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課程名稱 |
線性代數二
Linear Algebra (Ⅱ) |
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開課學期 |
108-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
余正道 |
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課號 |
MATH1104 |
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課程識別碼 |
201 49600 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
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上課地點 |
新303新303 |
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備註 |
「教學改善計畫」課程，配有教學助理，實施「小班輔導」。
限本系所學生(含輔系、雙修生)
總人數上限：90人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1082MATH1104 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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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 |
The course is the continuation of Linear Algebra I of the previous semester, during which we have covered chapters 1,2,3,4,5,7 of [FIS]. In this semester we will start from chapter 6 of [FIS]. |
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課程目標 |
See above. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週五 10:30~12:00
每週三 10:30~12:00 備註： Wednesday: Astro-Math 461 (余正道);
Friday: Astro-Math 555 (呂治鴻), Astro-Math 548 (王羿璁), Astro-Math 526 (林自立), Astro-
Math 103 (林浚沂) |
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指定閱讀 |
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參考書目 |
[FIS] Linear Algebra, 4th Edition
by Stephen Friedberg, Arnold Insel, and Lawrence Spence
Other references will be supplemented along the way. |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
3/04,3/06 |
Inner product space, Gram-Schmidt process (§8.1, part of §8.2) |
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Week 2 |
3/11,3/13 |
Orthogonal decomposition, orthogonal projection, adjoint operator (part of §8.2, §8.3) |
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Week 3 |
3/18,3/20 |
Orthogonal diagonalization of normal or self-adjoint operators, unitary operators (§§8.4, 8.5) |
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Week 4 |
3/25,3/27 |
Sesqui-linear forms, Hermitian forms, positive forms (§§9.2, 9.3); Quiz 1 |
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Week 5 |
4/01 |
Review, some matrix decomposition (up to §9.3) |
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Week 6 |
4/08,4/10 |
Bilinear forms, symmetric bilinear forms (§§10.1, 10.2); Quiz 2 |
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Week 7 |
4/15,4/17 |
Signature of real symmetric bilinear form, skew-symmetric bilinear forms (§§10.2, 10.3), remarks on groups preserving linear structures |
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Week 8 |
4/22,4/24 |
Quotient space (H-K, §§A.3 - A.5, Lax);
Midterm |
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Week 9 |
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[非同步遠距教學] Rayleigh quotient (Lax, pp.113-120) |
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Week 10 |
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Application to ODE and recurrence equations |
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Week 11 |
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Application to ODE, continued |
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Week 12 |
5/20,5/22 |
Operator norm (Lax, pp.89-100);
Quiz 3 |
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Week 13 |
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Matrix-valued functions (Lax, Chap.9, pp.121-135) |
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Week 14 |
6/05 |
Normed spaces (Lax, part of Chap.14, 15);
Quiz 4 |
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Week 15 |
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More on normed spaces (Lax, rest of Chap.14, 15) |
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Week 16 |
6/19 |
Final |
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