|
課程名稱 |
微積分1
CALCULUS (1) |
|
開課學期 |
109-1 |
|
授課對象 |
物理學系 |
|
授課教師 |
張志中 |
|
課號 |
MATH4006 |
|
課程識別碼 |
201 49810 |
|
班次 |
05 |
|
學分 |
2.0 |
|
全/半年 |
半年 |
|
必/選修 |
必帶 |
|
上課時間 |
第1,2,3,4,5,6,7,8,9 週
星期一10(17:30~18:20)星期二6,7(13:20~15:10)星期四8,9(15:30~17:20) |
|
上課地點 |
新303新303新303 |
|
備註 |
密集課程。統一教學.一10為實習課.初選將直接帶入此班次的微積分2.加退選階段請自行加選微積分2.
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH4006_05 |
|
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
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
這是一門半學期的課程，主要介紹單變數函數的微分運算，和微分在各領域豐富的應用。內容涵蓋極限與連續的定義，微分技巧，畫函數圖形，和極值問題等。課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算。
Differentiation on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem and more.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. |
|
課程目標 |
修完本課程學生能熟悉微積分工具，並應用在各學科。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations. |
|
課程要求 |
修這門課以前，學生要熟練高中數學。學生應積極參與課堂和習題課的活動與討論。
Students participating in the course should be already skilled in high school mathematics. They are expected to attend and participate actively in lectures as well as discussion sessions. |
|
預期每週課後學習時數 |
|
|
Office Hours |
|
|
指定閱讀 |
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition. |
|
參考書目 |
微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
台大微積分考古題: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
期考 |
50% |
第八週末 11/8(日) 09:00~11:30 考試以英文命題 |
2. |
小考1 |
20% |
暫定 第六週 舉行 |
3. |
小考2 |
20% |
暫定 第八週 舉行 |
4. |
WeBWorK作業 |
10% |
每週末於 線上習題系統 WeBWorK 進行 |
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
9/14,9/15,9/17 |
9/15: 1.4 exponential functions, 2.4 the precise definition of a limit, and 2.3 the limit laws
9/17: 2.6 limits at infinity and infinite limits, and the squeeze theorem in 2.3
--------------------------
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
2.1 The Tangent and Velocity Problems |
|
第2週 |
9/21,9/22,9/24 |
9/22: 2.5 Continuity (and various types of discontinuity) and 2.7 derivatives. A proof of the product rule of 3.2
9/24: 2.8 The Derivative as a Function; a fixed point theorem and some examples
-------------------------
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit |
|
第3週 |
9/28,9/29 |
9/29: 3.1, 3.2, and 3.4 (an alternative definition of differentiability, differentiation rules, derivatives of exponential functions, higher order derivatives, and the chain rule)
===========================
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
10/01 中秋節 |
|
第4週 |
10/05,10/06,10/08 |
10/6: 3.3 Derivatives of Trigonometric Functions, 3.5 Implicit Differentiation, and 3.6 Derivative of Logarithmic Function
10/8: Completion of 3.5 and 3.6 (Derivatives of Inverse Trigonometric Functions, logarithmic differentiation, examples, and more)
=================================
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule |
|
第5週 |
10/12,10/13,10/15 |
10/13: 3.8, 3.9, and 3.10
10/15: 4.1 and 4.2 (mean value theorem and Cauchy's MVT)
================================
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
3.8 Exponential Growth and Decay (✽) |
|
第6週 |
10/19,10/20,10/22 |
10/20: Applications of mean value theorem and 4.3
10/22: 4.4 L'Hospital's rule
============================
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions (✽)
4.1 Maximum and Minimum Values
第一次 小考，範圍至第5週教授之內容。一切考試以英文命題。
10/19(一) 17:30~18:20 Quiz 1 範圍至3.6 |
|
第7週 |
10/26,10/27,10/29 |
10/27: 4.5 Curve sketching and 4.7 optimization problems
10/29: 4.8*, 4.9 antiderivatives, and an application of Cauchy MVT
==============================
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
10/30(五) 微積分1停修截止 |
|
第8週 |
11/02,11/03,11/05 |
11/03: Discussion
11/05: Quiz 2 and recitation
=============================
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives
第二次 小考，範圍同期考之內容
11/05(四) 15:30~16:20 Quiz 2
期考 11/8(日) 09:00~11:30 |
|