微積分學(xué)(CALCULUS with Space Analytic Geometry)

前言

科學(xué)技術(shù)的高速發(fā)展，特別是互聯(lián)網(wǎng)的使用，使得知識(shí)信息可以跨越國(guó)界，實(shí)現(xiàn)全球共享，這就要求作為新科技人才培養(yǎng)基地的高等院校，其課程的內(nèi)容及形式都應(yīng)有新的發(fā)展。本書是根據(jù)國(guó)內(nèi)高等學(xué)校對(duì)數(shù)學(xué)教學(xué)的要求，并參考國(guó)外一些優(yōu)秀的微積分教程而編寫的一本英文高等數(shù)學(xué)教材。在內(nèi)容的深度及廣度方面，它包括了一元函數(shù)微積分學(xué)、多元函數(shù)微積分學(xué)、級(jí)數(shù)及空間解析幾何的有關(guān)內(nèi)容，并給出了相關(guān)概念在幾何、物理及經(jīng)濟(jì)方面的應(yīng)用實(shí)例。本書可以作為高等學(xué)?？萍加⒄Z(yǔ)專業(yè)的高等數(shù)學(xué)課程教科書，也可以作為文科類專業(yè)采用英文教學(xué)的高等數(shù)學(xué)課程教材。由于本書包括了微積分的所有基本內(nèi)容，它也可以作為高等學(xué)校工科各專業(yè)高年級(jí)學(xué)生及工程技術(shù)人員學(xué)習(xí)科技英語(yǔ)的一本輔助教材，同時(shí)可以作為外國(guó)留學(xué)生學(xué)習(xí)中文版高等數(shù)學(xué)課程相關(guān)內(nèi)容的一本對(duì)照參考書。本書由張鳳玲、姚妙新主編，由張鳳玲、姚妙新、張玉環(huán)編寫。全書共11章。第1～7章是一元函數(shù)微積分的內(nèi)容，第8章是有關(guān)級(jí)數(shù)的內(nèi)容，第9章是有關(guān)空間解析幾何的內(nèi)容，第10～11章是多元函數(shù)微積分的內(nèi)容。每章后面都配有習(xí)題，書后附有答案及部分習(xí)題的提示。本書作為天津大學(xué)教學(xué)改革“九五”重點(diǎn)教材，得到了天津大學(xué)教務(wù)處、出版社、數(shù)學(xué)系的大力支持，并在編寫排版過(guò)程中得到了數(shù)學(xué)系喻文喚、毛云英、楊正方、楊玉芳老師的幫助，在此表示衷心的感謝。

內(nèi)容概要

　　《微積分學(xué)（英文）》是根據(jù)國(guó)內(nèi)高等學(xué)校對(duì)數(shù)學(xué)教學(xué)的要求，并參考國(guó)外一些優(yōu)秀的微積分教程而編寫的一本英文高等數(shù)學(xué)教材。在內(nèi)容的深度及廣度方面，它包括了一元函數(shù)微積分學(xué)、多元函數(shù)微積分學(xué)、級(jí)數(shù)及空間解析幾何的有關(guān)內(nèi)容，并給出了相關(guān)概念在幾何、物理及經(jīng)濟(jì)方面的應(yīng)用實(shí)例?！　　段⒎e分學(xué)（英文）》可以作為高等學(xué)?？萍加⒄Z(yǔ)專業(yè)的高等數(shù)學(xué)課程教科書，也可以作為文科類專業(yè)采用英文教學(xué)的高等數(shù)學(xué)課程教材。

書籍目錄

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

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