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为贯彻《上海市教育委员会关于印发<上海高等教育内涵建设“085”工程实施方案>的通知》(沪教委科〔2009〕2号)的文件精神,切实落实“四大卓越计划”,我委决定从2009年起开展上海高校示范性全英语教学课程建设。
通过示范性全英语教学课程建设,旨在促进高校逐步培养一批教学理念先进、教学方法合理、教学水平高的全英语教学师资,形成与国际先进教学理念与教学方法接轨的、符合中国实际的、具有一定示范性和借鉴意义的课程教学模式,为培养学生的国际竞争意识和能力发挥重要作用。
为贯彻落实科学发展观,深化教学改革,全面提高教育教学质量,为上海“四个中心”建设培养具有国际竞争能力的各类人才,经研究,市教委决定从2009年起开展上海高校示范性全英语教学课程建设,旨在促进和形成一批教学理念先进、教学内容优化、教学方法合理、教学水平高的全英语教学课程,发挥课程的示范辐射作用,提高高等学校教学质量。为做好此项工作,特制定此办法。

课程介绍:

“全英语教学”是指使用英语进行全程授课(重要概念、关键词句等可用中文补充说明),包括课程设计、课堂讲授、实验、上机指导等。在全英语教学课程中,教师选用国外优秀的英文原版教材作为主教材,制作并使用英文课件,用英语讲授课程内容并与学生开展互动,布置并批阅英文作业,考试采用英文命题并要求学生用英文答题。

课程目标:

旨在促进和形成一批教学理念先进、教学内容优化、教学方法合理、教学水平高的全英语教学课程,发挥课程的示范辐射作用,提高高等学校教学质量。

课程考核:

考试三种形式:理论课、讨论课和计算机实验课。理论课重点考核对基本和重要概念、基本方法和基本计算的考试,讨论课的重点是对数学概念的理解和应用。计算机实验课主要考核对数学模型的模拟和实施。理论考试为闭卷考,讨论课考试以写读书报告考试内容,计算机实验考试为计算机实验结果。均要求全英文答卷。比例为50%、30%,20%。

课程负责人

职称

介绍

白延琴

教授

白延琴 教授 介绍

Prabhu Manyem

教授

Prabhu Manyem 教授 介绍

王远弟

教授

王远弟 教授 介绍

何幼桦

教授

何幼桦 教授 介绍

娄洁

副教授

娄洁 副教授 介绍

袁西英

讲师

袁西英 老师 介绍

彭亚新

讲师

彭亚新 老师 介绍

国外专家

 

聘请国外专家讲课 介绍

The  Syllabus  of  Calculus(教学纲要)

Chapter 1  The Derivative
1.     Content:
      Rate of change and slope; limits; The derivative;  Derivatives of constants. power forms, sums, products and quotients; Chain rule; Marginal analysis in business and economics.

2.     Focal point and difficult point:
Focal point:   (a).limit evaluation;
(b).The existence of the derivative.
(c).power rule, derivatives of sums, differences, products and quotients.
(d)Chain rule and combining rules of differentiation.
(e).Marginal cast, revenue and profit
   difficult point: (a) The applications of derivative;
(b) The evaluation of derivative.

3.     Profundity:
(a)              Master the technique of derivative’s evaluation.
(b)    Understand the definition of derivative.
(c)    Master the applications of derivative in business and economics

4.     Class hour’s distribution .
     Instruct 7 class hours. Review 2 class hours

5. Group activity: Minimal average cost.

Chapter 2 .Graphing and optimization

1.Content:
      Continuity and graphs; first derivative , second derivative and graphs; Optimization : absolute Maxim and minima.

2.Focal point and difficult point:
Focal point:   (a).The definition and properties of Continuity
(b).Increasing and decreasing functions;
(c).Local extreme and first-derivative test
(d).Concavity inflection points and second-derivative test.
(e).Absolute maxim and minima.
   difficult point: (a) The definition and properties of continuity;
(b) Analyzing graphs
(c)Limits at infinity

3.Profundity:
(a)              Grasp the definition and properties of continuity;
(b)    Sketch the graph of  by using the graphing strategy
(c)    Master the step in finding absolute maximum and minimum values of a continuous function  on a closed interval

4.Class hour’s distribution .
     Instruct 5 class hours. Review 2 class hours

5.     Group activity:
(1)  Maximizing  profit
(2) Minimizing construction costs.

Chapter 3  Additional derivative topics
1. Content:
      The constant  and continuous compound interest; Derivatives of Logarithmic and Exponential Functions; Chain rule ; Implicit Differentiation; Related Rates.

