本页根据申请人提供的雨课堂资料整理，保留原始截图供核对；并非学校发布的教学大纲或课程等效认定。
Higher Mathematics E(1)
The topics below are transcribed and grouped from the supplied Rain Classroom activity list. Repeated teaching sessions and administrative notices have been omitted.
| Topic summary | 截图中的课程主题（归并） |
|---|---|
| Functions: concepts, properties and common functions | 函数的概念及基本性质；常见函数 |
| Limits of functions and limit laws | 函数的极限；极限的性质及运算法则 |
| Examples in economics and management; continuity | 经济管理中的例子；函数的连续性 |
| Derivatives, differentiation rules and differentials | 导数概念；求导法则；微分 |
| Mean value theorem and L’Hôpital’s rule | 中值定理；洛必达法则 |
| Monotonicity, extrema, concavity and curve sketching | 函数的单调性与极值；凹凸性与函数作图 |
| Definite integrals and the fundamental theorem of calculus | 定积分概念及基本性质；微积分基本定理 |
| Integration methods and geometric applications of definite integrals | 基本积分法；定积分在几何学中的应用 |
Open original first-semester screenshot
View source screenshot / 查看原始截图
Higher Mathematics E(2)
The following summary is based on four readable Rain Classroom screenshots supplied by the applicant as the E(2) course record. The activity list and online modules use different chapter numbering; their labels are preserved separately. These are course-content records, not a university-issued syllabus.
Classroom activity topics / 课堂主题
| Source label and topic | 课程主题 |
|---|---|
Vector algebra and solid analytic geometry; planes, lines, quadric surfaces and space curves | 向量代数与空间解析几何；空间平面与直线；常见二次曲面与空间曲线 |
Functions of several variables: concepts, limits and continuity | 多元函数的概念、极限与连续性 |
Partial derivatives and total differentials | 偏导数；全微分 |
Applications of multivariable differential calculus | 多元函数微分学的应用 |
Double integrals: concepts, properties, evaluation and applications | 二重积分的概念、性质、计算方法及应用 |
Numerical series: concepts and properties | 常数项级数的概念与性质 |
Positive-term series | 正项级数 |
Series with terms of arbitrary sign | 任意项级数 |
Power series | 幂级数 |
Basic concepts of differential equations | 微分方程的基本概念 |
Homogeneous equations; first-order linear differential equations | 齐次方程；一阶线性微分方程 |
Second-order differential equations | 二阶微分方程 |
Differences and difference equations; first-order linear difference equations with constant coefficients | 差分与差分方程的概念；常系数一阶线性差分方程 |
Expanded online-module topics / 展开线上章节内容
Module 1 · Vector algebra and solid analytic geometry
| Topic detail | 章节内容（归并） |
|---|---|
| Cartesian coordinates in space; vectors, linear operations and coordinate representations | 空间直角坐标系；向量的概念、线性运算与坐标表示 |
| Vector magnitude and direction cosines; dot and cross products and their coordinate forms | 向量的模与方向余弦；数量积、向量积及坐标计算 |
| Conditions for perpendicular and parallel vectors; equations of planes and lines; angles | 向量垂直与平行的条件；平面、直线方程及夹角 |
| Spheres, cylinders, surfaces of revolution, quadric surfaces and space curves | 球面、柱面、旋转曲面、二次曲面与空间曲线 |
Module 2 · Multivariable differential calculus
| Topic detail | 章节内容（归并） |
|---|---|
| Planar point sets; definitions, graphs, limits and continuity of functions of two variables | 平面点集；二元函数的定义、图形、极限与连续性 |
| Partial derivatives and their meaning; derivatives of composite and implicit functions; higher-order partial derivatives | 偏导数的概念和意义；复合函数、隐函数的偏导数；高阶偏导数 |
| Total differentials; relationships among differentiability, partial derivatives and continuity; invariance of the first total differential | 全微分；可微、偏导数存在与连续之间的关系；一阶全微分形式不变性 |
| Tangent planes and normal lines to surfaces; partial derivatives in elasticity analysis | 曲面的切平面与法线；偏导数在弹性分析中的应用 |
| Necessary and sufficient conditions for extrema; constrained extrema; economic optimization | 二元函数极值的必要与充分条件；条件极值；经济优化问题 |
Module 3 · Multiple integrals
Visible entries: concepts of multiple integrals, applications of double integrals, and a chapter assessment.
可见条目：重积分概念、二重积分的应用、重积分章节测验。
Original screenshots / 原始截图
Supporting materials
Tianjin University of Commerce — official course overview
The School of Science’s public overview describes Higher Mathematics E as a 128-contact-hour course for Financial Management (Sino-Australian Cooperation), emphasizing calculation and solving practical problems. That overview does not list individual chapters.
Applicant-supplied textbook cover / 教材封面
