課程名稱 |
微積分甲上 Calculus (general Mathematics) (a)(1) |
開課學期 |
101-1 |
授課對象 |
經濟學系 |
授課教師 |
張鎮華 |
課號 |
MATH1201 |
課程識別碼 |
201 101A1 |
班次 |
03 |
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303新103新103 |
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:100人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1011_Calculus_A03 |
課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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課程概述 |
One variable calculus
統一教學網站: http://www.math.ntu.edu.tw/~mathcal/a/ |
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 |
預期每週課後學習時數 |
|
Office Hours |
每週三 15:20~17:20 |
參考書目 |
Salas, Hille and Etgen, Calculus: One and Several variables, Tenth Edition,
Wiley. |
指定閱讀 |
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期中考 |
40% |
11/10 (六) 13:30~16:00 考試範圍 2.1~5.9 (英文命題) |
2. |
期末考 |
40% |
1/5 (六) 13:30~16:00 考試範圍 6.1~11.7 (英文命題) |
3. |
小考及作業 |
20% |
約兩週一次小考 ***** 作業不必繳但在週一演習課上台做 |
|
週次 |
日期 |
單元主題 |
第0週 |
每週一第9節實習 每週三56節上課 每週五56節上課 |
實習教室: 新生303 (學號後三碼除以3餘0), 403 (餘1), 404 (餘2)
**************** 上課教室: 新生103 **********
Office hours: 張鎮華 週三78節 天數館521室 ***** 許祐鴻 週一56節 天數館544室 ********* 蘇哲聖 週五78節 天數館456室 ******** 吳宜欣 週四56節 教研館326室 |
第1週 |
9/10,9/12,9/14 |
[2.1] The Limit Process (An Intuitive Introduction).
[2.2] Definition of Limit.
[2.3] Some Limit Theorems.
[2.4] Continuity. |
第2週 |
9/17,9/19,9/21 |
[2.5] The Pinching Theorem; Trigonometric Limits.
[2.6] Two Basic Theorems.
[3.1] The Derivative.
[3.2] Some Differentiation Formulas |
第3週 |
9/24,9/26,9/28 |
[3.3] The d/dx Notation; Derivatives of Higher Order.
[3.4] The Derivative as a Rate of Change.
[3.5] The Chain Rule.
[3.6] Differentiating the Trigonometric Functions.
[3.7] Implicit Differentiation; Rational Powers |
第4週 |
10/01,10/03,10/05 |
[4.1] The Mean-Value Theorem.
[4.2] Increasing and Decreasing Functions.
[4.3] Local Extreme Values.
[4.4] Endpoint Extreme Values; Absolute Extreme Values. |
第5週 |
10/08,10/10,10/12 |
10/10 holiday
[4.5] Some Max-Min Problems.
[4.6] Concavity and Points of Inflection |
第6週 |
10/15,10/17,10/19 |
[4.7] Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps.
[4.8] Some Curve Sketching.
*[4.9] Velocity and Acceleration; Speed.
[4.10] Related Rates of Change Per Unit Time.
[4.11] Differentials.
*[4.12] Newton-Raphson Approximations. |
第7週 |
10/22,10/24,10/26 |
[5.1] An Area Problem; A Speed-Distance Problem.
[5.2] The Definite Integral of a Continuous Function.
[5.3] The Function f(x) = INT t from a to x f(t) dt
[5.4] The Fundamental Theorem of Integral Calculus. |
第8週 |
10/29,10/31,11/02 |
[5.5] Some Area Problems.
[5.6] Indefinite Integrals.
[5.7] Working Back from the Chain Rule; the u-Subtitution.
[5.8] Additional Properties of the Definite Integral.
[5.9] Mean-Value Theorems for Integrals; Average Value of a Function. |
第9週 |
11/05,11/07,11/09 |
[6.1] More on Area.
[6.2] Volume by Parallel Cross-Sections; Discs and Washers.
11/09 Buffer time **********
11/10(六) 13:30~16:00 期中考考試範圍 2.1~5.9 (英文命題). |
第10週 |
11/12,11/14,11/16 |
[6.3] Volume by the Shell Method.
[6.4] The Centroid of a Region; Pappus’s Theorem on Volumes.
7. The
Transcendental
Functions
[7.1] One-to-One Functions; Inverse Functions.
[7.2] The Logarithm Function, Part I. |
第11週 |
11/19,11/21,11/23 |
[7.3] The Logarithm Function, Part II.
[7.4] The Exponential Function.
[7.5] Arbitrary Powers; Other Bases.
[7.6] Exponential Growth and Decay. |
第12週 |
11/26,11/28,11/30 |
[7.7] The Inverse Trigonometric Functions.
[7.8] The Hyperbolic Sine and Cosine.
8. Techniques of
Integration
[8.1] Integral Tables and Review.
[8.2] Integration by Parts. |
第13週 |
12/03,12/05,12/07 |
[8.3] Powers and Products of Trigonometric Functions.
[8.4] Integrals Featuring root(aa-xx), root(aa+xx), root(xx-aa).
[8.5] Rational Functions; Partial Functions.
[8.6] Some Rationalizing Substitutions.
*[8.7] Numerical Integration. |
第14週 |
12/10,12/12,12/14 |
[9.1] First-Order Linear Equations.
[9.2] Integral Curves; Separable Equations.
[9.3] The Equation y''+ ay'+ by = 0.
10. The Conic
Sections; Polar
Coordinates;
Parametric
Equations
[10.2] Polar Coordinates.
[10.3] Graphing in Polar Coordinates. |
第15週 |
12/17,12/19,12/21 |
[10.4] Area in Polar Coordinates.
[10.5] Curves Given Parametrically.
[10.6] Tangents to Curves Given Parametrically.
[10.7] Arc Length and Speed.
[10.8] The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area. |
第16週 |
12/24,12/26,12/28 |
[11.1] The Least Upper Bound Axiom.
[11.2] Sequences of Real Numbers.
[11.3] The Limit of a Sequence.
[11.4] Some Important Limits.
[11.5] The Indeterminate Forms (0/0). |
第17週 |
12/31,1/02,1/04 |
[11.6] The Indeterminate Form (∞/∞); Other Indeterminate Forms.
[11.7] Improper Integrals.
1/04 Buffer time **********
1/5(六) 13:30~16:00 期末考考試範圍 6.1~11.7 (英文命題). |
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