3.3--16.17.21.41.42.43.46.47.50.53.54.55.56.57.59
3.4--4.8.11.13.16
3.5--10.16.17.19.23.25.26.36.37.38.40.41.43.45.59.60.61.63.64
3.6--7.9.15.17.27.28.29.30.47.49.52.53.60.68.70
3.7--18.19.23.25.37.45.57.58
review--10.11.25.42.45.46.55.56.57.58
4.1--12.13.15.17.20.22.24.25.31.32.42
4.2--5.9.10.11.18.19.24.37.38.39.40.41.42.51.57.58
4.3--16.17.18.25.27.34.35.36.40.43.44
4.4--13.17.19.20.21.25.26.27.28.29.30.45
4.5--25.35.38.41.43.49
4.6--3.6.35.36.40.42.43.47
4.8--19.20.21.23.26.29.30.35.38.42.56
2007年11月28日 星期三
2007年11月10日 星期六
2007年11月4日 星期日
Look at Arnold's cat map which is a hyperbolic map
Arnold 的貓映射，真有趣！
你能想像在一個TORUS上的一個映射一次比一次解構混亂，但在經過300步之後貓臉又神奇地幾乎回到原來的貓臉樣？看看這個。
http://en.wikipedia.org/wiki/Arnold%27s_cat_map
你能想像在一個TORUS上的一個映射一次比一次解構混亂，但在經過300步之後貓臉又神奇地幾乎回到原來的貓臉樣？看看這個。
http://en.wikipedia.org/wiki/Arnold%27s_cat_map
2007年9月19日 星期三
微乙課程大綱
I. Differentiation and Continuity of function of a real variable
1. History of calculus and some elementary prerequisites in analytical geometry and algebra. 2. Concept of infinitesimal and the concept of differentiation.
3. Differentiability and Continuity. First order approximation of a function value near a known function value.
4. Differentiation rules, arithmetic rules, and chain rule of elementary functions. Differentiation of inverse function.
5. Roll’s theorem, mean value theorem, intermediate value theorem. 6 Graphing of rational functions, trigonometric and inverse functions.
7. Extrema problems of continuous and differentiable functions. Applications of this extremal calculus。
8 Implicit differentiation of functions. How to locate the tangent line to a conics. II. Integration
9.Partition and integration of a continuous function, upper and lower sums, Riemann sums to prove arithmetic laws of integration. Fundamental theorem of calculus.
10. Elementary indefinite integrals of elementary functions.
大約以此為上下學期之分水嶺—
11. Region viewed as consists of line segments and hence the computation of the area based on the length of these line segments. Volume decided by cross sections. Volume of revolution of a region of function. Cavalieri principle.
12 Generalized mean value theorem and L’Hopital’s rule.
13. Center of mass of volume of revolution and the theorem of Pappus.
14. Exponential functions, logarithmic functions, their derivatives and integrations
15. Techniques of integration including substitution and integration by parts, trigonometric substitutions, partial fractions.
16. Numerical integrations. Trapezoidal rule, Simpson’s rule, error of these numerical estimations.
17. Differential equations and its application in physics, biology and ecology.
18. Taylor polynomial, Taylor remainders, Taylor series of a function relative to a point.
19. Taylor expansion and numerical approximation of higher order.
20. Partial derivative of function more than 1 variable. Gradient vector and the criteria of extrema of function of two variables. Lagrange method.
21. Double and triple integration. Repeated integration.
22. (option) Theory of series, criteria of convergence and divergence
先修 High school mathematics
教科書 Salas/Hille/Etgen : Calculus 10th edition
1. History of calculus and some elementary prerequisites in analytical geometry and algebra. 2. Concept of infinitesimal and the concept of differentiation.
3. Differentiability and Continuity. First order approximation of a function value near a known function value.
4. Differentiation rules, arithmetic rules, and chain rule of elementary functions. Differentiation of inverse function.
5. Roll’s theorem, mean value theorem, intermediate value theorem. 6 Graphing of rational functions, trigonometric and inverse functions.
7. Extrema problems of continuous and differentiable functions. Applications of this extremal calculus。
8 Implicit differentiation of functions. How to locate the tangent line to a conics. II. Integration
9.Partition and integration of a continuous function, upper and lower sums, Riemann sums to prove arithmetic laws of integration. Fundamental theorem of calculus.
10. Elementary indefinite integrals of elementary functions.
大約以此為上下學期之分水嶺—
11. Region viewed as consists of line segments and hence the computation of the area based on the length of these line segments. Volume decided by cross sections. Volume of revolution of a region of function. Cavalieri principle.
12 Generalized mean value theorem and L’Hopital’s rule.
13. Center of mass of volume of revolution and the theorem of Pappus.
14. Exponential functions, logarithmic functions, their derivatives and integrations
15. Techniques of integration including substitution and integration by parts, trigonometric substitutions, partial fractions.
16. Numerical integrations. Trapezoidal rule, Simpson’s rule, error of these numerical estimations.
17. Differential equations and its application in physics, biology and ecology.
18. Taylor polynomial, Taylor remainders, Taylor series of a function relative to a point.
19. Taylor expansion and numerical approximation of higher order.
20. Partial derivative of function more than 1 variable. Gradient vector and the criteria of extrema of function of two variables. Lagrange method.
