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。
By the end of this course students will be able to:
· apply calculus to parametric functions and vector-valued functions;
· understand the inner and cross products of vectors, and apply them to lines and planes in space;
· introduce the polar coordinates and the related equations;
· calculate partial derivatives, total differential and high-order partial derivatives of multivariable functions;
· find the derivative of implicit functions;
· explain the concepts of directional derivative and gradient and calculate them in two and three dimensions;
· apply partial derivatives to find the tangent plane and normal line of a surface;
· locate extreme values of a multivariable function, both unconstrained and under given conditions, and apply the Lagrange multiplier method;
· describe the meaning of double integrals (Cartesian coordinates and Polar coordinates) and evaluate them; similarly for triple integral (Cartesian coordinates, Polar coordinates and Spherical coordinates);
· evaluate open and closed line integrals of vector functions, aware that the results depends on the path in general;
· deetermine whether a line integral is independent of path;
· apply Green’s theorem to integrals in the plane;
· express given surfaces in an appropriate form and evaluate surface integrals over both open and closed surfaces;
· apply the theorems of Green, Gauss and Stokes to line, surface and volume integrals and explain their significance in engineering;
· explain what is meant by conservative, irrotational and solenoidal fields and explain their physical meaning；
· state what is meant by a sequence and series, find limits of sequence;
· apply criteria for convergence of series with terms of the same sign or alternating sign; distinguish between absolute convergence and conditional convergence;
· establish conditions for convergence of power series, other functional series and Taylor series;
· derive Maclaurin expansions of elementary transcedental functions such as sin(x) and cos(x);
· apply direct and indirect expansion methods of some simple functions to applications of power series in approximate calculations.
The First Week: 10 Infinite Sequences and Series
10.1 Definition of Sequence
10.2 Calculating the limit of Sequence I
10.3 Calculating the limit of Sequence II
10.4 Definition of Infinite Series
10.5 Convergence of Infinite Series
PPT-Chapter 10
Assignment 1
Answers of Assignment 1
The Second Week: 10 Infinite Sequences and Series
10.6 Integral Test I
10.7 Integral Test II
10.8 Comparison Test I
10.9 Comparison Test II
10.10 Ratio Test
10.11 Root Test
The Third Week: 10 Infinite Sequences and Series
10.12 Alternating Series I
10.13 Alternating Series II
10.14 Power Series I
10.15 Power Series II
10.16 Taylor Series
10.17 Convergence of Taylor Series
PPT-Chapter 10
Assignment 2
Assignment 3
Answers of Assignment 2
Assignment 4
Answers of Assignment 3
Unit Test-CH10
Answers of Assignment 4
The Fourth Week: 11 Parametric Equations and Polar Coordinates
11.1 Parametric Equations
11.2 Calculus of Parametric Curves
11.3 Polar Coordinates
11.4 Areas in Polar Coordinates
11.5 Length in Polar Coordinates
11.6 Conic Sections
PPT-Chapter 11
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
PPT-Chapter 12
Assignment 5
Assignment 6
Answers of Assignment 5
Answers of Assignment 6
The Fifth Week: 13 Vector-Valued Functions
13.1 Curves in Space and Their Tangents
13.2 Integrals of Vector-valued Functions
13.3 Arc Length
PPT-Chapter 13
Unit Test-CH11, 12, 13
Assignment 7
Answers of Assignment 7
The Sixth Week: 14 Partial Derivatives
14.1 Functions of several variables
14.2 Limits and Continuity I
14.3 Limits and Continuity II
14.4 Partial Derivatives I
14.5 Partial Derivatives II
14.6 Partial Derivatives III
PPT-Chapter 14---Part I
The Seventh Week: 14 Partial Derivatives
14.7 The Chain Rule
14.8 Directional Derivatives I
14.9 Directional Derivatives II
14.10 Tangent Planes
PPT-Chapter 14---Part II
The Eighth Week: 14 Partial Derivatives
14.11 Extreme Values I
14.12 Extreme Values II
14.13 Lagrange Multipliers Method
Assignment 8
Unit Test-CH14
Assignment 9
Answers of Assignment 8
Answers of Assignment 9
The Ninth Week: 15 Multiple Integrals
15.1 Double Integrals over Rectangles I
15.2 Double Integrals over Rectangles II
15.3 Double Integrals over General Regions I
15.4 Double Integrals over General Regions II
15.5 Area by Double Integration
PPT-Chapter 15
The Tenth Week: 15 Multiple Integrals
15.6 Double Integrals in Polar Form I
15.7 Double Integrals in Polar Form II
15.8 Triple Integrals in Rectangular Coordinates
The Eleventh Week: 15 Multiple Integrals
15.9 Triple Integrals in Cylindrical Coordinates I
15.10 Triple Integrals in Cylindrical Coordinates II
15.11 Triple Integrals in Spherical Coordinates I
15.12 Triple Integrals in Spherical Coordinates II
Unit Test-CH15
The Twelfth Week: 16 Integrations of Vector Fields
16.1 Line Integrals
16.2 Line Integrals of Vector Fields I
16.3 Line Integrals of Vector Fields II
16.4 Line Integrals of Vector Fields III
PPT-Chapter 16---Part I
The Thirteenth Week: 16 Integrations of Vector Fields
16.5 Path Independence
16.6 Conservative Fields
16.7 Green’s Theorem in the Plane I
16.8 Green’s Theorem in the Plane II
PPT-Chapter 16---Part II
The Fourteenth Week: 16 Integrations of Vector Fields
16.9 Surface and Area I
16.10 Surface and Area II
16.11 Surface Integrals I
16.12 Surface Integrals II
16.13 Stokes' Theorem I
16.14 Stokes' Theorem II
16.15 Divergence Theorem
16.16 Unified Theory of Calculus
Unit Test-CH16
Former Exam papers
2020-2021-2_Final
2021-2022-2_Final
Cal II Mid-term_Sample
2022-2023-2_Final
Calculus I
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《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
教授
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