《高等数学(下)(英文版)》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)(英文版)》的每一个部分都经过了精细的筛选，力求做到**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，**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)(英文版)》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
……
Chapter 9 The Differential Calculus for Multi-variable Functions
Chapter 10 Applications of Multi-variable Functions
Chapter 11 Multiple Integrals
Chapter 12 Line Integrals and Surface Integrals
Bibliography