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課程名稱 |
微積分乙上
Calculus (general Mathematics) (b)(1) |
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開課學期 |
109-1 |
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授課對象 |
職能治療學系 |
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授課教師 |
張志中 |
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課號 |
MATH1203 |
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課程識別碼 |
201 101B1 |
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班次 |
06 |
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學分 |
3.0 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四10(17:30~18:20) |
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上課地點 |
新102新102 |
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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：130人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH1203_06 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Differential and integral calculus of one variable functions with applications.
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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. |
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課程要求 |
High School Mathematics |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
Textbook: Thomas' calculus, early transcendentals. 13th edition in SI units.
Revised by M. D. Weir and J. Hass. Pearson 2016. 東華書局/新月圖書 代理
(以往可推舉代表 與 書局連絡，直接運書至新生大樓付錢取書。)
注意: 多數 微積分教科書的內容 大同小異，已有一本微積分書的同學可考慮不必再買
上述課本，只需研讀既有書本其相應的章節內容即可。學習數學必須動手習做，
因此會勾選課本每節較具代表性(講明白一點，較繁複)的計算題請同學練習。
原則上每週末於線上 WeBWork 做簡單測試，確定是否已了解當週所授內容。
沒有購買課本的同學請務必拿手中既有的書本的習題切實演練。
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中考 |
30% |
暫定 |
2. |
期末考 |
30% |
暫定 |
3. |
max {quiz 1, quiz 2} (暫定) |
15% |
暫定 |
4. |
max {quiz 3, quiz 4} (暫定) |
15% |
暫定 |
5. |
WeBWork |
10% |
暫定 (每週線上演習，以全學期答對率計算得分) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/15, 17 |
9/15: 1.5 exponential functions, 2.3 the precise definition of a limit, and the limit laws in 2.2 (a proof on the limit of linear combination of functions was given)
9/17: 2.4 one-sided limits and its relationship with two-sided limit. An introduction of WeBWork given by TAs
=========================
First week of 2019 Fall semester:
2.3 The precise definition of a limit
2.2 Limit of a function and limit laws
(a proof on the limit of linear combination of functions was given)
2.4 One sided limit and its relation with two-sided limit |
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第2週 |
9/22, 24 |
9/22: The squeeze theorem (Theorem 4 on p. 73) with an outline of the proof of Theorem 5, and an application to exercise 49 on p.84. 2.5 Continuity, intermediate value theorem, and examples of various types of discontinuity
9/24: Removable discontinuity and 2.6 limits at infinity and infinite limits; asymptotes of graphs
==============================
9/17: 2.5 Continuity, examples of various types of discontinuity, and 2.6 limits involving infinity.
9/19: Asymptotes of graphs, properties of continuity, and intermediate value theorem |
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第3週 |
9/29, 10/1* |
9/29: 3.1, 3.2, and 3.3 (differentiation rules, derivatives of exponential functions, and higher order derivatives) (3.4 is skipped)
==============================
9/24: 3.1, 3.2
9/26: 3.3 differentiation rules, derivatives of exponential functions, and higher order derivatives |
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第4週 |
10/6, 10/8 |
10/6: Theorem 7 on p. 104 (limit of (sin x)/x as x approaching zero) and related limits, 3.5 derivatives of trig. functions, and 3.6 the chain rule
10/8: 3.7 Implicit differentiation
=====================================
10/1: 3.5 derivatives of trig. functions, 3.6 the chain rule, and 3.7 implicit differentiation (3.4 is skipped)
10/3: 3.8 exponential and logarithmic functions |
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第5週 |
10/13, 10/15 |
10/13: Derivative of logarithmic function, logarithmic differentiation, a limit of e, and examples
10/15: Recitation 演習課
=================================
10/08: 3.11 linear approximation and differentials |
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第6週 |
10/20, 10/22 |
10/20: 3.11 linearization and differentials, 4.1, and the Rolles's theorem of 4.2
10/22: Quiz 1
================2019=================
10/15: 4.1 absolute/relative max. and min. values, extreme value theorem, and 4.2 mean value theorem
2019/10/17 (Thur.) Quiz 1 on chapters 2 and 3
-----------------2018---------------
10/16: 3.9 a brief introduction of inverse trigonometric functions (including their derivatives), and 3.11 linearization and differentials
10/18: absolute/relative max. and min. values, and extreme value theorem。後半小時發小考1考卷
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第7週 |
10/27, 10/29 |
10/27: 4.2 Mean value theorem, 4.3 first derivatives and the monotonic functions, and 4.4 concavity and curve sketching
10/29: 4.5 L'Hopital's rule
==========2019====================
10/22: 4.3 and 4.4 concavity and curve sketching
10/24: 4.4 examples of curve sketching, 後半小時發小考1考卷
----------2018------------------------------
10/23: theoretical parts of 4.1 - 4.3, and L'Hopital's rule in 4.5
10/25: 4.4 concavity and curve sketching |
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第8週 |
11/3, 11/5 |
11/3: 4.5 L'Hopital's rule
11/5: Recitation 發quiz 1 考卷 與 演習課
=================2019=============
10/29: 4.5 indeterminate forms
10/31: 4.6 applied optimization
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2018/10/30: more examples of curve sketching and indeterminate forms (4.4 and 4.5)
2018/11/01: quiz 2 |
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第9週 |
11/10, 11/12 |
11/10: 4.4 Curve sketching revisited and 4.6 applied optimization
11/12: 4.7*, 4.8*, and 5.3 the definite integral (only the definition is introduced)
=============2019===================
11/05: 4.8 antiderivatives, 5.2 and 5.3 definition and properties of Riemann sums and definite integrals.
