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

99-1

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302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/991calculusA04

課程簡介影片

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課程概述

上學期：單變數微積分
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates

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

每週五 15:30~16:30

指定閱讀

James Stewart, Calculus Early Transcendentals, 6th
edition.

參考書目

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Midterm exam	40%	微甲一組統一命題、閱卷
2.	Final exam	40%	微甲一組統一命題、閱卷
3.	Quizzes and/or homework	20%	四次小考成績、作業成績，及習題課上台表現

課程進度

週次	日期	單元主題
第1週	9/13,9/15,9/17	[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	9/20,9/22,9/24	9/22(三)中秋節放假一天 [2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit
第3週	9/27,9/29,10/01	[2.5] Continuity [2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change [2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions
第4週	10/04,10/06,10/08	Quiz 1 [3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions [3.4] The Chain Rule [3.5] Implicit Differentiation
第5週	10/11,10/13,10/15	[3.6] Derivatives of Logarithmic Functions [3.7] Rates of Change in the Natural and Social Sciences（※） [3.8] Exponential Growth and Decay [3.9] Related Rates [3.10] Linear Approximations and Differentials [3.11] Hyperbolic Functions（※）
第6週	10/18,10/20,10/22	[4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem 緩衝時間
第7週	10/25,10/27,10/29	[4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule [4.5] Summary of Curve Sketching [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems
第8週	11/01,11/03,11/05	Quiz 2 [4.8] Newton’s Method（※） [4.9] Antiderivatives [5.1] Areas and Distances [5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus
第9週	11/08,11/10,11/12	[5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule 緩衝時間 11/13(六)13:30∼16:00期中考考試範圍 1.5∼5.5 (英文命題)
第10週	11/15,11/17,11/19	[6.1] Areas between Curves [6.2] Volumes [6.3] Volumes by Cylindrical Shells [6.4] Work（※）
第11週	11/22,11/24,11/26	[6.5] Average Value of a Function [7.1] Integration by Parts [7.2] Trigonometric Integrals
第12週	11/29,12/01,12/03	[7.3] Trigonometric Substitution [7.4] Integration of Rational Functions by Partial Fractions
第13週	12/06,12/08,12/10	Quiz 3 [7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration [7.8] Improper Integrals
第14週	12/13,12/15,12/17	緩衝時間 [8.1] Arc Length [8.2] Area of a Surface of Revolution
第15週	12/20,12/22,12/24	[9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method [9.3] Separable Equations [9.4] Models for Population Growth
第16週	12/27,12/29,12/31	Quiz 4 [9.5] Linear Equations [9.6] Predator-Prey Systems （※） [10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves
第17週	1/03,1/05,1/07	[10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates 緩衝時間 1/8(六)13:30∼16:00期末考考試範圍 6.1∼10.4 (英文命題)