實分析導論
Introduction to Real Analysis
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 實分析導論 SA211（光復） | |
5 13:20–14:10 | 實分析導論 SA211（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
本課程屬大學部與研究所程度的實分析課程,授課偏重於數學理論與分析方法的介紹,是高等微積分的一部分也是進入實變數函數論的基礎課程。
calculus, linear algebra
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板書
學期作業: 60 % 考試: 40%
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| 週次 | 主題 |
|---|---|
| 第 0 週 | Intrgeation of differential forms: vector analysis The Lebesque Theorem: set function |
| 第 1 週 | Some special functions: power series the exponetial and logarithmic functions the trigonometric functions |
| 第 2 週 | Some special functions: the algebraic completeness of the complex field Fourier series |
| 第 3 週 | Some special functions: The Gamma functions Functions of several variables: linear transformations |
| 第 4 週 | Functions of several variables: Differentiation The contraction principles |
| 第 5 週 | Functions of several variables: The inverse function Theorem The Implicit function Theorem |
| 第 6 週 | Functions of several variables: The Rank Theorem Determinants |
| 第 7 週 | Functions of several variables: derivatives of higher order differentiation of Integrals Intrgeation of differential forms: integration |
| 第 8 週 | Intrgeation of differential forms: primitive mapping partition of unity change of variables |
| 第 9 週 | Intrgeation of differential forms: differential forms simplexes and chains |
| 第 10 週 | Intrgeation of differential forms: Stokes' Theorem closed forms and exact forms |
| 第 12 週 | The Lebesque Theorem: construction of Lebesque measure measure spaces measurable functions |
| 第 13 週 | The Lebesque Theorem: simple functions integration |
| 第 14 週 | The Lebesque Theorem: comparison with Riemann integration integration of complex functions |
| 第 15 週 | The Lebesque Theorem: functions of class L^2 |
| 第 16 週 | The Lebesque Theorem: functions of class L^p |
Rudin, Walter Principles of mathematical analysis New York : McGraw-Hill, c1976
- 地點
- SA348
- 時間
- Wednesday 4pm -5pm
- 聯絡方式
- Email: liming@math.nctu.edu.tw Tel: 56439