11/07: Quiz 2
------- 2018 ------------------------
11/6: 4.6 applied optimization
11/8: 4.8 antiderivatives and 5.2 partition of an interval, and so on.
4.7 and 5.1 are skipped
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第10週 |
11/17, 11/19 |
11/17: 5.4 The fundamental theorem of calculus
11/19: Quiz 2
===========2019=========================
11/12: 5.4 The fundamental theorem of calculus, and 5.5 integration by substitution
11/14: 發 quiz 2 考卷與演習課
----------2018-------------------------
11/13: Definition and properties of Riemann integrals.
11/15: 校慶 |
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第11週 |
11/24, 11/26 |
11/24: Midterm exam.
11/26: 5.5 integration by substitution and the first half of 5.6 (up to Theorem 8)
====================2019==================
11/19: Midterm exam.
11/21: 5.6 area between curves
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11/20: Midterm exam.
11/22: 5.4 The fundamental theorem of calculus |
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第12週 |
12/1, 12/3 |
12/1: 5.6 and 8.2 integration by parts
12/3: 8.2 reduction formulas (p. 479) of \sin^n x and \sec^n x, exercise 68, and Wallis product of \pi/2
==============2019============
11/26 and 11/28: 6.1 and 6.2 volumes by disk and shell methods
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11/27: 5.5 integration by substitution
11/29: 5.6 and 6.1 area between curves and volumes using cross-sections |
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第13週 |
12/8, 12/10 |
12/08: 8.3 integration of \sin^n x \cos^m x.第四堂發期中考考卷
12/10: Recitation 演習
==============2019===========
12/03: 6.3 arc length, inverse sine, and 7.1 formal definitions of logarithm and exponential functions (11:40-12:10 發，並檢討 期中考)
12/05: 7.2 separable differential equations, and 8.2 integration by parts
------------------------------
12/4: 6.1 and 6.2 volumes by disk and shell methods
12/6: 6.3 arc length |
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第14週 |
12/15, 12/17 |
12/15: 8.5 Integration of rational functions by partial fractions (only cases 1-3 were studied)
12/17: quiz 3
=======================2019=============
12/10: 8.1 and 8.2
12/12: Quiz 3 (up to 6.3)
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12/11: separable differential equations, integration by parts
12/13: Quiz 3 |
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第15週 |
12/22, 12/24 |
12/22: 8.5 (completed) and 8.8 Improper integrals (Type 1 discussed)
12/24: 8.8 Type 2 improper integrals, direct and limit comparison tests
=======2019===================
12/17: 8.5 integration of rational functions and partial fractions
12/19: 8.3 (sine and cosine)
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12/18: 8.2, 8.3 (sine and cosine), and 8.5
12/20: 8.5 |
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第16週 |
12/29, 12/31 |
12/29: First order separable and linear differential equations
12/31: Recitation (answer sheets of quiz 3 will be returned)
========2019============================
12/24: Improper integrals, comparison and limit comparison theorems
12/26: 18:00 - 18:20 發 quiz 3 考卷
-----------------------------------------
12/25: Improper integrals
12/27: Improper integrals (direct and limit comparison theorems)
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第17週 |
1/5, 1/7 |
1/5: 10:20-11:10 review, 11:20-12:10 recitation
1/7: Quiz 4
1/12: Final exam.
=============2019===========
(由這行說明開始，包含本週與以下之內容為系統複製去年課程之進度，其目的在提供同學了解往年課程進行之快慢及其內容。
日後隨著日期與課程進行，將會逐週進行更新。
同學請以最新逐週公布的『課程大綱』為準，進行複習，演練習題。）
12/31: review. 11:20 - 12:10 recitation
1/2: quiz 4
1/7: final exam.
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1/3: quiz 4 on separable differential equations, integration by parts, and integrals of rational functions
1/8: Final exam. |
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