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

97-1

授課對象

材料科學與工程學系

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

星期三5,6(12:20~14:10)星期五5,6(12:20~14:10)

上課地點

新102新102

備註

統一教學.大二以上限20人.一5為討論課.兼通識A6。
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/971cal01

課程簡介影片

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課程大綱

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課程概述

1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rule
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

After completing this course, students should be well versed in the mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering. They should also be well prepared for courses in differential equations, linear algebra, or advanced calculus.

課程要求

其它請上微積分統一教學網查詢：http://www.math.ntu.edu.tw/~calb/
課程講義、筆記、勾選習題，請上朱樺老師網站查詢：http://www.math.ntu.edu.tw/~hchu/Calculus/

預期每週課後學習時數

Office Hours

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.	期中考	40%
2.	期末考	40%
3.	作業	20%	小考+作業+演習課表現

課程進度

週次	日期	單元主題
第1週	9/17,9/19	[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	9/24,9/26	[2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit [2.5] Continuity [2.6] Limits at Infinity; HorizontalAsymptotes
第3週	10/01,10/03	[2.7] Derivatives and Rates of Change [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	10/08,10/10	[3.4] The Chain Rule [3.5] Implicit Differentiation [3.6] Derivatives of Logarithmic Functions
第5週	10/15,10/17	[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	10/22,10/24	[4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem [4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule
第7週	10/29,10/31	[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
第8週	11/05,11/07	[5.1] Areas and Distances [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	11/12,11/14	緩衝時間, Midterm Exam
第10週	11/19,11/21	[6.1] Areas between Curves [6.2] Volumes [6.3] Volumes by Cylindrical Shells [6.4] Work
第11週	11/26,11/28	[6.5] Average Value of a Function [7.1] Integration by Parts [7.2] Trigonometric Integrals [7.3] Trigonometric Substitution
第12週	12/03,12/05	[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	12/10,12/12	[7.8] Improper Integrals [8.1] Arc Length [8.2] Area of a Surface of Revolution [8.3] Applications to Physics and Engineering
第14週	12/17,12/19	[8.4] Applications to Economics and Biology [8.5] Probability [9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method
第15週	12/24,12/26	[9.3] Separable Equations [9.4] Models for Population Growth [9.5] Linear Equations [9.6] Predator-Prey Systems
第16週	12/31,1/02	[10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves [10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates
第17週	1/07,1/09	緩衝時間
第18週	1/14,1/16	Final Exam