2. Focal point and difficult point:
Focal point:   (a). continuous compound interest;
(b).Derivative formulas for  and
(c). Generalized derivative rules
(d)Implicit differentiation.
(e).Related Rates problems
   difficult point: (a) Growth of exponential and logarithmic functions
(b) Composite functions and Chain rule.
(c)Implicit differentiation.
(d) Related Rates problems

3. Profundity:
(a)              Grasp the derivative formulas for  and
(b)    Master the generalized derivative rules
(c)    Master implicit differentiation.
(d)    Understand the suggestions for Solving. Related Rates problems

4. Class hour’s distribution .
     Instruct 5 class hours. Review 2 class hours

5 . Group activity:
(a)  Elasticity of demand;
(b) Point of diminishing returns.

Chapter 4  Integration
1.Content:
      Anti-derivatives and indefinite integrals; Integration by Substitution; Differential equations; Geometric-Numeric introduction to the definite integral. Fundamental theorem of calculus.

2.Focal point and difficult point:
Focal point:   (a). Anti-derivatives and indefinite integrals: algebraic; exponential and Logarithmic forms.
(b). Reversing the chain rule
(c).Integration by substitution
(d)Population growth, radioactive decay and learning
(e).Rate area and total change
   difficult point: (a) Reversing the chain rule
(b)Integration by substitution
(c)  Definite integral as a limit of a sum
(d) Fundamental theorem of calculus.

3. Profundity:
(a)Master anti-derivatives and indefinite integrals: algebraic; exponential and Logarithmic forms.
(b) Master the method of integration by substitution
(c) Understand the definite integral as a limit of a sum
(d) Grasp the fundamental theorem of calculus.

4. Class hour’s distribution .
     Instruct 5 class hours. Review 2 class hours

5. Group activity:
(a)  Simpson’s rule;
(b) Bell-shaped curves

Chapter 5  Additional Integration Topics
1.Content:
      Area between curves; Integration by parts; Applications in business and economics

2.Focal point and difficult point:
Focal point:   (a). Area between two curves
(b).consumers’ and producers’ surplus;
(c). Integration by Parts
(d) Integration using tables
   difficult point: (a) Area between two curves
(b) Integration by Parts

3.Profundity:
(a) Master the Calculation of Area between two curves
(b) Master the method of integration by Parts
(c) Understand the integration’s applications in business and economic

4.Class hour’s distribution .
     Instruct 4class hours. Review 2 class hours

5.Group activity:
(a)  Analysis of income. Concentration form raw data;
(b)    Grain exchange

Chapter 6  Multivariable Calculus
1.Content:
      Functions of several variables; Partial derivatives Maxim and minima using Lagrange multipliers; Method of least squares ; Double integrals over rectangular regions.

2.Focal point and difficult point:
Focal point: (a).Functions of two or more independent variables
(b).Partial derivatives and second-order partial derivatives
(c).Second-derivative test for local extreme
(d).Maxim and minima using language multipliers
(e).Least Squares approximation;
(f)Definition of the double integral
   difficult point: (a) Partial derivatives;
(b)Maxim and minima using language multipliers
(c)Method of least Squares
          (d)Double integrals over rectangular regions

3.Profundity:
(a) Master the definition and method of partial derivatives
(b)Master the method of obtaining maxim and minima using language multipliers
(c)  Understand the method of least squares

4.Class hour’s distribution .
     Instruct 6 class hours. Review 2 class hours

5.Group activity:
(a)  city planning
(b) Numerical integration of multivariable

教学进度表
Calculus I
Chapter 1:Limits and Continuity (12 hours )
1.1 The Idea of Limit
1.2 Definition of Limit
1.3 Some Limit Theorems, Additional information on Infinite Limits
1.4 Continuity
1.5 The Pinching Theorem; Trigonometric Limits
1.6 Two Basic Properties of Continuous Functions
Chapter 2: Derivatives (12 hours )
2.1 The Derivative
2.2 Some Differentiation Formulas
2.3 The d/dx Notation; Derivatives of Higher Order
2.4 The Derivative as a Rate of Change
2.5 The Chain Rule
2.6 Differentiating the Trigonometric Functions
2.7 Implicit Differentiation; Rational Powers
Chapter 3: Applications of Derivatives (12 hours , 2 hours (pratice))
3.1. Extreme values of functions
3.2. The mean-value theorem and differential equations
3.3  The Mean-Value Theorem and Applications
3.4. The Shape and a graph
3.5. Graphical solution of autonomous differential equations
3.6. Modeling and optimization
3.7. Linearization and differentials
3.8. Newton's methods
Chapter 4: Integration (14 hours)
4.1 Indefinite integrals, differential equations, and modeling
4.2 Integral rules, integration by substitution
4.3 Estimate with finite sums
4.4 Riemann Sums and definite integrals
4.5. The mean value and fudametal theorem
4.6  Substitute in definite integrals
4.7 Numerical integration
Chapter 5: Applications of integrals: (4 hours for practice)
5.1 Volumes byslicing and rotation about am axis
5.2 Modeling volume using cylindical shells
5.3 Lengths of plane curves
5.4 Spring, pumping, and lifting
5.5 Fluid forces
5.6 Moments and centers of mass
Chapter 6 Transcendental functions and differential equation (14 hours)
6.1 Lograithms
6.2 exponential functions
6.3 derivatives of inverse trigomometric function: intgrals
6.4 Firs-order differential equation
6.5 Linear first-order differential equation
6.6 Euler’s methods: population models
6.7 Hyberbolic function
Chapter 7  Integration Techniques, L’Hoptial Rule, and Improper Integrals (14 hours )
7.1 Basic integration formulas
7.2 Integration by parts
7.3 Partial functions
7.4Trigonometric Substitutes
7.5 Integral table, computer algebra systems, and Monte Carlo integration (In practice 2 hours)
7.6 L’Hoptial Rule
7.7 Improper Integrals
Calculus II

