Calculus I
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spContent=源自欧美教学风格,采用原版经典英文教材《Thomas' Calculus》(第12版),全英文授课方式,给学习者带来不一样的微积分学习体验,有兴趣的同学来挑战吧!Welcome!
—— 课程团队
课程概述

      微积分课程是理、工、管理等大学本科专业最重要的数学基础课程,为学生学习后续课程和进一步获取数学知识尊定基础,也是培养学生理性思维和创新能力的重要载体。各大学历来重视课程建设与教师队伍建设。

      2013年秋至今,电子科技大学为了格拉斯哥学院学生的教学与培养需要,开设了全英语微积分课程,选用的教材是英语原版经典教材《ThomasCalculus》(第12版)。授课方式为全英语教学,并按照欧美教学方式:注重以学生为中心、课内与课外相结合、教学与研究相结合、知识背景与理论基础相结合的教育创新模式。教师在课程中积极与学生互动,注重学生发现问题、解决问题能力的培养,同时讲解问题时留有充分的想象空间与练习环节,并附有丰富的参考资料和大量的例题习题。

      本课程系统地介绍了微积分的基础知识和基本方法,分为Calculus ICalculus II两个部分。Calculus I主要包含一元函数的极限理论,一元函数微分学和积分学,常微分方程;Calculus II主要包含多元函数微分学与积分学,向量场积分以及无穷级数理论。


课程大纲

1 Introduction

1.1 Why study calculus?

1.2 What is calculus?

1.3 Why in English?

1.4 How to study calculus?

2 Limits and Continuity

2.1 Rate of change and tangents to curves

2.2 Limit of a function

2.3 Limit laws

2.4 How to find limits

2.5 One-sided limits

2.6 Limit involving sinx/x

2.7 Continuity

2.8 The intermediate value theorem

2.9 Limits involving infinity

3 Differentiation

3.1 Tangents of a curve

3.2 Derivative at a point

3.3 Derivative as a function

3.4 Differentiable on an interval

3.5 When does a function not have a derivative

3.6 Differentiability implies continuity

3.7 Differentiation rules

3.8 Derivatives of trigonometric functions

3.9 The Chain rule

3.10 The L'Hopital's law

3.11 Implicit differentiation

3.12 Linearization

3.13 Differentials

4 Applications of derivatives

4.1 The extreme value theorem

4.2 Where extreme values are located

4.3 Rolle's Theorem

4.4 Mean Value Theorem

4.5 Corollaries of Mean Value Theorem

4.6 Monotonicity

4.7 Concavity

4.8 Curve sketching

4.9 Newton's method

4.10 Antiderivatives and Indefinite integrals

5 Integration

5.1 Area and estimating with finite sums

5.2 Sigma notations

5.3 Limit of finite sums

5.4 Riemann sum and definite integral

5.5 Integrable and nonintegrable functions

5.6 Area under curve

5.7 Mean value theorem of definite integral

5.8 Fundamental theorem of Calculus 1

5.9 Fundamental theorem of Calculus 2

5.10 Relation between differentiation and integration

5.11 Total area

5.12 Substitution method for indefinite integral

5.13 Substitution method for definite integral

6 Applications of Definite Integral

6.1 Volume by cross-section

6.2 Disk method for volume

6.3 Washer method for volume

6.4 Volume by cylindrical shells

6.5 Arc Length

6.6 Areas of surfaces of revolution

7 Transcendental Functions

7.1 Inverse functions

7.2 Logarithmic functions

7.3 Exponential functions

7.4 Indeterminate Forms

7.5 Relative Rate of Growth

8 Techniques of Integration

8.1 Integration by parts

8.2 Trigonometric integrals

8.3 Trigonometric substitution

8.4 Integration of rational functions

8.5 Improper integrals 1

8.6 Improper integrals 2

9 Differential Equations

9.1 General first-order differential equations and solutions

9.2 Seperable differential equations

9.3 First order linear differential equations

9.4 Bernoulli equations

9.5 Second order linear differential equations-homogeneous 1

9.6 Second order linear differential equations-homogeneous 2

9.7 Nonhomogeneous differential equations

9.8 Euler equations


预备知识

函数的概念及其基本性质。

证书要求

课程成绩评定由两部分构成:

(1)单元测验:在每一章学习结束后有一次单元测验,所有单元测验分数占课程总成绩的40%。

(2)课程考试:课程结束后,学生可以参加课程的最后考试,考试成绩占总成绩的60%。

完成课程学习并考核合格(>=60分)的可获得合格证书,成绩优秀(>=85分)的可获得优秀证书。


参考资料

《Thomas' Calculus》, G. B. Thomas, M. D. Weir and J. R. Hass, 12th edition, Pearson's company, 2010:       http://www.mypearsonstore.com/bookstore/thomas-calculus-9780321587992