本书以高等学校非数学专业本科生高等数学课程教学大纲为依据，参考多种国外原版教材，以使语言表述准确、地道；在章节顺序和内容上参照大连理工大学应用数学系组编的《工科微积分》中文教材进行编写，涵盖了高等数学课程中的主要的数学概念、常见的专业词汇、重要的定理；为使学生在习惯用英文进行专业思考的同时，又熟悉相应的中文用语，在每章节列出了用中文书写的章节重点内容概述、关键单词和短语。其目的是为讲授高等数学的教师和学习高等数学的学生提供掌握相关内容的英文描述服务，进而使得学生学过本课程后，能够独立阅读相关的英文教材和文献。可作为学生的配套教材和扩大知识领域的参考书，也可作为科技英语专业高等数学课程的参考书。

5 Vector Algebra and Analytic Geometry in Space

 5.0 Citing examples

 5.1 Vectors and its operations

Key points of this section

单词和短语

5.1.1 Cpncept of vectors

5.1.2 Linear operations of vectors

5.1.3 Scalar products of vectors(dot product, inner product)

5.1.4 Vector products of vectors(cross product, outer product)

5.1.5 Mixed products of vectors

5.1.6 Summarization of solving methods and typical examples

 5.2 Coordinates of points and coordinates of vectors

Key points of this section

单词和短语

5.2.1 Rectangular coordinate systems in space

5.2.2 Coordinate representation of operations on vectors

5.2.3 Summarization of solving methods and typical examples

 5.3 Planes and lines in space

Key points of this section

单词和短语

5.3.1 Plane

5.3.2 Line

5.3.3 The position relations among points, planes and lines

5.3.4 Summarization of solving methods and typical examples

 5.4 Surface and curve

Key points of this section

单词和短语

5.4.1 Equations of surfaces and curves

5.4.2 Cylinder, surface of revolution and cone

5.4.3 Quadric surface

5.4.4 Summarization of solving methods and typical examples

 Exercises

6 Differential Calculus of Multivariable Functions and its Applications

 6.0 Citing examples

 6.1 The basic concepts of functions of several variables

Key points of this section

单词和短语

6.1.1 n-dimensional point set

6.1.2 Definition of function of several variables

6.1.3 Limit of function of two variables

6.1.4 Continuity of function of two variables

6.1.5 Summarization of solving methods and typical examples

 6.2 Partial derivative and higher partial derivative

Key points of this section

单词和短语

6.2.1 Partial derivative

6.2.2 Higher partial derivative

6.2.3 Summarization of solving methods and typical examples

 6.3 Total differential and its applications

Key points of this section

单词和短语

6.3.1 Definition of total differential

6.3.2 Relation between differentiability and partial derivability

6.3.3 Geometric meaning of total differential

6.3.4 Applications of total differential

6.3.5 Summarization of solving methods and typieal examples

 6.4 Differentiation of composite functions of several variables

Key points of this section

单词和短语

6.4.1 Chain rule

6.4.2 Invariance of total differential form

6.4.3 Derivative rule for implicit functions

6.4.4 Summarization of solving methods and typical examples

6.5 Applications for partial derivatives in geometry

Key points of this section

单词和短语

6.5.1 Tangent line and normal plane for space curve

6.5.2 Tangent plane and normal line of the surface

6.5.3 Summarization of solving methods and typical examples

 6.6 Extrernum of multivariable functions

Key points of this section

单词和短语

6.6.1 Extreme value,global maximum,global minimum of multivariable functions

6.6.2 Conditional extremum Lagrange multiplier method

6.6.3 Summarization of solving methods and typical examples

 6.7 Directional derivative and gradient

Key points of this section

单词和短语

6.7.1 Directional derivative

6.7.2 Gradient of scalar field

6.7.3 Summarization of solving methods and typical examples

 Exercises

7 Integral Calculus of Multivariable Scalar Functions

 7.0 Citing examples

 7.1 Concept and properties of integral for multivariable scalar functions

Key points of this section

单词和短语

7.1.1 The concept of integral of multivariable scalar functions

7.1.2 Properties of integral of multivariable scalar functions

7.1.3 The classifications of the integral for multivariable scalar functions

 7.2 Evaluation for double integral

Key points of this section

单词和短语

7.2.1 The evaluation of double integral under Kectangular coordinate system

7.2.2 The evaluation of double integral under polar coordinate system

7.2.3 Change of variables in double integral

7.2.4 Summarization of solving methods and typical examples

 7.3 The evaluation of triple integral

Key points of this section

单词和短语

7.3.1 The evaluation of triple integral under rectangluar coordinate system

7.3.2 Evaluation for triple integral in cylindrical and spherical coordinates

7.3.3 Summarization of solving methods and typical examples

 7.4 The evaluations of line and surface integral for scalar value functions

Key points of this section

单词和短语

7.4.1 The evaluations of line integral with the first form

7.4.2 The evaluations of surface integral with the first form

7.4.3 Summarization of solving methods and typieal examples

 7.5 Some typical applications of integrals of scalar valued functions in geometry and physics

Key points of this section

单词和短语

 Exercises

8 Line Integrals and Surface Integrals of Vector Functions

 8.0 Citing example

 8.1 Integrals of vector functions on directional curves

Key points of this section

单词和短语

8.1.1 Vector field

8.1.2 Concept of line integrals of the second form

8.1.3 Computation of the line integrals 0[ the second form

8.1.4 Summarization of solving method and typical examples

 8.2 Integrals of vector functions on oriented surface

Key points of this section

单词和短语

8.2.1 Lateral of surface

8.2.2 The concept of the surface integrals Of the second form

8.2.3 Computation of the surface integrals of the second form

8.2.4 Summarization of ,solving method and typical examples

 8.3 Relationships among iterated integral, line integral and surface integral

Key points of this section

单词和短语

8.3.1 Summarization of solving method and typical examples

 8.4 Conditions for line integral independent of path Key points of this section

8.4.1 Condition for line integral independent of path

8.4.2 Summarization of solving method and typical examples

 8.5 Introduction to field theory

Key points of this section

单词和短语

8.5.1 Summarization of solving method and typical examples

 8.6 Applications

 Exercises

9 Infinite Series

 9.0 Citing examples

 9.1 Series of number terms

Key points of this section

单词和短语

9.1.1 Concepts and basic properties of series of number terms

9.1.2 Summary of solving methods and typical examples

 9.2 Tests for convergence or divergence of positive terms series

Key points of this section

单词和短语

9.2.1 Convergence or divergence for positive terms series

9.2.2 Comparison test

9.2.3 Ratio test

9.2.4 Root test

9.2.5 Integral test

9.2.6 Summarization of solving method and typical examples

 9.3 Tests for Convergence or divergence of series with any terms

Key points of this section

单词和短语

9.3.1 Tests for convergence or divergence of alternating series

9.3.2 Absolute convergence and conditional conv, ergence

9.3.3 Summarization of solving method and typical examples

 9.4 Power series

Key points of this section

单词和短语

9.4.1 Basic conceptes of series with function terms

9.4.2 Power series and its convergence domain

9.4.3 Operations and properties of power series

9.4.4 Summarization of solving method and typical examples

 9.5 Fourier series

Key points of this section

单词和短语

9.5.1 Fourier series of function with the period 2π

9.5.2 Fourier series of function with the period 2l

9.5.3 Fourier expansion of functions defined on 1 [-l,l-]

9.5.4 Summarization of solving method and typical examples

Exercises

References