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課程名稱 |
應用數學一
APPLIED MATHEMATICS (I) |
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開課學期 |
97-2 |
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授課對象 |
理學院 物理學系 |
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授課教師 |
陳義裕 |
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課號 |
Phys2001 |
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課程識別碼 |
202 20310 |
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班次 |
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學分 |
3 |
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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 |
星期二7,8,9(14:20~17:20) |
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上課地點 |
新物111 |
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備註 |
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/972AppMath1 |
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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 |
應用數學一 |
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課程目標 |
Applied Math I, 2009
Syllabus
Instructor: Yih-Yuh Chen
Textbook: Richard Penney, “Linear Algebra, Ideas and Applications,” 3rd
ed. (2008), Wiley. (Authorized dealer in Taiwan: 開發圖書公司)
We plan to cover the following topics:
1. What does linear mean, and what is so good about it?
2. Solving systems of linear equations
(a) Elimination, the all-around method even in this computer age!
(b) Matrices
3. Vector spaces
(a) Vectors
(b) Independence, basis and dimension
(c) Linear transformations and their ranks
(d) Linear functionals (not in the textbook)
(e) Dual space (not in the textbook)
4. Determinants
(a) From elimination to determinants
(b) Cramer’s rule: when to use it, and when not to
5. Eigenvalues and eigenvectors
(a) Diagonalization: what is it good for?
(b) What does a complex eigenvalue mean?
(c) A taste of perturbation theory (not in the textbook)
6. Orthogonality
(a) Inner product
(b) Projections
(c) Gram-Schmidt process
(d) Fourier transform
(e) The principal-axis-theorem and normal modes
(f) The singular value decomposition
(g) Hermitian and unitary matrices, and their variational characteristics
(h) Positive-definite matrices
7. Generalized eigenvectors
(a) Jordan form
8. Some numerical aspects
(a) Gaussian elimination, again!
(b) Why does my program blow up solving that silly differential equation?
(c) Iterative methods
9. And there is more...
(a) Tensors: Just “larger” vectors
(b) A word on infinite dimensional linear algebra |
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課程要求 |
Grading Policy: Midterm 40%, Final 40%, Homework 20%
No late homework accepted!
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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 |
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參考書目 |
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評量方式
(僅供參考) |
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