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

102-1

授課對象

資訊管理學系

授課教師

朱樺

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/1021calculusA

課程簡介影片

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課程概述

One variable calculus
上課筆記:http://www.math.ntu.edu.tw/~hchu/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

指定閱讀

參考書目

Calculus: Early Transcendentals 7th edition，作者： James Stewart

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%	包含小考、作業、演習課表現等

課程進度

週次	日期	單元主題
第1週	9/09,9/11,9/13	[1.5] Exponential Functions</br> [1.6] Inverse Functions and Logarithms</br> [2.1] The Tangent and Velocity Problems</br> [2.2] The Limit of a Function</br> [2.3] Calculating Limits Using the Limit Laws
第2週	9/16,9/18,9/20	[2.4] The Precise Definition of a Limit</br> [2.5] Continuity
第3週	9/23,9/25,9/27	[2.6] Limits at Infinity; Horizontal Asymptotes</br> [2.7] Derivatives and Rates of Change</br> [2.8] The Derivative as a Function </br> [3.1] Derivatives of Polynomials and Exponential Functions
第4週	9/30,10/02,10/04	[3.2] The Product and Quotient Rules</br> [3.3] Derivatives of Trigonometric Functions</br> [3.4] The Chain Rule</br> [3.5] Implicit Differentiation</br> Quiz 1
第5週	10/07,10/09,10/11	[3.6] Derivatives of Logarithmic Functions</br> [3.7] Rates of Change in the Natural and Social Sciences（※）</br> [3.8] Exponential Growth and Decay</br> [3.9] Related Rates</br> [3.10] Linear Approximations and Differentials</br> [3.11] Hyperbolic Functions
第6週	10/14,10/16,10/18	[4.1] Maximum and Minimum Values</br> [4.2] The Mean Value Theorem</br> Quiz 2
第7週	10/21,10/23,10/25	[4.3] How Derivatives Affect the Shape of a Graph</br> [4.4] Indeterminate Forms and L’Hospital’s Rule</br> [4.5] Summary of Curve Sketching</br> [4.6] Graphing with Calculus and Calculators（※）</br> [4.7] Optimization Problems
第8週	10/28,10/30,11/01	[4.8] Newton’s Method（※）</br> [4.9] Antiderivatives</br> [5.1] Areas and Distances</br> Quiz 3</br> Midterm Exam on Nov. 2
第9週	11/04,11/06,11/08	[5.2] The Definite Integral</br> [5.3] The Fundamental Theorem of Calculus</br> [5.4] Indefinite Integrals and the Net Change Theorem</br> [5.5] The Substitution Rule
第10週	11/11,11/13,11/15	[6.1] Areas Between Curves </br> [6.2] Volumes</br> [6.3] Volumes by Cylindrical Shells</br> [6.4] Work（※）
第11週	11/18,11/20,11/22	[6.5] Average Value of a Function（※）</br> [7.1] Integration by Parts</br> [7.2] Trigonometric Integrals</br> [7.3] Trigonometric Substitution</br> [7.4] Integration of Rational Functions by Partial Fractions
第12週	11/25,11/27,11/29	[7.5] Strategy for Integration </br> [7.7] Approximate Integration</br> [7.8] Improper Integrals</br> [8.1] Arc Length</br> Quiz 4
第13週	12/02,12/04,12/06	[8.2] Area of a Surface of Revolution</br> [8.3] Applications to Physics and Engineering</br> [8.4] Applications to Economics and Biology（※）</br> [8.5] Probability（※）
第14週	12/09,12/11,12/13	[9.1] Modeling with Differential Equations</br> [9.2] Direction Fields and Euler’s Method（※）</br> [9.3] Separable Equations</br> [9.4] Models for Population Growth</br> Quiz 5
第15週	12/16,12/18,12/20	[9.5] Linear Equations
第16週	12/23,12/25,12/27	[10.1] Curves Defined by Parametric Equations</br> [10.2] Calculus with Parametric Curves</br> [10.3] Polar Coordinates </br> [10.4] Areas and Lengths in Polar Coordinates</br> [10.6] Conic Sections in Polar Coordinates</br> Quiz 6
第17週	12/30,1/01,1/03	Final Exam on Jan. 5