高等数学进阶课程详细信息

课程号 E2800060 学分 3
英文名称 Advanced Mathematics Progression
先修课程
中文简介 应光华管理学院邀请, 特别为该学院“未来领导者”项目开设一门完全用英语讲授的《高等数学》课程 。“未来领导者”项目是光华管理学院新开设的国际生项目, 从全球合作院校中遴选生源。入选学生应为本科3、4年级学生, 曾学习过一学期的基本大学微积分课程。由于入选学生原本学校的微积分课程内容与北大课程内容不尽相同,从已得到的入选学生已完成课程内容的初步评估,为保持和北大其他学生数学训练程度一致, 需要做补充。本课程旨在巩固入选学生已有微积分知识, 并在一学期内提升至符合本校《高等数学B》课程所要达到的数学素养。配合的课程内容大致和现有《高等数学B》重合, 视具体情况做课程难易 程度的调整。本课程要求全程用英语讲授,
英文简介 This course is tentatively named as "Advanced Mathematics (Future Leaders Program)", and it is offered at the request of Guanghua School of Management. It is specifically tailored to the needs of the newly established “Future Leaders” program. “Future Leaders” program is a two-year program designed for international undergraduate students from collaborating institutions across the globe. Eligible candidates should have completed their first two years of undergraduate studies at their home institutions, and are expected to spend further two years at Peking University. Eligible candidates are expected to have completed a one-semester undergraduate course on differential calculus. At Peking University, the general requirement on mathematics training requires the completion of a one-year training in calculus and related topics. This course is designed to be both a re-consolidation of differential calculus as well as to provide the necessary training on integral calculus, multivariable calculus, general integrals, Fourier transforms, and an introduction to ODEs (details on the topics to be covered by this course can be found in the syllabus  attached below). Successful completion of this course will equip its candidates the training equivalent to  “Advanced Mathematics B”  for their local peers at Peking University.
开课院系 光华管理学院
通选课领域  
是否属于艺术与美育
平台课性质  
平台课类型  
授课语言 英文
教材 无,无;
参考书
教学大纲 本课程是为国际学生专门开设的课程, 旨在为国际学生提供在北京大学学习而必须掌握的相应数学(微积分部分)的培训。课程内容大致和本校《高等数学B》相似。在教授过程中需要根据学生的具体情况 进行必要的补充和删减, 最终期望达到完成教授体现北京大学教学水平的数学知识和素养。本课程面对的学 生需要课程全程用英语讲授。
1.    Revision on the concepts of single-variable functions and their limits (basic properties of real numbers, elementary functions and general functions, sequence and limits, function limit and continuity); about 3 hours.
2.    Revision on the basic concepts of single-variable calculus (the concept of derivatives, derivatives of elementary functions, derivatives of compound functions and inverse functions, differentials and approximate calculations, higher order derivatives, original function and indefinite integrals, definite integrals); about 3 hours.
3.    Revision on basic theorems and techniques in calculus (integration by substitution and integration by parts, rational integration, simple applications and approximate calculations of definite integrals); about 3 hours
4.    Mean Value Theorem and Taylor`s Formula (Lagrange Mean Value Theorem, Cauchy Mean Value Theorem and L`H?pital`s rule, Taylor`s Formula, extreme value problem, monotonicity and convexity and concavity of functions); about 6 hours
5.    Introduction to vector algebra and spatial analytic geometry (the concept and calculation of vectors, representation of coordinates, equations of spatial lines and planes, classification of quadratic surfaces); about 6 hours
6.    Derivatives of multivariable functions (concept of multivariable functions, limits and continuity of multivariable functions, partial derivatives and total derivatives, chain rule, extreme values); about 6 hours
7.    Multiple integrals (definition and calculation of double integrals, definition and calculation of triple integrals, examples of application of multiple integrals); about 6 hours.
8.    Curve integral and surface integral (first and second type curve integral, Green`s formula, first and second type surface integral, Gauss formula and Stokes formula, introduction to field theory); about 6 hours.
9.     Introduction to ordinary differential equations (the concept of ordinary differential equations, the method of separating variables for solving first-order equations and other elementary solutions, the existence and uniqueness theorem of solutions, the structure of solutions for second-order linear equations, the solution of second-order linear constant coefficient equations); about 6 hours.
10. Series (Cauchy Convergence Principle and series convergence, positive series, arbitrary term series, functional series, power series, Taylor Series); about 6 hours.
本课程以课堂讲授为主。 考虑今年的特殊情况(暂停外籍人士入境), 且本课程学生全为国际学生, 在2020-2021学年第一学期开 学时有一定的概率学生不能到校, 如果届时开设本课程, 需要进行网上教学。
四次大作业和期末考试。
每次大作业占总评10%, 期末考试占总评60%。
教学评估 傅翔:
学年度学期:20-21-1,课程班:高等数学进阶1,课程推荐得分:null,教师推荐得分:null,课程得分分数段:null;
学年度学期:21-22-1,课程班:高等数学进阶1,课程推荐得分:0.0,教师推荐得分:3.06,课程得分分数段:80及以下;