本課程是微積分的直接延伸課程，目的是為了補足同學在大一微積分課程中，
對於多變數實數值、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能力。
過去在微積分（二）之中已介紹過多變數實數值函數的微分與積分，
本課程的重點為單變數向量值、多變數向量值函數的微分與積分，
這些觀念將有助於在日後學習機率、數理統計、複變數函數論、偏微分方程、深度學習等課程。
課程內容包括：
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。

This course is a direct extension of micro-scores, with the purpose of which is to supplement students' micro-scores courses in the freshman year.
The concept and calculation ability of differentiation and fractions of functions of multiple variable real value, single variable vector value, multiple variable vector value and other types.
In the past, the differential and fractions of multiple variables' real numerical functions have been introduced in microscore (2).
The focus of this course is the differential and fraction of the single variable vector value function,
These concepts will help learn courses such as chances, mathematical statistics, complex functions, partial differential equations, and in-depth learning in the future.
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.

1. Vector Calculus, 3rd Edition, by Susan J. Colley
2. Calculus (Metric Version), 11th edition, by Larson and Edwards
3. Thomas’ Calculus, 12th Edition, 2010, Pearson, by G. B. Thomas, M. D. Weir, & J. R. Hass.
4. Vector and Tensor Calculus Frankenstein’s Note, by Daniel Miranda (免費，可在網路下載)

1. Vector Calculus, 3rd Edition, by Susan J. Colley
2. Calculus (Metric Version), 11th edition, by Larson and Edwards
3. Thomas’ Calculus, 12th Edition, 2010, Pearson, by G. B. Thomas, M. D. Weir, & J. R. Hass.
4. Vector and Tensor Calculus Frankenstein’s Note, by Daniel Miranda (free, available for download online)