中、英文教学大纲
课程名称:高等数学(B)
开设单位:应用数学系基础数学教研室
教学目的和要求:
    高等数学充满了辩证法。高等数学是财经类各专业的必修课，是经济工作者从事经济数量分析的重要基础和有力工具。
    通过本课程的教学，使学生能全面理解和掌握高等数学的基本知识，基本理论，基本内容，基本运算方法和分析方法；学会理性的数学思维技术和模式，培养学生的创新意识和能力，在研究经济理论和经济管理的实践中灵活运用数学思想方法去分析问题和解决问题；并为后继课程的学习和进一步深造打下良好的基础。
    在讲授本课程时，考虑财经类学生的特点，以讲授基本理论和方法为主，重点放在理论的运用和运算技能上。同时，根据教学内容配备一定数量的习题给学生训练，以巩固学生掌握知识和提高学生的运用能力。
教学课时数 ： 6*13+4*18=150 课时
教学方式 ： 课堂讲授、习题演习与讨论
考核方法 ： 课堂练习，期末书面考试
试卷结构 ： 填空题 、选择题 、问答题 、计算题 、应用题 、证明题
指定教材 ： 《高等数学》上海财经大学出版社（上海财经大学应用数学系编），第一版， 2003 年 8 月
参考教材： 《高等数学》高等教育出版社（同济大学数学系编）
讲授提纲 :

备注：上学期 6 × 13=78 课时 内容从 ch1 — ch4 ， ch7 — ch8

      下学期 4 × 18=72 课时 内容从 ch5 — ch6, ch9,ch11,ch13

Teaching Out for Calculus

B .DEPARTMENT TO OFFER: APPLIED MATHEMATICS DEPARTMENT

C . The objective is to master ideas and methods of calculus so that the students can use these to solve the questions they meet in studying other courses and in life. It is also very important to improve quality of students in all aspects to analyse questions and solve problems .

D. The main content and the hours required:

1. limits and rate of change : 1)the tangent and velocity problem, 2)the limit of a function, 3)calculating limits using the limit laws, 4)the precise definition of a limit, 5)continuity6)tangents, velocities, and other rates of change (12 hours)

2. derivatives: 1)derivatives, 2)differentiation formulas,3)rates of change in the natural and social sciences,4)derivatives of trigonometric functions,5)the chain rule,6)implicit differentiation, 7)higher derivatives,8)related rates,9)differential, ar and quadratic approximations,10)Newton's method. (12 hours)

3. the mean value theorem and curve sketching: 1)maximum and minimum,2)the mean value theorem,3)monotonic functions and first derivative test,4)concavity and points of inflection,5)limit at infinity , horizontal asymptotes,6)curve sketcking,7)graphing with calculus,8)application to economics,9)antiderivatives (12 hours)

4. integrals: 1)sigma notation,2)area,3)the definite integral,4)fundamental theorem of calculus 5)substitution rule. (10hours)

5. applications of integration: 1)area between curves,2)volume,3)volumes by cylindrical shells, 4)work,5)average value of a function. (8 hours)

6.derivatives of some functions: 1)inverse functions and their derivative,2)derivatives of exponential functions,3)derivatives of logarithmic functions,4)derivatives of inverse trigonometric functions,5)hyperbolic functions,6)indeterminate form and L'hospital's rule. (10 hours)

7.techniques of integration: 1)integration by parts,2)trigonometric integral,3)trigonometric substitution,4)integration of rational functions by partial fractions,5)rationalizing substitutions,5)strategy for integration,6)using tables of integrals and computer algebra system,7)approximate integration,8)improper integral. (12 hours)

8. further applications of integration: 1)differential equations,2)arc length,3)area of a surface of revolution,4)moments and centers mass,5)hydrostatic pressure and force,6)application to economics,7)curves defined by parametric equations,2)tangents and areas,3)polar coordinates. (10 hours)

9. infinite sequences and series: 1)sequences,2)series,3)the integral test and estimates of sum,4)comparison tests,5)alternating series,6)absolute convergence and the ratio and root test,7)strategy of for testing series,8)power series,9)representation of functions as power series,10)Taylor and Maclaurin,11)The binomial series,12)Applications of Taylor polynomials (16 hours)

10.partial derivatives: 1)functions of several variables,2)limits and continuity,3)partial derivatives, 4)chain rule,5)maximum and minimum values,6)Langrange multipliers. (10 hours)

11.multiple integrals: 1)double integral over rectangle,2)iterated integrals,3)double integral over general regions,4)double integrals in polar coordinates,5)applications of double integrals, 6)surface area (10 hours)

12.differential equations: 1)basic concepts: separable and homogeneous equations,2)first-order ar equations,3)exact equations,4)strategy for solving first-order equations,5)second-order ar equations,6)nonhomogeneous ar equations,7)applications of second-order differential equations,8)series solutions 9)difference equations. (16 hours)

E. Examination: No bringing any reference. and textbook..

F. Composition of the examination ： choice ,fill, proof, computation.

G. Textbook: Calculus by James Stewart, published by Brooks/cole publishing company in 1995.

H. References: [1]P. Lax,S.Burstein,A. Lax, Calculus with Application and computing, Springer-Verlag.

[2] 上海财经大学应用数学系，《 高等数学 》，上海财经大学出版社

[3] 上海财经大学应用数学系，《 高等数学习题集 》，上海财经大学出版社