Consumers' and Producers Surplus7.7 Exercises8 Series8.1 Numerical Series8.1.1 Fundamental Concepts8.1.2 Elementary Properties8.1.3 Infinite Series of Nonnegative Terms8.1.4 Alternating Series8.1.5 Absolute and Conditional Convergence8.2 Functional Series8.2.1 Power Series8.2.2 Properties of Power Series8.3 Taylor Series8.4 ExercisesVector Algebra and Space Analytic Geometry9.1 Rectangular Coordinates in Space9.2 Vector Algebra9.2.1 Operations of Vectors9.2.2 The Coordinates of a Vector9.2.3 The Scalar Product9.2.4 The Vector Product9.3 The Planes and Lines in Space9.3.1 The Point-Normal Form Equations of a Plane9.3.2 Distance from a Point to a Plane9.3.3 The Angle between Two Planes9.3.4 The General Equation of a Line in Space9.3.5 Equations of a Line9.3.6 The Angle between Two Lines9.4 Equations for a Surface or a Curve9.4.1 The Equation for a Sphere9.4.2 The Equation of a Cylindrical Surface with Generators Paralleling to a Coordinate Axis9.4.3 Equation for the Intersection of Two Curved Surfaces9.4.4 The Parametric Equation of a Space Curve9.4.5 Equation for the Projecting Curve on a Coordinate Plane of a Space Curve9.5 Surfaces of Revolution9.6 Quadratic Surfaces9.6.1 Ellipsoids9.6.2 Hyperboloids of One Sheet9.6.3 Hyperboloids of Two Sheets9.6.4 Quadratic Cones9.6.5 Paraboloids9.6.6 Quadratic Cylinders9.7 Exercises10 Functions of Several Variables10.1 Fundamental Concepts10.2 Limits and Continuity10.3 Partial Derivatives10.4 The Chain Rule10.5 Approximation and Total Differential10.6 Applications of Partial Derivatives10.6.1 Geometric Application10.6.2 Extreme Values of Functions of Two Variables10.7 Exercises11 Multiple Integrals11.1 Double Integrals11.2 Properties of Double Integral11.3 Evaluation of Double Integrals11.4 Triple Integrals11.4.1 The Mass of an Object of Nonhomogeneous Density11.4.2 The Definition of Triple Integral11.4.3 Evaluation of Triple Integrals in Rectangular Coordinates11.5 Exercises

章节摘录

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《微积分学(英文)》由天津大学出版社出版。