21. Double and triple integration. Repeated integration.
22. (option) Theory of series, criteria of convergence and divergence
先修 High school mathematics
教科書 Salas/Hille/Etgen : Calculus 10th edition
2007年7月3日 星期二
微乙2007學期成績
成績計算方式：因為一再說明注重平時作業成績，亦經助教嚴格批改。所以
A.放大平時成績為20分 B.報告10分 C.（期中+期末）*40％
成績＝A+B+C+4
至於期中考成績＝MAX(第一次成績,50*(第2次成績/40)。此因第二次最高分者只得39分，故以40分為分母計算之。
注意：由於期中補考已經補正分母為40分。故成績皆有所改變
學號 學期成績
B94303050 33
B95401004 81
B95401010 96
B95401012 85
B95401018 72
B95401045 71
B95401046 67
B95401047 62
B95401049 90
B95401054 90
B95401057 86
B95401063 76
B95401068 99
B95401069 89
B95401070 90
B95401073 95
B95401076 76
B95401080 60
B95401085 42
B95401090 78
B95401096 66
B95401101 71
B95401104 68
B95401106 60
B95401107 64
B95401111 83
B95401112 95
B95401115 61
B95401119 76
B95401122 18
B95401123 6
B95401125 67
B95401126 72
B94403030 42
B95403009 63
B95403056 60
B95408016 76
B95408024 60
B95408028 48
B95408044 5
B95408047 84
B95409034 48
B95409044 60
B95603009 38
B95603019 12
B95603029 41
B95603036 34
B95603047 35
B95801002 92
B95801005 60
B95801018 63
B95801027 88
B95801046 50
B95801051 21
B95801055 60
B92801046 39
B95B01046 39
B95B01056 60
A.放大平時成績為20分 B.報告10分 C.（期中+期末）*40％
成績＝A+B+C+4
至於期中考成績＝MAX(第一次成績,50*(第2次成績/40)。此因第二次最高分者只得39分，故以40分為分母計算之。
注意：由於期中補考已經補正分母為40分。故成績皆有所改變
這是送成績股之成績。-------------------------
學號 學期成績
B94303050 33
B95401004 81
B95401010 96
B95401012 85
B95401018 72
B95401045 71
B95401046 67
B95401047 62
B95401049 90
B95401054 90
B95401057 86
B95401063 76
B95401068 99
B95401069 89
B95401070 90
B95401073 95
B95401076 76
B95401080 60
B95401085 42
B95401090 78
B95401096 66
B95401101 71
B95401104 68
B95401106 60
B95401107 64
B95401111 83
B95401112 95
B95401115 61
B95401119 76
B95401122 18
B95401123 6
B95401125 67
B95401126 72
B94403030 42
B95403009 63
B95403056 60
B95408016 76
B95408024 60
B95408028 48
B95408044 5
B95408047 84
B95409034 48
B95409044 60
B95603009 38
B95603019 12
B95603029 41
B95603036 34
B95603047 35
B95801002 92
B95801005 60
B95801018 63
B95801027 88
B95801046 50
B95801051 21
B95801055 60
B92801046 39
B95B01046 39
B95B01056 60
2007年6月9日 星期六
繳交報告
請微乙同學繳交級數這一章有關冪級數的報告。
成績佔學期總成績十分。
1.必須用手寫，必須是中文，有幾位僑生剛好相反，可以用英文。
2.A4紙張至少四頁，字體不可故意放大。若是，將打折。
3.是甚麼報告？必須包含一貫的知識體系與此知識之價值，與前面學過的哪些東西有關或哪些成為新的成果等等。
4.報告使你對知識有整體感，這是你要去自我闡述的。因此我當然不能、不該告訴你所謂的標準報告格式。格式自訂。
5.以自創性、完整性評分。反之抄襲，雖是報告，會給零分。
6.繳交期限，考試當天。是6月26日星期二。
成績佔學期總成績十分。
1.必須用手寫，必須是中文，有幾位僑生剛好相反，可以用英文。
2.A4紙張至少四頁，字體不可故意放大。若是，將打折。
3.是甚麼報告？必須包含一貫的知識體系與此知識之價值，與前面學過的哪些東西有關或哪些成為新的成果等等。
4.報告使你對知識有整體感，這是你要去自我闡述的。因此我當然不能、不該告訴你所謂的標準報告格式。格式自訂。
5.以自創性、完整性評分。反之抄襲，雖是報告，會給零分。
6.繳交期限，考試當天。是6月26日星期二。
2007年5月10日 星期四
學生學習問題諮詢資訊
1.『微積分教室』-- 數學系研究生所組成，服務時間週一至週五中午 12：20－ 14：20 ，新數101教室旁討論室。
2.另外，4/9 ~4/20 及 6/11~6/22 期中考、期末考期間增加服務時間下午16：30－18：30。
又----,
3.『微積分諮詢服務』--- 教務處教學發展中心於總圖 B1。可協助同學解決微積分問題。分為一對一、一對多進行，需事先至總圖B1預約。
2.另外，4/9 ~4/20 及 6/11~6/22 期中考、期末考期間增加服務時間下午16：30－18：30。
又----,
3.『微積分諮詢服務』--- 教務處教學發展中心於總圖 B1。可協助同學解決微積分問題。分為一對一、一對多進行，需事先至總圖B1預約。
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