|
課程名稱 |
應用數學一
Applied Mathematics (Ⅰ) |
|
開課學期 |
104-2 |
|
授課對象 |
理學院 物理學系 |
|
授課教師 |
趙挺偉 |
|
課號 |
Phys2001 |
|
課程識別碼 |
202 20310 |
|
班次 |
|
|
學分 |
3 |
|
全/半年 |
半年 |
|
必/選修 |
必帶 |
|
上課時間 |
星期二8,9,10(15:30~18:20) |
|
上課地點 |
新物111 |
|
備註 |
限本系所學生(含輔系、雙修生)
總人數上限：80人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042Phys2001_ |
|
課程簡介影片 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
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 |
|
課程目標 |
To cover most topics in the textbook |
|
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. |
|
預期每週課後學習時數 |
|
|
Office Hours |
每週三 16:00~18:00 |
|
指定閱讀 |
待補 |
|
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).
|
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Homework |
30% |
|
2. |
Midterm Exam |
30% |
|
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. |
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
2/23 |
Introduction, Vector Algebra, Vector Analysis. |
|
第2週 |
3/01 |
Divergence Theorem, Stokes Theorem, Schwarz Inequality, Triangle Inequality, Linear System, Gauss Elimination |
|
第3週 |
3/08 |
Gauss-Jordan Elimination, Matrix Algebra, Inverse Matrix, Vector Space |
|
第4週 |
3/15 |
Linear Independence, Dimension, Basis, Null space, Rank, Four Fundamental Subspace |
|
第5週 |
3/22 |
Orthogonality, Projector, Gram-Schmidt Orthonormalization |
|
第6週 |
3/29 |
Determinants, Dirac-delta function,
Position eigenvector |
|
第7週 |
4/05 |
Spring holiday |
|
第8週 |
4/12 |
Wave-Particle duality, Position operator and Momentum operator. Eigenvalues and Eigenvectors. Introduction to Group Theory |
|
第9週 |
4/19 |
Midterm Exam |
|
第10週 |
4/26 |
Eigenproblem, Application to Differential Equations |
|
第11週 |
5/03 |
Hermitian Matrix, Unitary Transformation, Hamilton-Caylay Theorem |
|
第12週 |
5/10 |
Singular Value Decomposition (SVD),
Rotation matrices, U(1), SO(2), and SO(3) groups |
|
第13週 |
5/17 |
Momentum, Translation
Angular Momentum, Rotation
SU(2) group
Linear Transformation |
|
第14週 |
5/24 |
Change of Basis,
Principles of Quantum Mechanics,
SU(2) algebra, and spin-j representation |
|
第15週 |
5/31 |
Spin-j representation of SU(2),
Gaussian integrals,
Fourier Series, Fourier Transform |
|
第16週 |
6/07 |
Fourier Transform,
Uncertainty Relation of Energy and Time,
Old Final Exam Questions |
|
第17週 |
6/14 |
Final Exam |
|