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課程名稱 |
應用數學一
Applied Mathematics (Ⅰ) |
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開課學期 |
105-2 |
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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 |
3.0 |
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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 |
星期二8,9,10(15:30~18:20) |
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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
外系人數限制：2人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052Phys2001_ |
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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:
G. Strang, Introduction to Linear Algebra, 4th edition, Wellesley-Cambridge (2009).
REFERENCE:
S. Leon, Linear Algebra with Applications, 8th edition, Pearson (2010).
THE following topics will be covered:
(A) VECTORS
(B) INDEPENDENCE, BASIS AND DIMENSION
(C) LINEAR TRANSFORMATIONS AND THEIR RANKS
(D) LINEAR FUNCTIONALS
(E) DUAL SPACE
(F) INNER PRODUCT
(G) PROJECTIONS
(H) GRAM-SCHMIDT PROCESS
(I) FOURIER TRANSFORM
(J) THE PRINCIPAL-AXIS-THEOREM AND NORMAL MODES
(K) EIGENVALUES AND EIGENVECTORS
(L) LINEAR TRANSFORMATIONS |
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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, to work out the homework assignments, and to take the midterm and final exams. |
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預期每週課後學習時數 |
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Office Hours |
每週三 16:00~18:00 |
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指定閱讀 |
待補 |
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參考書目 |
REFERENCE:
S. Leon, Linear Algebra with Applications, 8th edition, Pearson (2010).
TEXTBOOK:
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 |
2017/02/21 |
Introduction, Vector Algebra, Vector Analysis. |
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第2週 |
2017/03/07 |
Vector calculus, Gradient, Divergence, Curl, Divergence theorem |
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第3週 |
2017/03/14 |
Stokes theorem, Path Independence, Linear system, Gauss elimination, LU decomposition |
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第4週 |
2017/03/21 |
Matrix Multiplication, Block Multiplication, Inverse Matrix, Gauss-Jordan Algorithm, Permutation Matrix, Group |
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第5週 |
2017/03/28 |
recitation sessions on ps1-ps3 |
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第6週 |
2017/04/05 |
Spring holiday |
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第7週 |
2017/04/11 |
Vector space, Subspace, Column space, Null space, Complete solution of Ax=b |
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第8週 |
2017/04/18 |
Linear Independence, Basis, Dimension,
4 Fundamental Subspaces |
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第9週 |
2017/04/25 |
Othrogonality of 4 subspaces, Projection matrix, Normal equation, Least square approximations, Orthonormalization |
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第10週 |
2017/05/02 |
Determinants |
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第11週 |
2017/05/09 |
Eigenproblem, Applications to Ordinary Differential Equation |
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第12週 |
2017/05/16 |
Midterm Exam |
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第13週 |
2017/05/23 |
Normal matrix, Hermitian matrix, Unitary transformation, Hamilton-Cayley Theorem, Singular Value Decomposition (SVD) |
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第14週 |
2017/05/30 |
National holiday (Dragon Boat Festival) |
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第15週 |
2017/06/06 |
Linear Transformation |
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第16週 |
2017/06/13 |
Final Exam |
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