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課程名稱 |
數學物理專題
Special Topics in Mathematical Physics |
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開課學期 |
106-1 |
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授課對象 |
理學院 物理學研究所 |
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授課教師 |
陳義裕 |
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課號 |
Phys8133 |
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課程識別碼 |
222 D1990 |
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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 |
選修 |
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上課時間 |
星期一2,3,4(9:10~12:10) |
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上課地點 |
新物112 |
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備註 |
總人數上限：60人
外系人數限制：5人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061Phys8133_ |
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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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課程概述 |
This course introduces to the students some of the frequently used perturbation techniques and asymptotic analysis in physics. It is expected that the students taking this course are well-versed in materials treated in our undergraduate courses of Applied Math I-IV. Familiarity with classical mechanics and quantum mechanics is also assumed. |
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課程目標 |
Outline of Contents:
(The following is only a rough outline.)
1. Perturbation on roots of polynomials‐ a warm‐up:
The quadratic equation revisited
Regular perturbation theory, the way not to go!
Iteration, a typically much faster converging scheme
2. Perturbation of eigenvalue problems:
Regular (Rayleigh‐Schrodinger) perturbation and the solubility condition
A complex representation
Iteration, again
Degeneracy
Divergence of the perturbation series and level crossing
Rayleigh‐Ritz method
3. Multiple‐scale analysis:
Resonance and secular behavior
Two‐timing
Method of averaging
Action‐angle variables
Adiabatic invariant of classical mechanics
Periodic perturbation and Floquet theory
Mathieu’s equation and its solutions
JWKB approximation
4. Asymptotic expansion of integrals:
Integral representations. Why?
Integration by parts
Laplace’s method and Watson’s lemma
Method of stationary phase
Method of steepest descent
Stokes phenomenon
Asymptotic evaluation of sums |
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課程要求 |
Grading Policy:
This is a pass/fail course.
Homework: 100%. You pass the course with a grade >=70%.
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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 |
none |
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參考書目 |
References:
1. Carl M. Bender, Steven A. Orszag , Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer (1999). NTU campus access:
http://link.springer.com/book/10.1007%2F978-1-4757-3069-2
2. R.S. Johnson, Singular Perturbation Theory, Springer (2005).
NTU campus access:
http://link.springer.com/book/10.1007/b100957
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評量方式
(僅供參考) |
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