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課程名稱 |
應用數學四
APPLIED MATHEMATICS (IV) |
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開課學期 |
94-1 |
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授課對象 |
理學院 物理學系 |
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授課教師 |
吳俊輝 |
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課號 |
Phys3002 |
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課程識別碼 |
202 30340 |
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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 |
星期四7,8,9(14:20~17:20) |
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上課地點 |
新物111 |
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備註 |
先修科目:微積分甲上與微積分甲下(適用本系)。
限本系所學生(含輔系、雙修生) |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/941am4 |
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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 |
偏微分方程
傅利葉轉換
群論
電腦上機模擬及計算 |
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課程目標 |
1. PDE (Partial Differential Equations; Ref.2§8, Ref.1§8; 6weeks):
a. Classification and modeling of differential equations
b. Wave motion, diffusion, gravitational potential
c. The D’Alembert Solution of wave equation, separation of variables,
solutions of certain types of equations
2. Fourier Transform (Ref.3§12; Ref.1§15; 2weeks):
a. Convolution/deconvolution theorem, correlation theorem
b. Fast/finite Fourier transforms (FFT)
c. Wiener filtering, windowing, power spectrum
d. Solving differential equations (DE)
3. Matrices & Group Theory (Ref.1§3,4, Ref.2§4,5, Ref.4; 5weeks):
a. Matrix: multiplication, inversion, determinants, orthogonality; Hermitian &
unitary; diagonalization and eigenvalues/eigenvectors
b. Discrete groups & continuous groups
c. Generators; SU(2), SU(3) & nuclear particles
d. Lorentz group; Lee group & Lee algebra
4. Matlab& Mathematica (1.5weeks):
how to use the software
5. Numerical Methods (Ref.2§9; Ref.1§8.8; 0.5 week):
Finite-difference operators, integration & differentiation, roots of
equations, initial-value, boundary-value problems, solution of ODE/PDE
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課程要求 |
The final grade will be the higher result of the following two plans. Exams
are written, with a time limit of four hours.
Plan A Plan B
I. Exercises 0% 20%
II. Mid-semester exam (92.11.11) 50% 40%
III. Final exam (93.1.13) 50% 40%
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預期每週課後學習時數 |
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Office Hours |
每週五 12:00~13:00 |
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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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