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18.100 c实分析（麻省理工学院）18.100C Real Analysis (MIT) |
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| 课程网址: | http://ocw.mit.edu/courses/mathematics/18-100c-real-analysis-fall... |
| 主讲教师: | Prof. Paul Seidel |
| 开课单位: | 麻省理工学院 |
| 开课时间: | 2012-01-01 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.The three options for 18.100:Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement. |
| 关 键 词: | 数学分析; 可微性; 黎曼积分; 点集拓扑 |
| 课程来源: | 麻省理工学院公开课 |
| 最后编审: | 2024-02-03：chenjy |
| 阅读次数: | 359 |