課程資訊
 課程名稱 微積分甲下Calculus (general Mathematics) (a)(2) 開課學期 107-2 授課對象 化學工程學系 授課教師 陳子安 課號 MATH1202 課程識別碼 201E101A2 班次 05 學分 4.0 全/半年 全年 必/選修 必修 上課時間 星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) 上課地點 新202新202 備註 本課程以英語授課。統一教學.大二以上限20人.三10為實習課.限本系所學生(含輔系、雙修生)總人數上限：110人 Ceiba 課程網頁 http://ceiba.ntu.edu.tw/1072Calculus_A05 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 As a continuation of the course MATH1201 Calculus A, in which Calculus on functions of a single variable is discussed, this course turns to the introduction and applications of multivariable (mainly 2- and 3-variable) Calculus, which is the foundation of most of the practical use of Calculus in real life. Topics to be highlighted include definitions of partial derivatives and double/triple/line/surface integrals together with their geometric meanings, method of Lagrange Multipliers for solving extreme-value problems with constraints, and Green's/Stokes'/Divergence Theorem (multivariable version of the Fundamental Theorem of Calculus). For the completeness of the discussion on limits of a function or a sum of functions in the course of the study of Calculus, the definitions of limits of sequences and series are also introduced, which provide the theoretical basis of the introduction of power series. Power series is a generalisation of polynomials and can be used to represent elementary as well as more general functions, which paves the way for more advanced analysis of functions, necessary in practical applications in the non-idealistic world. 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 sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. 課程目標 Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus A (1) and (2)" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations. 課程要求 Students participating in the course should be already skilled in high school mathematics. They are expected to attend and participate actively in lectures as well as discussion sections. 預期每週課後學習時數 Office Hours 每週五 15:30~17:30 備註： The time slot shown here is the office hours of the instructor. For the office hours of our teaching assistants, see the section on contact information of teaching assistants. 參考書目 Textbook: James Stewart, Calculus Early Transcendentals, 8th edition. Website of the unified course on Calculus A: http://www.math.ntu.edu.tw/~mathcal/a/ NTU past-papers on Calculus A: http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7 Episte Math: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal Free online Desmos Graphing Calculator: https://www.desmos.com/calculator Online computational knowledge engine: https://www.wolframalpha.com 指定閱讀 James Stewart, Calculus Early Transcendentals, 8th edition (course textbook) 評量方式(僅供參考)
 課程進度
 週次 日期 單元主題 第1週 2/20,2/22,2/23 12.6 Cylinders and Quadric Surfaces 13.1 Vector Functions and Space Curves 13.2 Derivatives and Integrals of Vector Functions ※2/23(六)補3/1(五)的課 第2週 2/27 13.3 Arc Length and Curvature 13.4 Motion in Space: Velocity and Acceleration (✽) ※3/1(五)調整放假 第3週 3/06,3/08 14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 第4週 3/13,3/15 14.4 Tangent Planes and Linear Approximation 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector 第5週 3/20,3/22 14.7 Maximum and Minimum Values 14.8 Lagrange Multipliers 第6週 3/27,3/29 15.1 Double Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Double Integrals in Polar Coordinates 第7週 ※4/3(三)溫書假；4/5(五)民族掃墓節 第8週 4/10,4/12 15.4 Applications of Double Integrals 15.5 Surface Area 15.6 Triple Integrals 第9週 4/17,4/19,4/20 15.7 Triple Integrals in Cylindrical Coordinates 15.8 Triple Integrals in Spherical Coordinates 15.9 Change of Variables in Multiple Integrals ※期中考 4/20(六) 09:00~11:30 考試範圍 12.6~15.9(英文命題) 第10週 4/24,4/26 16.1 Vector Fields 16.2 Line Integrals 16.3 The Fundamental Theorem for Line Integrals 第11週 5/01,5/03 16.4 Green's Theorem 16.5 Curl and Divergence 16.6 Parametric Surfaces and Their Areas 第12週 5/08,5/10 16.7 Surface Integrals 16.8 Stokes' Theorem 16.9 The Divergence Theorem 第13週 5/15,5/17 16.10 Summary 11.1 Sequences 11.2 Series 第14週 5/22,5/24 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 第15週 5/29,5/31 11.6 Absolute Convergence and the Ratio and Root Tests 11.7 Strategy for Testing Series 11.8 Power Series 第16週 6/05 11.9 Representations of Functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials ※ 6/7(五)端午節 第17週 6/12,6/14,6/15 17.1 Second-Order Linear Equations (✽) 17.2 Nonhomogeneous Linear Equations (✽) ※期末考 6/15(六) 09:00~11:30 考試範圍 Ch11+Ch16(英文命題)