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課程名稱 |
應用數學一
Applied Mathematics (Ⅰ) |
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開課學期 |
99-2 |
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授課對象 |
理學院 物理學系 |
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授課教師 |
趙挺偉 |
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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/992APMI |
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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 |
APPLIED MATH (I), 2011
INSTRUCTOR: Professor Ting-Wai Chiu
TEXTBOOK:
S. Leon, Linear Algebra with Applications, 8th edition, Pearson (2010).
THE following topics will be covered:
1. VECTOR ALGEBRA, VECTOR ANALYSIS
2. SOLVING SYSTEMS OF LINEAR EQUATIONS
3. VECTOR SPACES
(A) VECTORS
(B) INDEPENDENCE, BASIS AND DIMENSION
(C) LINEAR TRANSFORMATIONS AND THEIR RANKS
(D) LINEAR FUNCTIONALS
(E) DUAL SPACE
4. DETERMINANTS
5. EIGENVALUES AND EIGENVECTORS
6. ORTHOGONALITY
(A) INNER PRODUCT
(B) PROJECTIONS
(C) GRAM-SCHMIDT PROCESS
(D) FOURIER TRANSFORM
(E) THE PRINCIPAL-AXIS-THEOREM AND NORMAL MODES |
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課程目標 |
To cover most topics in the textbook |
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課程要求 |
To attend the lectures, to participate the discussions in class, and to work out the homework assignments |
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預期每週課後學習時數 |
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Office Hours |
每週一 14:00~17:00 |
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指定閱讀 |
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參考書目 |
TEXTBOOK:
S. Leon, Linear Algebra with Applications, 8th edition, Pearson (2010).
REFERENCE:
G. Strang, Introduction to Linear Algebra, 4th edition, Wellesley-Cambridge (2009).
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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. |
Homework |
30% |
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2. |
Midterm Exam |
30% |
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3. |
Final Exam |
40% |
If your final exam score is higher than 80 out of 100, then it could be counted as 100% provided that it is greater than the normal score with the 30%-30%-40% scheme. |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22 |
Introduction,
Vector Algebra,
Vector Analysis. |
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第2週 |
3/01 |
Representation of Vector, Linear System,
Gauss Elimination |
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第3週 |
3/08 |
Group, Field, Vector Space, Matrix Algebra, Elementary Matrices |
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第4週 |
3/15 |
Dimension, Basis, Null space, Dual space |
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第5週 |
3/22 |
More on the Dual Space,
Determinants |
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第6週 |
3/29 |
Properties of Determinants,
Cramers rule,
Linear operators,
Rotation operator. |
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第7週 |
4/05 |
Spring holiday |
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第8週 |
4/12 |
Linear Transformations |
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第9週 |
4/19 |
Orthogonality |
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第10週 |
4/26 |
Midterm Exam |
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第11週 |
5/03 |
Gram-Schmidt Orthonormalization, Inner Product Space, Orthonormal Sets |
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第12週 |
5/10 |
Orthogonal Polynomials,
Eigenproblem, Hermitian Matrix |
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第13週 |
5/17 |
Hermitian Matrices, System of Linar Differential Equations |
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第14週 |
5/24 |
Schur's Theorem |
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第15週 |
5/31 |
Singular Value Decomposition |
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第16週 |
6/07 |
Dirac-delta function, Quadratic Forms, Positive Definite Matrices, |
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第17週 |
6/14 |
Gaussian integrals, wave-particle duality, wave equations, introduction to QM |
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第18週 |
06/21 |
Final Exam |
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