Not open in course pre-registration period。 The course is conducted in English。Intensive courses。

Calculus 2 (微積分2) 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 and explore applications of Calculus under the guidance of teaching assistants. 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計算並探索微積分的應用。

Upon completing this course, students are expected to be able to : 1. Define the integral of a continuous function over a closed and bounded interval and express it using the corresponding Riemann sum. 2. Derive and apply the Fundamental Theorem of Calculus to compute definite integrals. 3. Use techniques such as substitution and integration by parts to compute indefinite integrals. 4. Apply integration to calculate geometric quantities such as areas and volumes; and quantities in Economics such as Gini index and surplus. 5. Define improper integrals, compute their values and apply them in computing probability. 6. Formulate and solve separable and first-order linear differential equations. 7. Explain the concept of higher-order approximations and write the Taylor’s series for elementary functions. 學生修習本課程後，應具備下列能力： 1. 能定義連續函數於封閉有界區間上的積分。 2. 能推導並應用微積分基本定理計算定積分。 3. 能運用變數代換、分部積分等技巧求出函數之不定積分。 4. 能利用積分計算面積、體積等幾何量，與 Gini index，surplus 等經濟學數值。 5. 能定義瑕積分並將其應用於機率之計算。 6. 能解出可分離變數型及一階線性微分方程式。 7. 能說明高階估計的概念，並寫出基本函數的泰勒展式。

Before taking this course, students should be skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test https://cool.ntu.edu.tw/courses/50879 which is designed for NTU freshmen. Students are expected to attend and participate actively in lectures as well as discussion sessions. 學生應熟練高中數學，並完成為台大新生預備的線上「微積分學前自我檢測」https://cool.ntu.edu.tw/courses/50879。 學生應出席並積極參與課堂與習題課的討論。

Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition, Metric Version. ISBN: 978-626-7533-06-2 Other useful websites 其他相關資訊  微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html 台大微積分考古題:  http://www.math.ntu.edu.tw/~calc/cl_n_34455.html 數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal  免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator  免費知識型計算引擎: https://www.wolframalpha.com