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内容推荐 本书是根据“国际本科学术互认课程”(ISEC)项目对高等数学系列课程的要求,同时结合ISEC项目培养模式进行编写的“微积分”双语教材。全书共分4章,内容包括:空间解析几何初步、多元函数的微分、二重积分、无穷级数等。在内容选择上,既考虑到ISEC学生未来学习和发展的需要,又兼顾学生数学学习的实际情况,以适用、够用为原则,切合学生实际,在体系完整的基础上对通常的“微积分”课程内容进行适当的调整,注重明晰数学思想与方法,强调数学知识的应用;在内容阐述上,尽量以案例模式引入,由浅入深,由易到难,循序渐进地加以展开,并且尽量使重点突出,难点分散,便于学生对知识的理解和掌握;在内容呈现上,以英文和中文两种文字进行编写,分左、右栏对应呈现,方便学生学习与理解。 本书既可作为ISEC项目培养模式下“微积分”课程的教材,也可作为普通高等院校“微积分”课程的教学参考书,特别是以英文和中文两种语言学习和理解“微积分”的参考资料。 目录 Chapter 1 Preliminary Analysis of Space Analytic Geometry 第1章 空间解析几何初步 1.1 Vectors and Linear Operations 1.1 向量及线性运算 1.The Concept of Vector 1.向量的概念 2.Linear Operations of Vectors 2.向量的线性运算 3.Space Cartesian Coordinate System 3.空间直角坐标系 1.2 Scalar Product and Cross Product 1.2 数量积与向量积 1.Definition and Operation Law of Scalar Product 1.数量积的定义及运算规律 2.Cartesian Coordinate Operation of Scalar Product 2.数量积的直角坐标运算 3.The Definition and Operation Rule of Cross Product 3.向量积的定义及运算规律 4.Cartesian Coordinate Operation of Cross Product 4.向量积的直角坐标运算 5.The Relationship and Its Judgement of Vectors 5.向量的关系及其判定 1.3 Plane and Its Equation 1.3 平面及其方程 1.Point Normal form Equation of the Plane 1.平面的点法式方程 2.General Equation of the Plane 2.平面的一般式方程 3.Intercept Equation of the Plane 3.平面的截距式方程 4.Three Points Equation of the Plane 4.平面的三点式方程 5.The Angle Between Two Planes and the Positional Relationship 5.两平面的夹角和位置关系 6.Distance from Point to Plane 6.点到平面的距离 1.4 Space Straight Lines and Their Equations 1.4 空间直线及其方程 1.Symmetric Equation of a Straight Line 1.直线的对称式方程 2.Parametric Equation of a Straight Line 2.直线的参数式方程 3.General Equation of a Straight Line 3.直线的一般式方程 4.The General Formula of Linear Equation and Transformation of Symmetric Formula 4.直线方程的一般式与对称式的转化 5.The Angle and Positional Relation Between Two Straight Lines in Space 5.空间中两直线的夹角和位置关系 6.The Angle and Position Relation Between a Line and a Plane 6.直线与平面的夹角和位置关系 7.Distance from Point to Line 7.点到直线的距离 1.5 Quadratic Surfaces and Their Equations 1.5 二次曲面及其方程 1.Spherical Surface 1.球面 2.Ellipsoid 2.椭球面 3.Hyperboloid 3.双曲面 4.Paraboloid 4.抛物面 5.Cylinder 5.柱面 6.Rotating Surface 6.旋转曲面 1.6 Space Curves and Their Equations 1.6 空间曲线及其方程 1.General Equation of Space Curve 1.空间曲线的一般方程 2.Parametric Equation of Space Curve 2.空间曲线的参数方程 3.The Projection of a Space Curve on a Coordinate Surface 3.空间曲线在坐标面上的投影 Exercises 1 习题1 Chapter 2 Derivatives for the Function of Several Variables 第2章 多元函数的微分 2.1 The Basic Concept of the Function of Several Variables 2.1 多元函数的基本概念 1.Planar Point Set 1.平面点集 2.The Concept of the Function of Several Variables 2.多元函数的概念 2.2 Limit and Continuity of the Function of Two Variables 2.2 多元函数的极限与连续性 1.Limit of the Function of Two Variables 1.二元函数的极限 2.Continuity of the Function of Two Variables 2.二元函数的连续性 2.3 Partial Derivatives 2.3 偏导数 1.Concept of the Partial Derivatives 1.偏导数的概念 2.Rule for Finding Partial Derivatives 2.求偏导数的法则 3.Geometric Interpretations of Partial Derivative 3.偏导数的几何解释 4.Partial Derivatives of Higher Order 4.高阶偏导数 5.More than Two Variables 5.多于两个变量的情形 2.4 Total Differential 2.4 全微分 1.The Concept of Total Differential 1.全微分的概念 2.The Application of Total Differential in Approximate Calculation 2.全微分在近似计算中的应用 2.5 The Derivative Rule of Multivariate Composite Function 2.5 多元复合函数的求导法则 2.6 The Derivative Rule of Implicit Function 2.6 隐函数的求导法则 2.7 Local Extremum, Maximum and Minimum 2.7 局部极值,最值 1.Local Extremum 1.局部极值 2.Maximum and Minimum 2.最值 Exercises 2 习题2 Chapter 3 Double Integral |