本課程是微積分的直接延伸課程，主要目標為：介紹多變數實數值、單變數向量值、多變數向量值等類型之函數的微分與積分的觀念與計算。
其中多變數實數值函數的微分與積分在本系『微積分（二）』的課程中已經概述過---本課程將快速複習，並且引入進階的內容；而單變數向量值、多變數向量值函數的微分與積分的觀念在『微積分（二）』的課程中可能因授課時數的限制未能詳細介紹。
課程內涵包括：
1. 連續、微、梯度、散度、旋度
2. 參數化曲線、參數化曲面
3. 重積分、線積分、面積分、Green 定理、Stoke 定理。
本課程強調觀念與計算，特別是計算，熟悉上述計算將可奠立學習機率、數理統計、複變數函數論、偏微分方程、深度學習等課程的基礎。This course is a direct extension of calculus. The main goal is to introduce the concepts and calculations of differential and integral functions of multi-variable real values, single-variable vector values, multi-variable vector values and other types of functions.
Among them, the differentiation and integration of multi-variable real-valued functions have been outlined in the course "Calculus (2)" of this department---this course will be a quick review and introduce advanced content; while single-variable vector values, multi-variable vectors The concepts of differentiation and integral of value functions may not be introduced in detail in the course "Calculus (2)" due to the limitation of teaching hours.
Course contents include:
1. Continuous, micro, gradient, divergence, curl
2. Parametric curves and parametric surfaces
3. Double integral, line integral, area integral, Green’s theorem, Stoke’s theorem.
This course emphasizes concepts and calculations, especially calculations. Being familiar with the above calculations will lay the foundation for learning courses such as probability, mathematical statistics, function theory of complex variables, partial differential equations, and deep learning.
1. 林琦焜,向量分析（第二版）, 2022, 滄海書局
2. Daniel Miranda, Vector and Tensor Calculus Frankenstein’s Note. (GNU Free Documentation)
3. David A. Santos, Multivariable and Vector Calculus Calculus. (GNU Free Documentation)
附註：
1. 參考書2,3可在網路免費下載。
1. Lin Qikun, Vector Analysis (Second Edition), 2022, Canghai Bookstore
2. Daniel Miranda, Vector and Tensor Calculus Frankenstein’s Note. (GNU Free Documentation)
3. David A. Santos, Multivariable and Vector Calculus Calculus. (GNU Free Documentation)
Note:
1. Reference books 2 and 3 can be downloaded for free from the Internet.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 作業成績 作業成績 Homework results |
20 | 每週依教學進度指派習題，繳交後由教師給成績。 |
| 考試 考試 exam |
80 | 包括期中考、期末考，每次40% |
