本課程中文授課,使用英文教科書。密集課程。統一教學.四10為實習課.初選將直接帶入此班次的微積分2.加退選階段請自行加選微積分2.

「微積分1」上課時間為第一週至第八週。 這是一門半學期的課程，主要介紹單變數函數的微分運算，和微分在各領域豐富的應用。內容涵蓋極限與連續的定義、微分技巧、畫函數圖形、和極值問題等。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。 Differentiation 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 definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem and more. 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.

修完本課程學生能熟悉微積分工具，並應用在各學科。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。 Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. Calculus 1, 2, 3, and 4 provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.

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」。 學生應出席並積極參與課堂與習題課的討論。 Before taking this course, students should be already skilled in high school mathematics and finish the online "Pre-Calculus Self Diagnostic Test" which is designed for NTU freshmen. Students are expected to attend and participate actively in lectures as well as discussion sessions.

為了達到良好的學習效果，鼓勵同學每周花4-6小時課後時間完成以下任務 1. 理解並背下定義、定理與公式 2. 複習重要例題 3. 寫 webwork 作業、紙本作業 Students are encouraged to dedicate 4 to 6 hours per week to accomplish the following tasks. 1. Comprehend and memorize definitions, theorems, and formulas. 2. Review important examples. 3. Complete webwork homework and written homework.

Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition. 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