課程資訊
課程名稱
 微積分甲下
Calculus (general Mathematics) (a)(2) 
開課學期
 101-2 
授課對象
 材料科學與工程學系  
授課教師
 容志輝 
課號
 MATH1202 
課程識別碼
 201 101A2 
班次
 02 
學分
 4 
全/半年
 全年 
必/選修
 必修 
上課時間
 星期一9(16:30~17:20)星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) 
上課地點
 新203新203新203 
備註
 統一教學.大二以上限20人.一9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：130人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1012calculus02 
課程簡介影片
 
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課程概述

章節 週次 課程進度
9. Sequences, Series, and Power Series 第一週
(2/20~2/24) 9.1 Sequences and Convergence
9.2 Infinite Series
9.3 Convergence Tests for Positive Series
9.4 Absolute and Conditional Convergence
第二週
(2/27~3/2) 9.5 Power Series
9.6 Taylor and Maclaurin Series
9.7 Applications of Taylor and Maclaurin Series
9.8 The Binomial Theorem and Binomial Series
10. Vectors and Coordinate Geometry in 3-Space 第三週
(3/5~3/9) 10.3 The Cross Product in 3-Space
10.5 Quadric Surfaces
10.6 Cylindrical and Spherical Coordinates
10.7 A Little Linear Algebra（※）
11. Vector Functions and Curves 第四週
(3/12~3/16) 緩衝時間
11.1 Vector Functions of One Variable
11.3 Curves and Parametrizations
第五週
(3/19~3/23) 11.4 Curvature, Torsion, and the Frenet Frame
12. Partial Differentiation 12.1 Functions of Several Variables
12.2 Limits and Continuity
第六週
(3/26~3/30) 12.3 Partial Derivatives
12.4 Higher-Order Derivatives
12.5 The Chain Rule
12.6 Linear Approximations, Differentiability, and Differentials
第七週
(4/2~4/6)　 4/3(二)?4/6(五)放假
第八週
(4/9~4/13)　 12.7 Fradients and Directional Derivatives
12.8 Implicit Functions


13. Applications of Partial Derivatives 13.1 Extreme Values
13.2 Extreme Values of Functions Defined on Restricted Domains
第九週
(4/16~4/20) 13.3 Lagrange Multipliers
13.4 The Method of Least Squares（※）
緩衝時間
期中考4/22（日）09：00?11：30 考試範圍：9.1?13.4（英文命題）
14. Multiple Integration 第十週
(4/23~4/27) 14.1 Double Integrals
14.2 Iteration of Double Integrals in Cartesian Coordinates
14.3 Improper Integrals and a Mean-Value Theorem
14.4 Double Integrals in Polar Coordinates
第十一週
(4/30~5/4) 14.5 Triple Integrals
14.6 Change of Variables in Triple Integrals
14.7 Applications of Multiple Integrals
15. Vector Fields 第十二週
(5/7~5/11) 緩衝時間
15.1 Vector and Scalar Fields
15.2 Conservative Fields
第十三週
(5/14~5/18) 15.3 Line Integrals
15.4 Line Integrals of Vector Fields
15.5 Surfaces and Surface Integrals
15.6 Oriented Surfaces and Flux Integrals
16. Vector Calculus 第十四週
(5/21~5/25) 緩衝時間
16.1 Gradient, Divergence, and Curl
16.2 Some Identities Involving Grad, Div, and Curl
第十五週
(5/28~6/1) 16.3 Green's Theorem in the Plane
16.4 The Divergence Theorem in 3-Space
16.5 Stokes's Theorem
16.7 Orthogonal Curvilinear Coordinates（※）
17. Ordinary Differential Equations 第十六週
(6/4~6/8) 緩衝時間
17.1 Classifying Differential Equations
17.2 Solving First-Order Equations
17.4 Differential Equations of Second Order
第十七週
(6/11~6/15) 17.5 Linear Differential Equations with Constant Coefficients
17.6 Nonhomogeneous Linear Equations
緩衝時間
期末考6/17（日）09：00?11：30 考試範圍：14.1?17.6（英文命題）
說明：（※）此符號標示之課程，可由任課教師自行決定是否為教學內容，不列入考試範圍中 

課程目標
 Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. 
課程要求
 High School Mathematics

☆08-11班：上課時間：三78 五12 、 實習課時間：三9
12班：上課時間：二78 四56 、 實習課時間：二9
☆各班實習課分組教室：將公告於微積分甲統一教學網站公佈。
☆微積分甲統一教學網站：http://www.math.ntu.edu.tw/~mathcal/a/ 。
☆各班助教Office Hour時間：將公告於微積分甲統一教學網站公佈。
☆習題：習題繳交與否依各授課教師規定；習題解答將於公佈於微積分甲統一教學網站。
☆期中、期末考題目以英文命題。
 
預期每週課後學習時數
  
Office Hours
 另約時間 
參考書目
 Calculus: A Complete Course seventh edition. 
指定閱讀
  
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/18,2/20,2/22  Infinite Series, Positive Term Series, Alternating Series. 
第2週
 2/25,2/27,3/01  Absolute and Conditional Convergence, Power Series, Taylor's Formula with Remainder, Taylor's Theorem.
 
第3週
 3/04,3/06,3/08  Taylor's Series, Maclaurin's Series, Algebra of R^n Space. 
第4週
 3/11,3/13,3/15  Quiz 1, Scalar Triple Product and Cross Product in R^3, Topology of R^n, Limits and Continuity for (Vector-Valued) Functions of Several Variables. 
第5週
 3/18,3/20,3/22  Directional Derivatives, Partial Derivatives, Total Derivatives. 
第6週
 3/25,3/27,3/29  Mean-Value Theorem, Chain Rule, Implicit Function Theorem. 
第7週
 4/01,4/03,4/05  TA Time, Holiday. 
第8週
 4/08,4/10,4/12  Extreme Problems, Lagrange Multipliers, Parameterized Curves 
第9週
 4/15,4/17,4/19  Quiz 2, Regular Curves, Tangent Vector Fields, Arc Length, Reparameterization, Curvature, Osculating Planes, Torsion, Frenet-Serret Equations, Fundamental Theorem of Space Curves. 
第10週
 4/22,4/24,4/26  Double Integral, Fubini's Theorem, Iterated Integration, Midterm(4/27). 
第11週
 4/29,5/01,5/03  Double Integral for Arbitrary Bounded Regions, Intermediate Value Theorem and Mean Value Theorem for Double Integrals, Double Integrals in Polar Coordinate, 2-D Inverse Function Theorem, Change of Variables for Double Integrals. 
第12週
 5/06,5/08,5/10  Riemann Integral on R^n. 
第13週
 5/13,5/15,5/17  Cylindrical Coordinates, Spherical Coordinates, Potential Functions, Curve Integrals. 
第14週
 5/20,5/22,5/24  Quiz 3, Curve Integrals with Respect to Arc Length, Parametric Surfaces in R^3, Surface Area. 
第15週
 5/27,5/29,5/31  Surface Integrals, Green's Theorem in R^2, Del Operator,Divergence, Curl. 
第16週
 6/03,6/05,6/07  Stokes' Theorem, Divergence Theorem, Laplacian, Irrotational Vector Fields. 
第17週
 6/10,6/12,6/14  Quiz 4, Solenoidal Vector Fields.  
第18週
 6/16  Final Examination (13:30 - 16:00).