這是一門半學期的課程,主要介紹單變數函數的積分運算,和積分在各領域豐富的應用。內容涵蓋積分的定義,微積分基本定理,積分技巧,積分在機率的應用,和初步的微分方程等。最後,課程將簡介級數與泰勒展式,解釋如何以多項式逼近複雜的函數。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。

Integration on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, applications of integrals in probability, solving elementary differential equations and more. In addition to these, series and Taylor expansions are briefly introduced in the end of this course to explain how complicated functions are approximated by polynomials. 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.