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《Thomas' Calculus》(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 I和Calculus 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。
Calculus I
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
《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