課程資訊

Calculus (general Mathematics) (a)(2)

100-2

MATH1202

201 101A2

11

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1002calculus_a_2_11

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

(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
10.6 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

(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

(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

(4/2~4/6)　 4/3(二)∼4/6(五)放假

(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

(4/16~4/20) 13.3 Lagrange Multipliers
13.4 The Method of Least Squares（※）

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

(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

(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
16.2 Some Identities Involving Grad, Div, and Curl

(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

(6/11~6/15) 17.5 Linear Differential Equations with Constant Coefficients
17.6 Nonhomogeneous Linear Equations

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.

High School Mathematics

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12班：上課時間：二78 四56 、 實習課時間：二9
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☆期中、期末考題目以英文命題。

Office Hours

Calculus: A Complete Course seventh edition.

Calculus: A Complete Course seventh edition.

(僅供參考)

 No. 項目 百分比 說明 1. 期中 40% 2. 期末 40% 3. 作業 5% 4. 小考 15%

 課程進度
 週次 日期 單元主題 第1週 2/22,2/24 Sequences and Infinite Series. 第2週 2/29,3/02 Positive Term Series, Alternating Series, and Power Series. 第3週 3/07,3/09 Sequences of Functions, Taylor Series, Binomial Series. 第4週 3/14,3/16 Algebra of R^n Space, Quadric Surfaces, Cylindrical and Spherical Coordinates. 第5週 3/21,3/23 Determinants, Cross Product in R^3, Topology of R^n, Quadratic Forms, Eigenvalues, Linear Transformation and Representation Matrix, and Limits of Vector-Valued Functions of Several Variables. 第6週 3/28,3/30 Continuity, Partial Derivatives, Directional Derivatives, Total Derivatives, and Gradients. 第7週 4/04,4/06 No Class. (Spring Vacation) 第8週 4/11,4/13 The Chain Rule, Equality of Mixed Partial Derivatives, Implicit Function Theorem, Extreme Problems and Lagrange Multipliers. 第9週 4/18,4/20 Regular Curves, Reparameterization, Arc-Length, Curvature, Torsion and Frenet-Serret Frame. (Mid-Term Exam on 4/22) 第10週 4/25,4/27 Riemann Integrals on R^n and Fubini's Theorem. 第11週 5/02,5/04 Inverse Function Theorem, Taylor Theorem, Change of Variables in Multiple Integrals, Improper Integrals, and Mean-Value Theorem. 第12週 5/09,5/11 Potential Functions and Curve Integrals. 第13週 5/16,5/18 Surface Integrals 第14週 5/23,5/25 Curl, Jordan Curve Theorem, Green's Theorem, and Stokes' Theorem. 第15週 5/30,6/01 Divergence Theorem (Gauss' Theorem), and Further Properties of the Gradient, Divergence, and Curl. 第16週 6/06,6/08 Exact Differential Equations, Integrating Factors. 第17週 6/13,6/15 Second Order Differential Equations, Variation of Parameters.