This book systematically introduces some of the main contents of calculus．It consists of six chapters，including vectors and the geometry of space，partial derivatives，multiple integrals，line integralsand surface integrals，infinite series and differential equations．We try to assure that the content of thetextbook easy to understand．In addition，we focus on introducing basic ideas and methods，in order tofacilitate teaching and selLstudy．At the end of each section and each chapter，we arrange exercises forstudents to consolidate their knowledge and review． This book can be used as a textbook or reference book for international undergraduates majoring science and technology in colleges and universities，as well as for Chinese undergraduates who are interestedin calculus in English．
作者介紹
編者:付乳燕//田記//姚香娟//王林林|責編:李長波//龐亭亭
目錄
Chapter 1 Vectors and the Geometry of Space 1.1 Three Dimensional Coordinate System 1.2 Vectors 1.3 The Dot Product 1.4 The Cross Product 1.5 Equations of Lines and Planes in Space 1.6 Cylinders and Quadric Surfaces Chapter 1 Review Chapter 2 Partial Derivatives 2.1 Functions of Several Variables 2.2 Partial Derivatives 2.3 The Chain Rule 2.4 Directional Derivatives and Gradient Vectors 2.5 Geometric Application of Differentiation Calculus of Multivariable Functions 2.6 Maximum and Minimum Values Chapter 2 Review Chapter 3 Multiple Integrals 3.1 Double Integrals over Rectangles 3.2 Iterated Integrals 3.3 Double Integrals over General Regions 3.4 Double Integrals in Polar Coordinates 3.5 Triple Integrals 3.6 Triple Integrals in Cylindrical Coordinates 3.7 Triple Integrals in Spherical Coordinates Chapter 3 Review Chapter 4 Line Integrals and Surface Integrals 4.1 Line Integrals with Respect to Arc Length 4.2 Line Integrals with Respect to z and y 4.3 Green』s Theorem 4.4 IndeDendence of Path 4.5 Surface Integrals Chapter 4 Review Chapter 5 Infinite Series 5.1 Sequences 5.2 Series 5.3 Convergence Test of Constant—term Series 5.4 Absolute Convergence and the Ratio and Root Tests 5.5 Power Series 5.6 ReDresentations of Functions as Power Series Chapter 5 Review Chapter 6 Differential Equations 6.1 Basic Concepts of Differential Equations 6.2 Separable Equations 6.3 Homogeneous Equations 6.4 Linear Equations 6.5 Second-order Linear Homogeneous Equations 6.6 Second order Linear Nonhomogeneous Equations Chapter 6 Review References
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