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CALCULUS Ⅰ
第5次开课
开课时间: 2022年10月18日 ~ 2023年01月31日
学时安排: 待定
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spContent=A very well-qualified team consisting of experienced professors from NUDT will guide and accompany you through the mysteries of calculus.
A very well-qualified team consisting of experienced professors from NUDT will guide and accompany you through the mysteries of calculus.
—— 课程团队
课程概述

Calculus originated in the second half of the 17th century with the collaboration of many great minds. It is a branch of advanced mathematics that focuses on Derivatives, Integrals, Limits of Functions, and Infinite Series, as well as related concepts and applications. What’s more, it has been widely applied in fields such as Astronomy, Physics, Engineering Science, Economics, Management Science, Sociology, Biological Sciences, and among many others.

A very well-qualified team consisting of experienced professors from the Department of Mathematics at National University of Defense Technology will guide and accompany you through the mysteries of calculus.

      Through the study of this course, you will not only acquire an applicable working knowledge of this riveting field, but also feel the great charm of calculus! Let's start our wonderful learning journey together!


课程大纲

Week One

Promotion Video

Lecture 1. A Preview of Calculus

Lecture 2. Sets and Mappings

Lecture 3. Concepts of Functions and Their Properties

Test for Lecture 2

Test for Lecture 3

Week Two

Lecture 4. Elementary Functions

Lecture 5 Parametric Equations and Ploar Coordinats

Lecture 6 Concepts of limits for functions

Test for Lecture 5

Test for Lecture 6

Test for Lecture 4

Week Three

Lecture 7 Properties and Laws for Limits

Lecture 8 Tests for the Existence of a Limit

Lecture 9 Infinitesimals and Infinite Limits

Test for Lecture 7

Test for Lecture 8

Test for Lecture 9

Week Four

Lecture 10 Concepts of Continuous Functions

Lecture 11 Properties of Continuous Functions

Lecture 12 Concepts of Derivatives

Test for Lecture 10

Test for Lecture 11

Test for Lecture 12

Week Five

Lecture 13 Rules of Derivatives

Lecture 14 Implicit and Parametric Differentiation

Lecture 15 Linear Approximations and Differentials

Test for Lecture 15

Test for Lecture 13

Test for Lecture 14

Week Six

Lecture 16 Rates of Change in Physical Problems

Lecture 17 Antiderivatives and Indefinite Integrals

Lecture 18 Maximum and Minimum values and Fermat Theorem

Test for Lecture 16

Test for Lecture 18

Test for Lecture 17

Week Seven

Lecture 19 Mean Value Theorem

Lecture 20 Indeterminate Forms and L’Hospital’s Rule

Lecture 21 Taylor's Theorem

Test for Lecture 20

Test for Lecture 21

Test for Lecture 19

Week Eight

Lecture 22 How Derivatives Affect the Shape of a Graph

Lecture 23 Curvatures of Plane Curves

Lecture 24 Concepts of Definite Integrals

Test for Lecture 24

Test for Lecture 23

Test for Lecture 22

Week Nine

Lecture 25 Properties of Definite Integrals

Lecture 26 The Fundamental Theorem of Calculus

Lecture 27 Integration by Substitution

Test for Lecture 27

Test for Lecture 25

Test for Lecture 26

Week Ten

Lecture 28 Integration by Parts

Lecture 29 Techniques of Integration

Lecture 30 Improper Integrals

Test for Lecture 29

Test for Lecture 28

Test for Lecture 30

Week Eleven

Lecture 31 Applications to Area and Volume

Lecture 32 Applications to Physics

Lecture 33 Modeling with Differential Equations

Test for Lecture 31

Test for Lecture 33

Test for Lecture 32

Week Twelve

Lecture 34 First-Order Differential Equations

Lecture 35 Second-Order Linear Differential Equations

Lecture 36 Nonhomogeneous Linear Equations

Test for Lecture 34

Test for Lecture 36

Test for Lecture 35

展开全部
预备知识

Elementary Mathematics


参考资料

[1] Zhu Jianmin and Li Jianping, Advanced Mathematics (The 2th edition), Higher Education Press, 2015 (in Chinese)

      [2] James Stewart. Calculu: Early Transcendentals (The 8th edition),2014

[3] George B. Thomas, Maurice D. Weir, Joel Hass. Thomas' Calculus(The 14th edition), Pearson,2018


National University of Defense Technology
12 位授课老师
Fang SU

Fang SU

Associate Professor

Xiao WANG

Xiao WANG

Professor

Jianmin ZHU

Jianmin ZHU

Professor

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