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 calculus, with the purpose of supplementing students’ skills in freshman calculus course.
The concept and calculation ability of differential and integral functions of multi-variable real values, single-variable vector values, multi-variable vector values ​​and other types of functions.
In the past, the differentiation and integration of real-valued functions with multiple variables have been introduced in Calculus (2).
The focus of this course is the differentiation and integration of single-variable vector-valued and multi-variable vector-valued functions.
These concepts will be helpful in studying courses such as probability, mathematical statistics, function theory of complex variables, partial differential equations, and deep learning in the future.
Course content includes:
1. Continuity, differentiation, gradient, divergence, curl, implicit function theorem, Lagrange multiplier.
2. Parametric curves and parametric surfaces
3. Double integral, line integral, area integral, Green’s theorem, Stoke’s 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)