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

98-1

授課對象

資訊管理學系

授課教師

蔡雅如

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505新304新304

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/981calculusA04

課程簡介影片

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

透過課堂講論及實習課演練，學習一維函數的微積分觀念與演算。

課程目標

上完本課程後，學生能夠熟悉極限的觀念、並將之應用在微分的求導及積分的運算上。學生也會學到各式的微分與積分技巧，並熟悉微分積分的應用。

課程要求

學生必須上課並出席習題課。每週會勾選習題，學生需練習並繳交這些習題。

預期每週課後學習時數

Office Hours

每週五 15:10~16:10

指定閱讀

參考書目

James Stewart, Calculus Early Transcendentals, 6th edition.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	平時成績	20%	評分細項請看公佈欄
2.	期末考	40%	微甲01-05班統一命題
3.	期中考	40%	微甲01-05班統一命題

課程進度

週次	日期	單元主題
第1週	9/14,9/16,9/18	[1.5] Exponential Functions [1.6] Inverse Functions and Logarithms [2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function
第2週	9/21,9/23,9/25	[2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit [2.5] Continuity [2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change
第3週	9/28,9/30,10/02	[2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions [3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions
第4週	10/05,10/07,10/09	[3.4] The Chain Rule [3.5] Implicit Differentiation [3.6] Derivatives of Logarithmic Functions [3.7] Rates of Change in the Natural and Social Sciences（※） [3.8] Exponential Growth and Decay
第5週	10/12,10/14,10/16	[3.9] Related Rates [3.10] Linear Approximations and Differentials [3.11] Hyperbolic Functions（※） [4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem
第6週	10/19,10/21,10/23	Quiz 1 [4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule 緩衝時間
第7週	10/26,10/28,10/30	[4.5] Summary of Curve Sketching [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems [4.8] Newton’s Method（※） [4.9] Antiderivatives [5.1] Areas and Distances
第8週	11/02,11/04,11/06	[5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus [5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule
第9週	11/09,11/11,11/13	Quiz 2 [6.1] Areas between Curves [6.2] Volumes 緩衝時間停課
第10週	11/16,11/18,11/20	[6.3] Volumes by Cylindrical Shells [6.4] Work（※） [6.5] Average Value of a Function [7.1] Integration by Parts
第11週	11/23,11/25,11/27	[7.2] Trigonometric Integrals [7.3] Trigonometric Substitution
第12週	11/30,12/02,12/04	[7.4] Integration of Rational Functions by Partial Fractions [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration
第13週	12/07,12/09,12/11	[7.8] Improper Integrals 緩衝時間
第14週	12/14,12/16,12/18	Quiz 3 [8.1] Arc Length [8.2] Area of a Surface of Revolution [9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method
第15週	12/21,12/23,12/25	[9.3] Separable Equations [9.4] Models for Population Growth [9.5] Linear Equations [9.6] Predator-Prey Systems （※）
第16週	12/28,12/30,1/01	[10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves 1/1(五) 元旦放假
第17週	1/04,1/06,1/08	Quiz 4 [10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates 緩衝時間