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，和多重積分的變數變換等等。除此之外，我們將簡介指數成長/遞減模型，牛頓冷卻律，與 logistic 模型，示範各領域如何利用「數學模型」掌握關鍵規律，並解釋這些微分方程式的求解技巧。
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。

Calculus of multivariable functions together with its profound applications 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 more. In addition to these, exponential growth/ decay models, Newton’s law of cooling, and Logistic models are introduced as examples of how mathematical models describe various types of phenomena. Then techniques of solving separable differential equations and first order linear differential equations are presented.

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 make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.