這是一門半學期的課程，主要介紹多變數函數的微積分運算，和其在各領域豐富的應用。

微分主題包含多變數函數的極限，偏微分，方向導數，切平面，線性逼近，和微分連鎖律；
並討論求函數極值，Lagrange乘子法等應用問題。 積分部分涵蓋多重積分與逐次積分的定
義，Fubini定理，和變數變換；並探究機率如何使用重積分。課堂上將講解定義並推導重要
定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微
積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算
並完成學習單上的小型研究題目。
Calculus of multivariable functions together with its profound applications in various
subject areas are introduced in this half-semester course. Especially, topics about
differentiation include limits, partial derivatives, directional derivatives, tangent planes,
linear approximations, and the chain rule. Also, applications such as finding extreme
values and methods of Lagrange multipliers are discussed. Topics about integration
involve definitions of multiple integrals and iterated integrals, Fubini’s theorem, change of
variables, and how multiple integrals are used in probability.
Definitions are discussed and the most important theorems are derived in the lectures with
a view to help students to develop their abilities in logical deduction and analysis. Practical
applications of Calculus in various fields are illustrated in order to promote a more organic
interaction between the theory of Calculus and students' own fields of study. This course
also provides discussion sessions in which students are able to improve their skills in
handling calculations in Calculus and complete small projects under the guidance of our
teaching assistants.