課程名稱 |
微擾法 Perturbation Methods |
開課學期 |
110-2 |
授課對象 |
工學院 應用力學研究所 |
授課教師 |
潘斯文 |
課號 |
AM7189 |
課程識別碼 |
543EM6480 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二5,6(12:20~14:10)星期四5(12:20~13:10) |
上課地點 |
應109應109 |
備註 |
本課程以英語授課。 限學士班四年級以上 總人數上限:24人 |
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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 |
課程大綱
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課程概述 |
This course will provide an introduction to some of the (numerous) techniques that are available to provide approximate solutions to differential (and other) equations when there are no exact solutions. Unsurprisingly many equations do not have exact solutions; although in many cases numerical solutions will be adequate, it is often valuable to obtain an approximate solution to gain insight into the behaviour of the system being described. Such approximate solutions can also be very valuable in validating numerical solvers.
There are many different techniques available and the precise choice will depend to a large extent on the exact nature of the equation being studied. The course will provide an overview of the more common techniques and examples. We will follow very closely the book ‘Introduction to Perturbation Methods’ by Holmes. |
課程目標 |
To gain a thorough understanding of a variety of perturbation methods and to understand how and when to apply them in a wide range of applications. |
課程要求 |
Basic calculus, up to solutions to ODEs and PDEs. |
預期每週課後學習時數 |
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Office Hours |
備註: Office hours will be Wednesday 1-2pm (IAM room 412). |
指定閱讀 |
Course textbook: Introduction to Perturbation Methods (second edition). Springer, 2013. Holmes. |
參考書目 |
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory. Springer, 1999. Bender and Orszag. |
評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
Week 1 |
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Introduction and overview of course |
Week 2 |
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Introduction to asymptotic approximations: Part I |
Week 3 |
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Introduction to asymptotic approximations: Part II |
Week 4 |
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Matched asymptotic expansions: Part I |
Week 5 |
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Matched asymptotic expansions: Part II |
Week 6 |
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Matched asymptotic expansions: Part III |
Week 7 |
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Multiple scales: Part I |
Week 8 |
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Multiple scales: Part II |
Week 9 |
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First exam |
Week 10 |
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WKB and related methods: Part I |
Week 11 |
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WKB and related methods: Part II |
Week 12 |
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Homogenisation: Part I |
Week 13 |
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Homogenisation: Part II |
Week 14 |
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Introduction to bifurcation and stability: Part I |
Week 15 |
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Introduction to bifurcation and stability: Part II |
Week 16 |
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Final exam |