Fall 2016 MATH 1011E
Calculus 1 數學系微積分(一)
Syllabus 課程大綱
宣導事項
- 9/12/2016: 週三(9/14)若因颱風停課，則 Homework 0 順延至 9/19 之課堂繳交(每人交一份)，Homework 1 則與 Homework 2 一併繳交。上台報告與分組資訊將另行公布。
- 9/14/2016: 下週一(9/19)演習課改為正課，不用做報告，全班皆在水利系4671教室。
- 9/14/2016: Homework 0 繳交時間改為9/19星期一。
- 9/19/2016: Homework 1 已更新完畢，Homework 2 已上傳完畢，請注意截止日期並請盡快開始勿拖到最後一刻。
- 9/21/2016: 因進度問題，Homework 1 第5題(b)部分先不要做。
- 9/21/2016: 本週五(9/23)劉之中Office Hour因公事，改為11:00-12:00(有需要可再延長)。
- 9/26/2016: Homework 2 第三題先不要做。
- 9/26/2016: 台南市政府颱風停班停課消息未公布前，請先假設星期三照常上課，作業1，2繳交時間也依樣。
- 9/27/2016: 週三9/28/2016因颱風停課，Homework 1,2 請於週五9/30/2016 17:00 前，至老師辦公室繳交。辦公室門口將置有投遞箱，請將作業投入適當位置。
- 9/29/2016: Homework 3 有些許更新，請參考。截止日期未定，但下星期一不用報告。
- 9/29/2016: 10/3星期一演習課改為正課，請所有同學至水利系4671上課。
- 10/13/2016: Homework 4 若因教學進度落後而無法完成，可在星期五(10/15/2016)17:00前至老師辦公室繳交。
- 10/13/2016: Homework 4 第一題提示有誤，已修正。
- 10/26/2016: Midterm 1 將於10/31演習課討論並發回，請所有同學八點十分至水利系4671上課。
- 11/2/2016: Homework 7 加了若干註解，補充今天來不及講到的內容。
- 11/2/2016: Homework 7 做了稍許修改。
教學進度
9/12/2016(星期一): set and notations, functions and graphs, Intuitive idea of limit, review of numbers.
9/14/2016(星期三): 颱風停課。
9/19/2016(星期一): least upper bound/greatest lower bound, definition of real numbers, limit of functions.
9/21/2016(星期三): basic properties of limit, squeeze theorem, some basic computations.
9/26/2016(星期一): some basic limit computations, limit at infinity, introduction to sequences.
9/28/2016(星期三): 颱風停課。
10/3/2016(星期一): convergence vs. bounded, subsequences, upper and lower limits.
10/5/2016(星期三): finish upper and lower limits, quick introduction to metric spaces, introduction to Cauchy sequences.
10/10/2016(星期一): 台灣國慶日，停課。
10/12/2016(星期三): completeness of R, introduction to series.
10/17/2016(星期一): convergence of series, kth term test, p series, basic comparison test.
10/19/2016(星期三): limit comparison test, root test, ratio test.
10/24/2016(星期一): finish ratio tests, the constant e, the function e^x, exponential function.
10/26/2016(星期三): Midterm Exam 1.
10/31/2016(星期一): conditional convergence vs. absolute convergence, alternating series tests, power series.
11/2/2016(星期三): Introduction to continuous functions, basic topology on R.
11/7/2016(星期一): Compact sets on R, extreme value theorem.
11/9/2016(星期三): Intermediate value theorem, introduction to differentiation.
11/14/2016(星期一): Differentiation formula, chain rules.
11/16/2016(星期三): Generalized mean value theorem, mean value theorem, continuity of differentiation.
11/21/2016(星期一): L'Hospital rule, linear approximations.
11/23/2016(星期三): Higher derivatives, Taylor's Theorem.
11/28/2016(星期一): Derivations of some Taylor series, Euler's formula, introduction to term-by-term differentiations.
11/30/2016(星期三): Real analytic functions, introduction to optimizations.
12/5/2016(星期一): Optimizations, curve sketching.
12/7/2016(星期三): Finish curve sketching, related rates, implicit differentiations.
12/8/2016(星期四): Introduction to Riemann integrals.
12/12/2016(星期一): No class (教師出差)。
12/14/2016(星期三): Midterm 2.
12/19/2016(星期一): Some Riemann sum computations of integrals.
12/21/2016(星期三): Introduction to more integrable functions, properties of integrals.
12/22/2016(星期四): Fundamental theorem of calculus.
12/26/2016(星期一): Fundamental theorem of calculus, u-substitutions, area.
12/28/2016(星期三): areas, volume by cross sections, volume of revolutions (disk and washer method), Darboux integration.
1/4/2017(星期三): volume of revolutions (shell method), average, centroids.
作業
Homework 0 (所有人皆須繳交，截止日9/19/2016):
Download here
Homework 1 (分組模式，截止日 9/28/2016 星期三，與 Homework 2 一併繳交):
Download here, Solutions for 1-6,Solutions to all
Homework 2 (所有人皆須繳交，截止日 9/28/2016 星期三):
Download here, Solutions
Homework 3 (分組模式，截止日 10/19/2016，報告日 10/17/2016 ):
Download here, 部分提示,Solutions for 1-6
Homework 4 (所有人皆須繳交，截止日 10/19/2016):
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Homework 5 (所有人皆須繳交，截止日 10/26/2016):
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Homework 6 (所有人皆須繳交，截止日 11/2/2016):
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Homework 7 (分組模式，截止日 11/9/2016，報告日 11/7/2016 ):
Download here, 報告截影, Solutions
Homework 8 (分組模式，截止日 11/16/2016，報告日 11/14/2016 ):
Download here, 提示與簡化, 報告截影, Solutions
Homework 9 (分組模式，截止日 11/23/2016，報告日 11/21/2016 ):
Download here, 報告截影, Solutions
Homework 10 (分組模式，截止日 11/30/2016，報告日 11/28/2016 ):
Download here, 報告截影, Solutions
Homework 11 (小考模式，抽考日 12/5/2016，截止日 12/7/2016 ):
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Homework 12 (所有人皆須繳交，截止日 12/14/2016 ):
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Homework 13 (所有人皆須繳交，截止日 12/21/2016 ):
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Homework 14 (分組模式，截止日 12/28/2016，報告日 12/26/2016):
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Homework 15 (所有人皆須繳交，截止日 1/9/2017 與期末考一起繳交 ):
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分組資訊
Homework 1
Homework 3
Homework 7
Homework 8
Homework 9
Homework 10
Homework 14 + 報告時間限制
考試相關
講義
10/13課堂證明錯誤更正請下載
10/13課堂證明錯誤更正請limsup/liminf 補充資訊
第一週難度指標: 5