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。

      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。

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。


预备知识

Calculus I

授课大纲

The First Week: 10 Infinite Sequences and Series

10.1 Definition of Sequence

10.5 Convergence of Infinite Series

10.2 Calculating the limit of Sequence I

10.3 Calculating the limit of Sequence II

10.4 Definition of Infinite Series

The Second Week: 10 Infinite Sequences and Series

10.8 Comparison Test I

10.11 Root Test

10.7 Integral Test II

10.6 Integral Test I

10.10 Ratio Test

10.9 Comparison Test II

The Third Week: 10 Infinite Sequences and Series

10.16 Taylor Series

10.14 Power Series I

10.17 Convergence of Taylor Series

10.12 Alternating Series I

10.15 Power Series II

10.13 Alternating Series II

Unit Test-CH10

The Fourth Week: 11 Parametric Equations and Polar Coordinates

11.6 Conic Sections

11.4 Areas in Polar Coordinates

11.3 Polar Coordinates

11.2 Calculus of Parametric Curves

11.5 Length in Polar Coordinates

11.1 Parametric Equations

The Fifth Week: 13 Vector-Valued Functions

13.3 Arc Length

13.2 Integrals of Vector-valued Functions

13.1 Curves in Space and Their Tangents

Unit Test-CH11, 12, 13

The Fifth Week: 12 Vectors and Geometry in Space

12.1 Three-Dimensional Coordinate and Vectors

12.2 Vector Products

12.3 Line and Plane in Space

The Sixth Week: 14 Partial Derivatives

14.1 Functions of several variables

14.5 Partial Derivatives II

14.6 Partial Derivatives III

14.4 Partial Derivatives I

14.3 Limits and Continuity II

14.2 Limits and Continuity I

The Seventh Week: 14 Partial Derivatives

14.7 The Chain Rule

14.9 Directional Derivatives II

14.10 Tangent Planes

14.8 Directional Derivatives I

The Eighth Week: 14 Partial Derivatives

14.13 Lagrange Multipliers Method

14.12 Extreme Values II

14.11 Extreme Values I

Unit Test-CH14

The Ninth Week: 15 Multiple Integrals

15.3 Double Integrals over General Regions I

15.1 Double Integrals over Rectangles I

15.2 Double Integrals over Rectangles II

15.4 Double Integrals over General Regions II

15.5 Area by Double Integration

The Tenth Week: 15 Multiple Integrals

15.7 Double Integrals in Polar Form II

15.6 Double Integrals in Polar Form I

15.8 Triple Integrals in Rectangular Coordinates

The Eleventh Week: 15 Multiple Integrals

15.11 Triple Integrals in Spherical Coordinates I

15.12 Triple Integrals in Spherical Coordinates II

15.9 Triple Integrals in Cylindrical Coordinates I

15.10 Triple Integrals in Cylindrical Coordinates II

Unit Test-CH15

The Twelfth Week: 16 Integrations of Vector Fields

16.4 Line Integrals of Vector Fields III

16.3 Line Integrals of Vector Fields II

16.2 Line Integrals of Vector Fields I

16.1 Line Integrals

The Thirteenth Week: 16 Integrations of Vector Fields

16.8 Green’s Theorem in the Plane II

16.6 Conservative Fields

16.7 Green’s Theorem in the Plane I

16.5 Path Independence

The Fourteenth Week: 16 Integrations of Vector Fields

16.15 Divergence Theorem

16.16 Unified Theory of Calculus

16.9 Surface and Area I

16.13 Stokes' Theorem I

16.12 Surface Integrals II

16.10 Surface and Area II

16.14 Stokes' Theorem II

16.11 Surface Integrals I

Unit Test-CH16

参考资料

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