微积分是高等数学中研究函数的微分、积分以及有关概念和应用的数学分支，它是数学的一个基础学科，是理工科院校一门重要的基础理论课。它推动了其他学科的发展，推动了人类文明与科学技术的发展，它的作用是举足轻重的。

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微积分是高等数学中研究函数的微分、积分以及有关概念和应用的数学分支，它是数学的一个基础学科，是理工科院校一门重要的基础理论课。它推动了其他学科的发展，推动了人类文明与科学技术的发展，它的作用是举足轻重的。

--Course Introduction

--Introduction to Limits

--Rigorous Study of Limits

--Limit Theorems

--Limits Involving Trigonometric Functions

--Limits at Infinity, Infinite Limits

--Continuity of Functions

--Chapter Review

--Assignments for Chapter 1

--Discussion Topics of Chapter 1

--Homework and Answer of Chapter 1

--Homework 1

--Two Problems with One Theme

--The Derivative

--Rules for Finding Derivatives

--Derivate of Trigonometric Functions

--The Chain Rule

--Higher-Order Derivative

--Implicit Differentiation

--Related Rates

--Differentials and Approximations

--Chapter Review

--Assignments for Chapter 2

--Discussion Topics of Chapter 2

--Homework and Answer of Chapter 2

--Homework 2

--Maxima and Minima

--Monotonicity and Concavity

--Local Extrema and Extrema on Open Intervals

--Practical Problems

--Graphing Functions Using Calculus

--The Mean Value Theorem for Derivatives

--Solving Equations Numerically

--Anti-derivatives

--Introduction to Differential Equations

--Chapter Review

--Assignments for Chapter 3

--Discussion Topics of Chapter 3

--Homework and Answer of Chapter 3

--Test 1

--Introduction to Area

--The Definite Integral

--The First Fundamental Theorem of Calculus

--The Second Fundamental Theorem of Calculus and the Method of Substitution

--The Mean Value Theorem for Integrals and the Use of Symmetry

--Numerical Integration

--Chapter Review

--Assignments for Chapter 4

--Discussion Topics of Chapter 4

--Homework and Answer of Chapter 4

--Homework 4

--The Area of a plane region

--Volumes of Solids: Slabs, Disks

--Volumes of Solids of Revolution: Shells

--Length of a plane curve

--Work and Fluid Force

--Moments and Center of Mass

--Probability and Random Variables

--Chapter Review

--Assignments for Chapter 5

--Discussion Topics of Chapter 5

--Homework and Answer of Chapter 5

--Homework 5

--The Natural Logarithm Function

--Inverse Functions

--The Natural Exponential Function

--General Exponential and Logarithm Function

--Exponential Growth and Decay

--First-Order Linear Differential Equations

--Approximations for Differential Equations

--The Inverse Trigonometric Functions and Their Derivatives

--The Hyperbolic Functions and Their Derivatives

--Chapter Review

--Basic Integration Rules

--Integration by parts

--Some Trigonometric Integrals

--Rationalizing Substitutions

--Integration of Rational Functions Using Partial Fraction

--Strategies for Integration

--Chapter Review

--Assignments for Chapter 7

--Discussion Topics of Chapter 7

--Homework and Answer of Chapter 7

--Homework 7

--Indeterminate Forms of Type

--Other Indeterminate Forms

--Improper Integrals: Infinite Limits of Integration

--Improper Integrals: Infinite Integrands

--Chapter Review

--Assignments for Chapter 8

--Discussion Topics of Chapter 8

--Homework and Answer of Chapter 8

--Test 2

Deng Xue, Ph.D., Professor, Master’s supervisor. Research field is portfolio and risk analysis. As the first author, she has published more than 40 scientific research and teaching papers in the top journals of SCI, such as “Information Sciences”, “Applied Soft Computing” and “Computers & Industrial Engineering”. In the past five years, she has presided over more than 10 projects, including the Humanities and Social Sciences Youth Fund of the Ministry of Education, the Natural Science Fund of Guangdong Province, and the Soft Science of Guangdong Province. She has won "one hundred most influential and outstanding domestic academic papers in 2016 and 2013" (the first author, with 3020 citations); twice "Nanguang Award" for teaching excellence of South China University of Technology, "special award for teaching achievements", twice "undergraduate excellent teaching demonstration course"; and "excellent instructor Award" of Guangdong financial modeling competition.

Yang Qigui, the second level Professor, doctor, postdoctoral, doctoral supervisor, vice president. He is a famous teacher of South China University of Technology and the provincial training object of "one hundred and ten" talent project in Guangdong Province. 118 papers have been published in important academic journals at home and abroad, 102 of which have been included in SCI. SCI cited positively for more than 1500 times. He won the first prize of Guangxi science and technology progress (ranking first). Four undergraduate courses and five postgraduate courses. In 2002, he won the second prize (independent) of excellent thesis in higher education and teaching in Guangxi, the first prize of excellent teaching at the school level of South China University of technology from 2013 to 2014, the second prize (ranking: 1), the second prize (ranking: 2) and the second prize (ranking: 2) of the sixth Provincial Higher Education in Guangdong Province.

Liang Yong, Ph.D., teacher of the School of Mathematics, South China University of Technology. The research field is nonlinear wave. He has taught the "Calculus", "Linear Algebra" and "Analytic Geometry" and other courses for more than 14 years. He won the first-prize (Rank No. 1) in the Young Teachers' Teaching Competition of South China University of Technology for two times and won the 2017-Teaching Excellence Award. He presided over the Basic Research Funding for the Central University of South China University of Technology, and participated in four National Natural Science Foundation projects. He has presided over one Guangdong Province Education Reform project, three SCUT Education Reform projects (including one major project), and one Undergraduate Micro-Course project.

Liu Xiaolan, Ph.D., associate professor, master supervisor. Mainly engaged in machine learning and optimization algorithm research. The course focuses on calculus, mathematics experiment, operation research, information theory and coding technology. She has published more than 20 scientific research papers in Information Sciences, IEEE transaction on image processing, Siam Journal on scientific computing and other important journals, and published the textbook typical cases of mathematical experiments in Higher Education Press. In the past five years, she has presided over many projects of NSFC and provincial and ministerial level. She has won the first prize of excellent teaching and the second prize of excellent instructor of students' scientific and technological innovation in South China University of technology.

Gao Wenhua, Ph.D., associate professor, master supervisor. The main courses of graduate students are stochastic optimal control, mathematical modeling and mathematical experiments. She has won the third prize of the second Excellent University Alliance young teachers' teaching innovation competition, the first prize of undergraduate teaching excellence of South China University of technology and the excellent teaching and research paper award. Presided over many projects such as the teaching, research and teaching reform project of Guangdong Provincial Department of education, the basic scientific research business expenses of Central Universities and the school level teaching, research and teaching reform, and participated in many projects funded by the National Natural Science Foundation. She participated in the preparation of higher mathematics teaching guidance book published by higher education press and published more than 20 papers.