課程大綱

課程資訊

課程名稱

微積分甲下
Calculus (general Mathematics) (a)(2)

開課學期

103-2

授課對象

化學系

授課教師

莊正良

課號

MATH1202

課程識別碼

201 101A2

班次

學分

全/半年

全年

必/選修

必修

上課時間

星期三7,8,9(14:20~17:20)星期五1,2(8:10~10:00)

上課地點

新303新303

備註

統一教學.大二以上限20人.三9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：100人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1032MATH1202_09

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課程概述

[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

實習課教室分配：
以學號末三碼除以三之餘數分班
餘一班：新生303 (薛竣壬助教)
餘二班：新生301 (蔡宜霖助教)
餘零班：新生302 (林上景助教)

課程目標

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.

課程要求

High School Mathematics

預期每週課後學習時數

Office Hours

指定閱讀

待補

參考書目

James Stewart, Calculus Early Transcendentals, 7th edition.

評量方式
(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	<html> <head> <title> </title> </head> <body> [11.1] Sequences <br> [11.2] Series <br> 註：2/27(五)和平紀念日遇例假日補假 <br> </body> </html>
第2週	3/04,3/06	<html> <head> <title> </title> </head> <body> [11.3] The Integral Test and Estimates of Sums <br> [11.4] The Comparison Tests <br> [11.5] Alternating Series <br> [11.6] Absolute Convergence and the Ratio and Root Tests <br> </body> </html>
第3週	3/11,3/13	<html> <head> <title> </title> </head> <body> [11.7] Strategy for Testing Series <br> [11.8] Power Series <br> [11.9] Representations of Functions as Power Series <br> </body> </html>
第4週	3/18,3/20	<html> <head> <title> </title> </head> <body> [11.10] Taylor and Maclaurin Series <br> [11.11] Applications of Taylor Polynomials <br> [12.6] Cylinders and Quadric Surfaces <br> [13.1] Vector Functions and Space Curves <br> Quiz 1 (3/18) <br> </body> </html>
第5週	3/25,3/27	<html> <head> <title> </title> </head> <body> [13.2] Derivatives and Integrals of Vector Functions <br> [13.3] Arc Length and Curvature <br> [14.1] Functions of Several Variables <br> [14.2] Limits and Continuity <br> [14.3] Partial Derivatives <br> </body> </html>
第6週	4/01,4/03	<html> <head> <title> </title> </head> <body> 4/1(三) 溫書假 <br> 4/3(五) 溫書假 <br> </body> </html>
第7週	4/08,4/10	<html> <head> <title> </title> </head> <body> [14.4] Tangent Planes and Linear Approximations <br> [14.5] The Chain Rule <br> [14.6] Directional Derivatives and the Gradient Vector <br> Quiz 2 (4/8)<br> </body> </html>
第8週	4/15,4/17	<html> <head> <title> </title> </head> <body> [14.7] Maximum and Minimum Values <br> [14.8] Lagrange Multipliers <br> </body> </html>
第9週	4/22,4/24	<html> <head> <title> </title> </head> <body> 緩衝時間 <br> Quiz 3 (4/22) <br> 期中考 4/25（六）09：00∼11：30 考試範圍：11.1∼14.8（英文命題） <br> </body> </html>
第10週	4/29,5/01	<html> <head> <title> </title> </head> <body> [15.1] Double Integrals over Rectangles <br> [15.2] Iterated Integrals <br> [15.3] Double Integrals over General Regions <br> </body> </html>
第11週	5/06,5/08	<html> <head> <title> </title> </head> <body> [15.4] Double Integrals in Polar Coordinates <br> [15.5] Applications of Double Integrals <br> [15.6] Surface Area <br> [15.7] Triple Integrals <br> </body> </html>
第12週	5/13,5/15	<html> <head> <title> </title> </head> <body> [15.8] Triple Integrals in Cylindrical Coordinates <br> [15.9] Triple Integrals in Spherical Coordinates <br> [15.10] Change of Variables in Multiple Integrals <br> Quiz 4 (5/13)<br> </body> </html>
第13週	5/20,5/22	<html> <head> <title> </title> </head> <body> 緩衝時間 <br> [16.1] Vector Fields <br> [16.2] Line Integrals <br> </body> </html>
第14週	5/27,5/29	<html> <head> <title> </title> </head> <body> [16.3] The Fundamental Theorem for Line Integrals <br> [16.4] Green's Theorem <br> Quiz 5 (5/27) </body> </html>
第15週	6/03,6/05	<html> <head> <title> </title> </head> <body> [16.5] Curl and Divergence <br> [16.6] Parametric Surfaces and Their Areas <br> [16.7] Surface Integrals <br> </body> </html>
第16週	6/10,6/12	<html> <head> <title> </title> </head> <body> [16.8] Stokes' Theorem <br> [16.9] The Divergence Theorem <br> [16.10] Summary <br> Quiz 6 (6/10) </body> </html>
第17週	6/17, 6/19	<html> <head> <title> </title> </head> <body> 緩衝時間<br> 期末考 6/19（五）09：00∼11：30 考試範圍：15.1∼16.10 （英文命題） <br> </body> </html>