The course "calculus" mainly studies limit, derivative and its application, definite integral and its application, transcendental function, integral skill, indefinite integral and abnormal integral. Through the study of this course, students can obtain the basic concept, basic theory and basic operation skills of univariate function calculus. At the same time of imparting knowledge, we should pay attention to the cultivation of students' abstract thinking ability, logical reasoning ability, spatial imagination ability and self-study ability, especially the ability to analyze and solve problems by comprehensively using the learned knowledge.

Teaching contents: Calculus is the branch of mathematics that studies differentiation, integration and related concepts and applications in advanced mathematics. It is a basic subject of mathematics. It is an important basic theory course in universities of science and engineering. It has promoted the development of other disciplines and human civilization and science and technology, and its function is of great importance. Calculus (I) is a compulsory course for undergraduates. The basic requirements of the course include functions, limits, continuity of function, derivatives and their applications, integrals and their applications, the limits of indefinite forms and generalized integrals. The limit is the basic concept of calculus. Differential and integral are the limits of forms of a process. 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. Therefore, we can cultivate international talents with international competitiveness and meet the needs of the state and society.

At the same time, MOOC also has many special sections, such as courseware download, homework, discussion area, reference answers and other related learning materials, to realize online and offline communication. Combine knowledge, ability and quality organically, conduct in-depth analysis and bold query. Introduce the achievements of academic frontier and scientific and technological development into the teaching content. Take students as the center, carry out the individualized teaching with students as the center, and cultivate innovative talents.

Teaching Objective: The purpose of this

course is to enable students to master the basic concepts, theories and

operations of one variable calculus. By the study of this course, in theory,

students can master the basic definition, basic theory and basic operation

skills of one variable calculus. At the same time, we should pay attention to

the cultivation of students’ abstract thinking ability, logical reasoning ability,

spatial imaginary ability and self-learning ability in the process of imparting

knowledge and teaching. In particular, the ability of analyzing and solving

problems is trained by using the learned knowledge. This course is taught in English, and the

mathematical concept is permeated into the specific teaching links. It aims to

make students get used to learning calculus in English and achieve the goal of

"win-win". The details are as follows: (1) Knowledge level: Enable

students to make full use of fragmented time, study independently, master the

basic concept, basic theory and basic operation skills of univariate function

calculus, and have excellent English expression ability. (2) Ability level: Pay

attention to cultivate students' abstract thinking and logical reasoning

ability, especially use critical thinking to analyze and solve problems. (3)

Quality level: Teachers feel the importance of teaching in the teaching

process. In this process, students have positive emotional experience and have

correct outlook on life, values and the world.

Maths in High School, English

Do you have any matching textbooks?

Calculus, (US/9th edition) Varberg, D., Purcell, E.J., Rigdon, S.E., Beijing: Machinery Industry Press, 2009.8.

What are the reference materials?

Reference: Advanced Mathematics, Seventh Edition (Volume I and Volume II), by Department of mathematics, Tongji University. Beijing: Higher Education Press, April 2016.

Q1: Is there any matching textbook?

A1: Textbook, Calculus, Ninth Edition (Varberg, D., Purcell, E.J., Rigdon, S.E.). Beijing: Mechanical Industry Publisher, 2009.8.

Q2: What reference materials do you have?

A2: Reference: Advanced Mathematics, Seventh Edition (Volume I and Volume II), by Department of mathematics, Tongji University. Beijing: Higher Education Press, April 2016.

Q3: What are the requirements for the self-study content?

A3: Most of the self-study contents are the basic knowledge of high school. Students need to review and understand the basic concepts.

Q4: What tasks do we need to finish in advance?

A4: Understand the basic concepts, basic theorems. Master the basic mathematical calculations and skills. Give the feedback of knowledge difficulties.

Q5: What basic knowledge do I need to master before I take this course?

A5: A solid foundation of high school mathematics; a good command of English in listening, speaking, reading and writing.