(1) Enhance your general math ability and maturarity.
(2) Enable (hopefully) you to do rigorous math proofs.
(3) Learn a rigorous version of calculus.(1) Enhance your general math ability and maturity.
(2) Enable (hopefully) you to do rigorous math proofs.
(3) Learn a rigorous version of calculus.
高等微積分課程分上下學期，目標是大二學生。主要教學目的在使學生在學習大一微積分的技巧之後，進一步瞭解微分與積分的基本原理，並培養學生基本數理分析的能力。課程內容大致包含下列各項：
一、點集拓樸 (Point set topology)。
二、數列與極限 (Sequences and limits)。
三、函數與連續性 (Functions and continuity)。
四、微分 (Differentiation)。
五、微分的應用 (Applications of differentiation)。
六、無窮級數 (Infinite series)。
七、測度理論 (Measure theory)。
八、黎曼積分 (Riemann integration)。
九、積分的應用 (Applications of integration)。
學生應具備大一微積分的基礎。本課程之訓練有助於修習本系大學部高階數理課程，如機率論與數理統計。另外本課程嚴謹的基礎數學訓練，對現代大學生在各專業領域學習之重要性不可忽視。
The advanced calculus course is divided into two semesters and is aimed at sophomore students. The main teaching purpose is to enable students to further understand the basic principles of differential and integral calculus after learning the skills of freshman calculus, and to cultivate students' basic mathematical analysis abilities. The course content generally includes the following items:
1. Point set topology.
2. Sequences and limits.
3. Functions and continuity.
4. Differentiation.
5. Applications of differentiation.
6. Infinite series.
7. Measure theory.
8. Riemann integration.
9. Applications of integration.
Students should have a foundation in freshman calculus. The training in this course is helpful for studying advanced mathematics and physics courses in the department, such as probability theory and mathematical statistics. In addition, the rigorous basic mathematics training in this course cannot be ignored for the importance of modern college students studying in various professional fields.
Analysis with an Introduction to Proof, 5 ed, Steven R. Lay, Pearson International.
Analysis with an Introduction to Proof, 5 ed, Steven R. Lay, Pearson International.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| quiz 1quiz 1 quiz 1 |
20 | Do not miss the test. |
| midtermmidterm midterm |
25 | Do not miss the test. |
| quiz 2quiz 2 quiz 2 |
20 | Do not miss the test. |
| finalfinal final |
25 | Do not miss the test. |
