課程資訊

Calculus (general Mathematics) (a)(2)

103-2

MATH1202

201 101A2

09

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1032MATH1202_09

[11. Infinite Sequences and Series]
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials

[13. Vector Functions]
13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions
13.3 Arc Length and Curvature
13.4 Motion in Space: Velocity and Acceleration

[14. Partial Derivatives]
14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives
14.4 Tangent Planes and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector
14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers

[15. Multiple Integrals]
15.1 Double Integrals over rectangles
15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals in Polar Coordinates
15.5 Applications of Double Integrals
15.6 Triple Integrals
15.7 Triple Integrals in Cylindrical Coordinates
15.8 Triple Integrals in Spherical Coordinates
15.9 Change of Variables in Multiple Integrals

[16. Vector Calculus]
16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem for Line Integrals
16.4 Green's Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem
16.10 Summary

After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus.

High School Mathematics

Office Hours

James Stewart, Calculus Early Transcendentals, 7th edition.

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 2. 期末考 40% 3. 平時成績 20%

 課程進度
 週次 日期 單元主題 第1週 2/25,2/27 [11.1] Sequences
[11.2] Series

[11.4] The Comparison Tests
[11.5] Alternating Series
[11.6] Absolute Convergence and the Ratio and Root Tests

[11.8] Power Series
[11.9] Representations of Functions as Power Series

[11.11] Applications of Taylor Polynomials
[12.6] Cylinders and Quadric Surfaces
[13.1] Vector Functions and Space Curves
Quiz 1 (3/18)

[13.3] Arc Length and Curvature
[14.1] Functions of Several Variables
[14.2] Limits and Continuity
[14.3] Partial Derivatives

4/3(五) 溫書假

[14.5] The Chain Rule
[14.6] Directional Derivatives and the Gradient Vector
Quiz 2 (4/8)

[14.8] Lagrange Multipliers

Quiz 3 (4/22)

[15.2] Iterated Integrals
[15.3] Double Integrals over General Regions

[15.5] Applications of Double Integrals
[15.6] Surface Area
[15.7] Triple Integrals

[15.9] Triple Integrals in Spherical Coordinates
[15.10] Change of Variables in Multiple Integrals
Quiz 4 (5/13)

[16.1] Vector Fields
[16.2] Line Integrals

[16.4] Green's Theorem
Quiz 5 (5/27) 第15週 6/03,6/05 [16.5] Curl and Divergence
[16.6] Parametric Surfaces and Their Areas
[16.7] Surface Integrals

[16.9] The Divergence Theorem
[16.10] Summary
Quiz 6 (6/10) 第17週 6/17, 6/19 緩衝時間