Overview

数学对于现实生活的影响正在与日俱增，数学技术将是一种应用最广泛、最直接、最及时和最富创造力的实用技术。微积分是大学数学的核心课程，主要研究函数的微分、积分等相关概念和应用，是其他数学课程如概率论、复变函数的学习基础，是理工科的专业课程的基本工具，所以微积分是理工科院校的一门重要基础理论课。微积分（II）是本科生的一门必修课，内容主要包括级数、多元函数、多重积分的理论知识及其应用。通过全英教学，学生在学会用英语获取数学知识的同时又通过学习数学掌握和运用英语，达到数学与英语双赢的目的。从而培养具有国际竞争力并适应国家和社会需要的国际化人才。

The influence of mathematics on real life is increasing day by day. Mathematical technology will be a practical technology with the most extensive, direct, timely and creative application. Calculus is the core course of university mathematics. It mainly studies the differential, integral and other related concepts and applications of functions. It is the basis for learning other mathematics courses such as probability theory and complex variable function. It is the basic tool of professional courses in science and engineering. Therefore, calculus is an important basic theory course in universities of science and engineering. Calculus (II) is a compulsory course for undergraduates. The basic requirements of the course include the theoretical knowledge and application of series, multivariate function and multiple integral. Through the teaching of English, students learn to acquire mathematical knowledge in English while mastering and using English in the process of learning mathematics to achieve a win-win goal of mathematics and English. Therefore, we can cultivate international talents with international competitiveness and meet the needs of the state and society.

Syllabus

Chapter 9 Infinite Series

9.1 Infinite Sequences
9.2 Infinite Series
9.3 Positive Series: The Integral Test
9.4 Positive Series: Other Tests
9.5 Alternating Series, Absolute Convergence, and Conditional Convergence
9.6 Power Series
9.7 Operations on Power Series
9.8 Taylor and Maclaurin Series
9.9 The Taylor Approximation to a Function

Chapter 10 Conics and Polar Coordinate

10.1 The Parabola
10.2 Ellipses and Hyperbolas
10.3 Translation and Rotation of Axes
10.4 Parametric Representation of Curves in the Plane
10.5 The Polar Coordinate System
10.6 Graphs of Polar Coordinates
10.7 Calculus in Polar Coordinates

Chapter 11 Geometry in Space and Vectors

11.1 Cartesian Coordinates in Three-Space
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
11.5 Vectro-Valued Funcions and Curvilinear Motion
11.6 Lines and Tangent Lines in Three-space
11.7 Curvature and Components of Acceleration
11.8 Surfaces in Three-Space
11.9 Cylindrical and Spherical Coordinates

Test 1

Chapter 12 Derivatives for Functions of Two or More Variables

12.1 Functions of Two or More Variables
12.2 Partial Derivatives
12.3 Limits and Continuity
12.4 Differentiability
12.5 Directional Derivatives and Gradients
12.6 The Chain Rule
12.7 Tangent Lines, Tagent Planes and Approximations
12.8 Maxima and Minima
12.9 The Method of Lagrange Multipliers

Chapter 13 Multiple Integrals

13.1 Double Integrals over Rectangles
13.2 Iterated Integrals
13.3 Double integrals over nonrectangular regions
13.4 Double integrals in polar coordinates
13.5 Applications of Double Integrals
13.6 Surface Area
13.7 Triple Integrals in Cartesian Coordinates
13.8 Triple Integrals in Cylindricals and Spherical Coordinates
13.9 Change of Variables in Multiple Integrals

Chapter 14 Vector Calculus

14.1 Vector Fields
14.2 Line Integrals
14.3 Independence of Path
14.4 Green’s Theorem in the Plane
14.5 Surface Integrals
14.6 Gauss’s Divergence Theorem
14.7 Stoke's Theorem

Test 2

Exercises

Exercises Lesson（I）
Exercises Lesson（II）
Exercises Lesson（III）
Exercises Lesson（IV）

Final Test

Taught by

Xue Deng , Yong Liang , Xiaolan Liu , Wenhua Gao , and Qigui Yang

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Calculus II

微积分-2

微积分1（Calculus I）

微积分——多元函数与重积分

微积分（下）

应用微积分

10 Best Calculus Courses for 2024: Derivatives and Integrals

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