課程大綱

課程資訊

課程名稱

微積分甲上
Calculus (general Mathematics) (a)(1)

開課學期

101-1

授課對象

資訊工程學系

授課教師

張鎮華

課號

MATH1201

課程識別碼

201 101A1

班次

學分

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

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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

指定閱讀

參考書目

Salas, Hille and Etgen, Calculus: One and Several variables, Tenth Edition,
Wiley.

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

課程進度

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).