本課程是微積分的直接延伸課程，主要目標為：
1. 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；
2. 介紹張量微積分的觀念與計算（如果時間允許）。
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）』的課程中因授課時數的限制未能介紹。
課程內涵包括：
1. 連續、微分、梯度、散度、旋度、隱函數定理、Lagrange multiplier.
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 micro points, with the main goals:
1. Introduce the concept and calculation of differential and fractional functions of types such as multivariate actual numerical values, single variable vector values, multivariate vector values, etc.;
2. Introduce the concept and calculation of micro-points of the meter (if time permits).
The differential and scores of the multivariate real numerical function have been outlined in the course of "Micro Score (2)" in this department--This course will be quickly replicated and introduce advanced content; while the concept of the differential and scores of the single variable vector value, the differential and scores of the multivariate vector value function cannot be introduced in the course of "Micro Score (2)" due to the limitation of the teaching time.
The course content includes:
1. Continuity, differential, gradient, divergence, rotation, function theorem, Lagrange multiplier.
2. Parameter curves, parameter surfaces
3. Re-score, line score, area score, Green theorem, Stoke theorem.
This course emphasizes the concept and calculation, especially calculation. Being familiar with the above calculation will establish the foundation of courses such as learning probability, mathematical statistics, complex functions, partial differential equations, and in-depth learning.
機率學主要的目的在於介紹和解析機會的結構及其相關之變數與函
數。
這方面的知識為許多進一步研究涉不確定性因素問題的學問的
基礎。本課程引導同學接觸一些有趣的理論和實例。
The main purpose of opportunity learning is to introduce and analyze the structure of opportunities and their related variables and functions.
Number.
This knowledge is a study of many further research on the problems of uncertain factors.
Basic. This course guides students to come across some interesting theories and examples.
1. Daniel Miranda, Vector and Tensor Calculus Frankenstein’s Note. (GNU Free Documentation)
2. David A. Santos, Multivariable and Vector Calculus Calculus. (GNU Free Documentation)
附註：
1. 上述主要參考書都是免費，可在網路下載。
1. Daniel Miranda, Vector and Tensor Calculus Frankenstein’s Note. (GNU Free Documentation)
2. David A. Santos, Multivariable and Vector Calculus Calculus. (GNU Free Documentation)
Note:
1. The above main reference books are free and can be downloaded online.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 平時成績平時成績 Regular achievements |
30 | 包含作業、助教隨堂測驗等成績 |
| 考試考試 exam |
80 | 包括二次小考、期中考、期末考，每次20% |