Chapter 8: Infinite Series (14 hours)
8.1 Limits of sequences of numbers
8.2 Subsequences, bounded sequences, and Picard’s methods
8.3 Infinite series
8.4 Series of Nonnegative terms
8.5 Alternating series, absolute and conditional; convergence
8.6 Power series
8.7 Taylor series
8.8 Applications of power series

Chapter 9: Vectors in the plane and polar functions (14 hours)
9.1 Vector in the plane
9.2 Dot Products
9.3 Vector-valued function
9.4 Modeling projectile Motion
9.5 Polar coordinate and Graphs
9.6 Calculus of polar curves

Chapter 10: Vectors and Motion in Space (12 hours)
10.1 Cartesian Coordinate and vectors in space
10.2 Dot and Cross products
10.3 Lines and plane in space
10.4 Cylinders and quadratic surfaces
10.5 vector-valued functions and space curves
10.6 Arc length and the unit tangent vector T
10.7 The TNB frame: Tangential and Normal components of acceleration
10.8 Planetary motion and satellites

Chapter 11: Multivariable functions and their derivatives (12 hours)
11.1 functions of several variables
11.2 limits and continuity in higher dimension
11.3 Partial derivatives
11.4 Chain rule
11.5 Directional derivative,
11.6 Linearization and differentials
11.7 extreme values and saddle points

Chapter 12: Multiple Integrals (14 hours)
12.1 Double integral
12.2 areas, moments and centers of Mass
12.3 Double integral in polar coordinates

Chapter 13: Integration in Vector fields (12 hours)
13.1 Linear integrals
13.2 Vector fields,
13.3 Path independence
13.4 Green’s theorem
13.5 Surface area and surface integrals

课程内容

编号

课程内容链接

1

课程内容/2.pdf

2

课程内容 preparation-chapter 1.pdf

3

课程内容 preparation-chapter 2.pdf

4

课程内容 preparation-chapter 3.pdf

5

课程内容 preparation-chapter 4.pdf

6

课程内容 preparation-chapter 6.pdf

7

课程内容 tcu11_02_01.pdf

8

课程内容 tcu11_02_02.pdf

9

课程内容 tcu11_06_01.pdf

10

课程内容 tcu11_06_02.pdf

11

课程内容 tcu11_06_03.pdf

12

课程内容 tcu11_06_04.pdf

13

课程内容 tcu11_06_05.pdf

14

课程内容 Thomas_Ch7.pdf

15

教学教案1

16

教学教案2

习题集1

编号

习题链接

1

习题1 cont.pdf

2

习题1 curves1.pdf

3

习题1 curves2.pdf

4

习题1 defn.pdf

5

习题1 higher.pdf

6

习题1 diff.pdf

习题集2

编号

习题链接

1

习题2 tan.pdf

2

习题2 alseries.pdf

3

习题2 defn.pdf

4

习题2 integral.pdf

5

习题2 limits.pdf

6

习题2 poseries.pdf

7

习题2 sequence.pdf

课程考核试卷

编号

考核试卷

1

课程考核试卷 1114.pdf

2

课程考核试卷 1115.pdf

3

课程考核试卷 1116.pdf

参考文献

1.Thomas' Calculus, 第十版, 科学出版社, 影印版  2004
2. Calculus-James-Stewar, Brooks/Cole,  (2008)
3. Calculus, Tom M. Apostol, John Wiley & Sones. Inc. (paperback) 2005
4. 高等数学  (上册, 下册) 同济大学数学教研室编写 , 高等教育出版社出版, 2004
5. 高等数学(上册, 下册), 杨则燊边馥萍 主编, 天津大学出版社, 2005 .
6. 高等数学(上册, 下册), 上海大学数学系主编, 上海大学出版社, 2006.
7. http://webcast.berkelay.
8. Web: Thomas' Cauculus

