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

104-1

授課對象

地質科學系

授課教師

黃志強

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

星期一6,7(13:20~15:10)星期五1,2(8:10~10:00)

上課地點

普103普103

備註

大二以上限20人。
限本系所學生(含輔系、雙修生)
總人數上限：110人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1041MATH1201_11

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課程概述

1. Limits and continuity
2. Differentiation
3. Mean-value theorem and applications
4. Integration
5. Applications of the integral
6. The transcendental functions
7. Techniques of integration
8. Polar coordinate

課程目標

Understand "Limit,Continuity, Differentiation and Integration".

課程要求

預期每週課前或/與課後學習時數

Office Hours

每週三 13:30~15:30 備註： (助教Office Hour)

指定閱讀

參考書目

10th edition. Calculus/ Larson;Edwards;Shann

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	期中考(Midterm Exam)	30%
2.	期末考(Final Exam)	40%
3.	其他(Others)	30%	A.小考(Quiz)4選3(30%) or B.小考(Quiz)4選3(15%)+ 作業6選5(Homework)(15%) 加分(Bonus):出席(Attendance) (5%): 4-7(1%);8-11(2%);12-15(3%);16-19(4%); 20 up(5%)

本校尚無訂定 A+ 比例上限。
本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見學習評量專區 (連結)。

課程進度

週次	日期	單元主題
第1週	9/14,9/18	1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically
第2週	9/21,9/25	1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Innite Limits Homework 1 (Due Date: 10/02) 1.2 #36,#64 1.3 #56,#58,#65,#72,#124 1.4 #66,#111 1.5 #23
第3週	9/28,10/02	Mid-Autumn Festival 2.1 The Derivative and the Tangent Line Problem 2.2 Basic Dierentiation Rules and Rates of Change
第4週	10/05,10/09	Quiz 1 (10/05)--Chapter 1 2.3 Product and Quotient Rules and Higher-Order Derivatives 10/09Double tenth day
第5週	10/12,10/16	2.3 Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation 2.6 Related Rates 3.1 Extrema on an interval Homework 2 (Due Date:10/23)
第6週	10/19,10/23	3.2 Rolle’s Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching
第7週	10/26,10/30	3.7 Optimization Problems 3.9 Differentials 4.1 Antiderivatives and Indefinite Integration 4.2 Area Quiz 2 (Chapter 2) Homework 3 (Due Date:11/02)
第8週	11/02,11/06	4.3 Riemann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus 4.5 Integration by Substitution
第9週	11/09,11/13	Midterm Exam(ch1-ch4)
第10週	11/16,11/20	5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration
第11週	11/23,11/27	5.5 Bases Other Than e and Applications 5.6 Inverse Trigonometric Functions: Differentiation 5.7 Inverse Trigonometric Functions: Integration 5.8 Hyperbolic Functions Homework 4
第12週	11/30,12/04	5.8 Hyperbolic Functions 8.1 Basic Integration Rules 8.2 Integration by Parts 8.3 Trigonometric Integrals
第13週	12/07,12/11	8.4 Trigonometric Substitution 8.5 Partial Fractions 8.6 Integration by Tables and Other Integration Techniques 8.7 Indeterminate Forms and L’Hôpital’s Rule
第14週	12/14,12/18	8.7 Indeterminate Forms and L’Hôpital’s Rule 8.8 Improper Integrals Quiz 3 (5.1-5.7,8.1-8.4) 6.1 Slope Fields and Euler’s Method 6.2 Differential Equations: Growth and Decay Homework 5
第15週	12/21,12/25	6.3 Separation of Variables and the Logistic Equation 6.4 First-Order Linear Differential Equations 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method
第16週	12/28,1/01	7.2 Volume: The Disk Method 7.3 Volume: The Shell Method 7.4 Arc Length and Surfaces of Revolution Homework 6 New Year's Day
第17週	1/04,1/08	7.5 Work 7.6 Moments, Centers of Mass, and Centroids Quiz 4 (Ch1-Ch8:Formulas) Review(Ch1-Ch8)
第18週	1/11,11/15	Final Exam (Ch1-Ch8) Ending