| 5Vector Algebra and Analytic Geometry in Space 5.0Citing examples 5.1Vectors and its operations Key points of this section 单词和短语 5.1.1Cpncept of vectors 5.1.2Linear operations of vectors 5.1.3Scalar products of vectors(dot product, inner product) 5.1.4Vector products of vectors(cross product, outer product) 5.1.5Mixed products of vectors 5.1.6Summarization of solving methods and typical examples 5.2Coordinates of points and coordinates of vectors Key points of this section 单词和短语 5.2.1Rectangular coordinate systems in space 5.2.2Coordinate representation of operations on vectors 5.2.3Summarization of solving methods and typical examples 5.3Planes and lines in space Key points of this section 单词和短语 5.3.1Plane 5.3.2Line 5.3.3The position relations among points, planes and lines 5.3.4Summarization of solving methods and typical examples 5.4Surface and curve Key points of this section 单词和短语 5.4.1Equations of surfaces and curves 5.4.2Cylinder, surface of revolution and cone 5.4.3Quadric surface 5.4.4Summarization of solving methods and typical examples Exercises 6Differential Calculus of Multivariable Functions and its Applications 6.0Citing examples 6.1The basic concepts of functions of several variables Key points of this section 单词和短语 6.1.1n-dimensional point set 6.1.2Definition of function of several variables 6.1.3Limit of function of two variables 6.1.4Continuity of function of two variables 6.1.5Summarization of solving methods and typical examples 6.2Partial derivative and higher partial derivative Key points of this section 单词和短语 6.2.1Partial derivative 6.2.2 Higher partial derivative 6.2.3Summarization of solving methods and typical examples 6.3Total differential and its applications Key points of this section 单词和短语 6.3.1Definition of total differential 6.3.2Relation between differentiability and partial derivability 6.3.3Geometric meaning of total differential 6.3.4Applications of total differential 6.3.5Summarization of solving methods and typieal examples 6.4Differentiation of composite functions of several variables Key points of this section 单词和短语 6.4.1Chain rule 6.4.2Invariance of total differential form 6.4.3Derivative rule for implicit functions 6.4.4Summarization of solving methods and typical examples 6.5Applications for partial derivatives in geometry Key points of this section 单词和短语 6.5.1Tangent line and normal plane for space curve 6.5.2Tangent plane and normal line of the surface 6.5.3Summarization of solving methods and typical examples 6.6Extrernum of multivariable functions Key points of this section 单词和短语 6.6.1Extreme value,global maximum,global minimum of multivariable functions 6.6.2Conditional extremumLagrange multiplier method 6.6.3Summarization of solving methods and typical examples 6.7Directional derivative and gradient Key points of this section 单词和短语 6.7.1Directional derivative 6.7.2Gradient of scalar field 6.7.3Summarization of solving methods and typical examples Exercises 7Integral Calculus of Multivariable Scalar Functions 7.0Citing examples 7.1Concept and properties of integral for multivariable scalar functions Key points of this section 单词和短语 7.1.1The concept of integral of multivariable scalar functions 7.1.2Properties of integral of multivariable scalar functions 7.1.3The classifications of the integral for multivariable scalar functions 7.2Evaluation for double integral Key points of this section 单词和短语 7.2.1The evaluation of double integral under Kectangular coordinate system 7.2.2The evaluation of double integral under polar coordinate system 7.2.3Change of variables in double integral 7.2.4Summarization of solving methods and typical examples 7.3The evaluation of triple integral Key points of this section 单词和短语 7.3.1The evaluation of triple integral under rectangluar coordinate system 7.3.2Evaluation for triple integral in cylindrical and spherical coordinates 7.3.3Summarization of solving methods and typical examples 7.4The evaluations of line and surface integral for scalar value functions Key points of this section 单词和短语 7.4.1The evaluations of line integral with the first form 7.4.2The evaluations of surface integral with the first form 7.4.3Summarization of solving methods and typieal examples 7.5Some typical applications of integrals of scalar valued functions in geometry and physics Key points of this section 单词和短语 Exercises 8Line Integrals and Surface Integrals of Vector Functions 8.0Citing example 8.1Integrals of vector functions on directional curves Key points of this section 单词和短语 8.1.1Vector field 8.1.2Concept of line integrals of the second form 8.1.3Computation of the line integrals 0[ the second form 8.1.4Summarization of solving method and typical examples 8.2Integrals of vector functions on oriented surface Key points of this section 单词和短语 8.2.1Lateral of surface 8.2.2The concept of the surface integrals Of the second form 8.2.3Computation of the surface integrals of the second form 8.2.4Summarization of ,solving method and typical examples 8.3Relationships among iterated integral, line integral and surface integral Key points of this section 单词和短语 8.3.1Summarization of solving method and typical examples 8.4Conditions for line integral independent of path Key points of this section 8.4.1Condition for line integral independent of path 8.4.2Summarization of solving method and typical examples 8.5Introduction to field theory Key points of this section 单词和短语 8.5.1Summarization of solving method and typical examples 8.6Applications Exercises 9Infinite Series 9.0Citing examples 9.1Series of number terms Key points of this section 单词和短语 9.1.1Concepts and basic properties of series of number terms 9.1.2Summary of solving methods and typical examples 9.2Tests for convergence or divergence of positive terms series Key points of this section 单词和短语 9.2.1Convergence or divergence for positive terms series 9.2.2Comparison test 9.2.3Ratio test 9.2.4Root test 9.2.5Integral test 9.2.6Summarization of solving method and typical examples 9.3Tests for Convergence or divergence of series with any terms Key points of this section 单词和短语 9.3.1Tests for convergence or divergence of alternating series 9.3.2Absolute convergence and conditional conv, ergence 9.3.3Summarization of solving method and typical examples 9.4Power series Key points of this section 单词和短语 9.4.1Basic conceptes of series with function terms 9.4.2Power series and its convergence domain 9.4.3Operations and properties of power series 9.4.4Summarization of solving method and typical examples 9.5Fourier series Key points of this section 单词和短语 9.5.1Fourier series of function with the period 2π 9.5.2Fourier series of function with the period 2l 9.5.3Fourier expansion of functions defined on 1 [-l,l-] 9.5.4Summarization of solving method and typical examples Exercises References |
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