课程名称:高等数学

主讲教材 书名:Calculus
版次:6
作者:Stewart
版权年:2008
ISBN 9780495383628

 

内容简介:
James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart’s trademark style

About the author:
James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Brooks/Cole. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, and Indonesian.
A talented violinist, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. Having explored the connections between music and mathematics, Stewart has given more than 20 talks worldwide on Mathematics and Music and is planning to write a book that attempts to explain why mathematicians tend to be musical.
Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.

 

参考教材教学大纲(pdf)

 

参考教材
English Version:
Thomas’ Calculus (第十版); 科学出版社,影印本,2004年。
Calculus (Stewart's Calculus Series),Thomson Brook/Cole  James Stewart, 2009.
Chinese version:
《高等数学》第四版,同济大学高等数学教研室编, 高教出版社,1996年。
《高等数学》上海交通大学等编
《高等数学》第二版,盛祥耀编,高教出版社,1985年。

 

教学手段
        本专业现在采用全英语授课,并通过多种教学手段组织教学活动。出教师讲授理论知识外,还组织学生以学习小组为单位进行讨论,充分利用多媒体教学、网络资源和课外资料,从而提高了授课效果与效率,为提高学生的素质培养。

理论教学

采用国际上优秀教材之一,最新版《Thomas’ Calculus》和同济大学出版社《高等数学》、上海大学出版社《高等数学》进行备课,使学生对于函数、极限、连续性、导数、微分、偏导数、全微分、函数的极值、不定积分、定积分、二重积分、三重积分、曲线积分、曲面积分、无穷级数的敛散性、无穷级数的和、有关空间解析几何及常微分方程有更好地理解。

全英文教学

通过以英语为主中文为辅的双语教学,不但保证了学生对高等数学基本概念、基本方法和基本计算正确理解和掌握,也为工科本科生今后英文数学文献的查阅奠定专业基础,同时培养了学生的自主学习能力和研究性学习能力,提高了同学们对数学课程学习的兴趣。

多媒体教学

(照片)

网络教学

为将网络教学模式引入课堂,使更多的学生能自学本课程,______年,高等数学网络教程研制完成,并在我校网络课程平台上发布使用。

网络教学包括两部分,一是知识讲授,二是师生交互。 网络教学可以随时随地进行,具有充分的灵活性,学生可以由自己安排学习。

网络教学还可以使学生轻松享有内容丰富、趣味盎然的互动式多媒体课程材料,同时通过网络的超文本链接功能方便地获得大量的与课程内容相关的其它信息或材料。学生能够很容易地从教师那里获得个别化的学习指导和帮助,从而培养他们之间相互协作的精神,并增进彼此的了解和友谊。

讨论式教学
(图片)

 

课堂教学:

(各老师的教学视频)

自主学习——“教会学生怎样自学”是上海大学钱伟长校长一贯倡导的,在教学中课程只是一种载体,通过课程载体使学生掌握自主学习的方法,进行自学能力的培养。

还按排以学生学习小组为单位的讨论式教学,学生通过课外阅读和查找资料,对教师指定的学习内容进行自主学习,在讨论的基础上,选出代表上讲台作英文讲解这部分内容,最后由老师对所讲内容进行点评。

师生讨论

讨论课时,教师以中文进行指导,重要概念和单词配合英文讲解,学生用英文完成讨论报告。

 (照片)

课堂内外--师生互动

上海大学办学理念“拆除四堵墙”中的“拆除教与学之间的墙”是本课程努力实现的目标之一,运用网络手段,构建师生互动平台,教师和学生在这个平台上教学相长。

课堂内外--网络学习

教学形式走出课堂,走向世界,教学资源走出教本,走向社会,网络提供了向无穷空间和时间延伸的可能。___年,高等数学课程网络教程研制成功,为之实现提供了基础条件。

 

实践活动

设置计算机实验课,应用数学软件MATLAB、Mathematica 对课堂内容进行数学建模以及计算机模拟。

6e_liesmycomp_stu.pdf
6e_reviewofalgebra.pdf
6e_reviewofanalgeom.pdf

近两年,本科生的课程得到了学生评价分数是90.8、81.6、83.3、82.3。教学团队成员袁西英得到上海大学教学一等奖。 教学录像要点: 通过对导数的应用讲解,利用数学语言国际化的特点,注重课程的数学知识结构、定量分析的逻辑思维的培养。营造全英语授课环境、师生互动、和英语思维能力的培养。