北京邮电大学高等数学双语教学组编写的这本《高等数学(下)》是英文版高等数学教材，以6章篇幅，分别介绍了微分方程及其简单应用、解析几何、多元函数的微分及其应用、多元函数的积分及其应用，以及曲线、曲面积分。内容编排和讲解上适当吸收了欧美国家微积分教材的一些优点。适用于高等学校理工科各专业学生的双语教学，同时也可作为其他专业的教材和参考教材。

北京邮电大学高等数学双语教学组编写的《高等数学(下)》为《高等数学》双语教材的第二部分，主要内容包括微分方程及其简单应用、解析几何、多元函数的微分及其应用、多元函数的积分及其应用，以及曲线、曲面积分。

《高等数学(下)》的每一个部分都经过了精细的筛选，力求做到重点突出、层次分明、叙述清楚、深入浅出、简明易懂。全书例题较为丰富，并且每一节之后均配有一定数量的习题。习题分为两个部分，第一部分主要是对基本知识和基本方法的训练，第二部分则主要强调对基本知识和方法的灵活运用能力。《高等数学(下)》适用于高等学校理工科各专业学生的双语教学，同时也可作为其他专业的教材和参考教材。

Chapter 7 Differential equations

 7.1 Basic concepts of differential equations

7.1.1 Examples of differential equations

7.1.2 Basic concepts

7.1.3 Geometric interpretation of the first-order differential equation

 Exercises 7.1

 7.2 First-order differential equations

7.2.1 First-order separable differential equation

7.2.2 Homogeneous first-order equations

7.2.3 Linear first-order equations

7.2.4 Bernoulli's equation

7.2.5 Some other examples that can be reduced to linear first-order equations

 Exercises 7.2

 7.3 Reducible second-order differential equations

 Exercises 7.3

 7.4 Higher-order linear differential equations

7.4.1 Some examples of linear differential equation of higher-order

7.4.2 Structure of solutions of linear differential equations

 Exercises 7.4

 7.5 Higher-order linear equations with constant coefficients

7.5.1 Higher-order homogeneous linear equations with constant coefficients

7.5.2 Higher-order nonhomogeneous linear equations with constant coefficients

 Exercises 7.5

 7.6 Euler's differential equation

 Exercises 7.6

 7.7 Applications of differential equations

 Exercises 7.7

Chapter 8 Vectors and solid analytic geometry

 8.1 Vectors in plane and in space

8.1.1 Vectors

8.1.2 Operations on vectors

8.1.3 Vectors in plane

8.1.4 Rectangular coordinate system

8.1.5 Vectors in space

 Exercises 8.1

Part a

Part b

 8.2 Products of vectors

8.2.1 Scalar product of two vectors

8.2.2 Vector product of two vectors

8.2.3 Triple scalar product of three vectors

8.2.4 Applications of products of vectors

 Exercises 8.2

Part a

Part b

 8.3 Planes and lines in space

8.3.1 Equations of planes

8.3.2 Equations of lines in space

 Exercises 8.3

Part a

Part b

 8.4 Surfaces and space curves

8.4.1 Cylinders

8.4.2 Cones

8.4.3 Surfaces of revolution

8.4.4 Quadric surfaces

8.4.5 Space curves

8.4.6 Cylindrical coordinate system

8.4.7 Spherical coordinate system

 Exercises 8.4

Part a

Part b

Chapter 9 The differential calculus for multi-variable functions

 9.1 Definition of multi-variable functions and their basic properties

9.1.1 Spacer2 andrn

9.1.2 Multi-variable functions

9.1.3 Visualization of multi-variable functions

9.1.4 Limits and continuity of multi-variable functions

 Exercises 9.1

Part a

Part b

 9.2 Partial derivatives and total differentials of multi-variable functior

9.2.1 Partial derivatives

9.2.2 Total differentials

9.2.3 Higher-order partial derivatives

9.2.4 Directional derivatives and the gradient

 Exercises 9.2

Part a

Part b

 9.3 Differentiation of multi-variable composite and implicit functions

9.3.1 Partial derivatives and total differentials of multi-variable composit functions

9.3.2 Differentiation of implicit functions

9.3.3 Differentiation of implicit functions determined by equation systems

 Exercises 9.3

Part a

Part b

Chapter 10 Applications of multi-variable functions

 10.1 Approximate function values by total differential

 10.2 Extreme values of multi-variable functions

10.2.1 Unrestricted extreme values

10.2.2 Global maxima and minima

10.2.3 The method of least squares

10.2.4 Constrained extreme values

10.2.5 The method of lagrange multipliers

 Exercises 10.2

Part a

Part b

 10.3 Applications in geometry

10.3.1 Arc length along a curve

10.3.2 Tangent line and normal plane of a space curve

10.3.3 Tangent planes and normal lines to a surface

10.3.4 Curvature for plane curves

 Exercises 10.3

Part a

Part b

Synthetic Exercises

Chapter 11 Multiple integrals

 11.1 Concept and properties of double integrals

11.1.1 Concept of double integrals

11.1.2 Properties of double integrals

 Exercises 11.1

 11.2 Evaluation of double integrals

11.2.1 Geometric meaning of double integrals

11.2.2 Double integrals in rectangular coordinates

11.2.3 Double integrals in polar coordinates

11.2.4 Integration by substitution for double integrals in general

 Exercises 11.2

Part a

Part b

 11.3 Triple integrals

11.3.1 Concept and properties of triple integrals

11.3.2 Triple integrals in rectangular coordinates

11.3.3 Triple integrals in cylindrical and spherical coordinates

11.3.4 Integration by substitution for triple integrals in general

 Exercises 11.3

Part a

Part b

 11. 4 Applications of multiple integrals

11.4.1 Surface area

11.4.2 The center of gravity

11.4.3 The moment of inertia

 Exercises 11.4

Part a

Part b

Chapter 12 Line integrals and surface integrals

 12.1 Line integrals

12.1.1 Line integrals with respect to arc length

12.1.2 Line integrals with respect to coordinates

12.1.3 Relations between two types of line integrals

 Exercises 12.1

Part a

Part b

 12.2 Green's formula and its applications

12.2.1 Green's formula

12.2.2 Conditions for path independence of line integrals

 Exercises 12.2

Part a

Part b

 12.3 Surface integrals

12.3.1 Surface integrals with respect to surface area

12.3.2 Surface integrals with respect to coordinates

 Exercises 12.3

Part a

Part b

 12.4 Gauss' formula

 Exercises 12.4

Part a

Part b

 12.5 Stokes' formula

12.5.1 Stokes' formula

12.5.2 Conditions for path independence of space line integrals

 Exercises 12.5

Bibliography