課程名稱 |
數學建模 Mathematical Modeling |
開課學期 |
106-1 |
授課對象 |
理學院 數學研究所 |
授課教師 |
林太家 |
課號 |
MATH5426 |
課程識別碼 |
221 U6130 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期五7,8,9(14:20~17:20) |
上課地點 |
天數304 |
備註 |
與鄧君豪合授 總人數上限:40人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061MATH5426_ |
課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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 |
林太家教授推導數學模型的方法與數學分析的技巧,主題如下(上課6週):
1. Introduction to differential equation models
2. Models of molecular dynamic simulations
3. Monte Carlo simulations
4. Energetic variational approaches
5. Conservation laws
6. Drift-diffusion equations
7. Techniques of Fourier analysis
鄧君豪教授常微、偏微分方程式的數值模擬方法及其應用 (上課6週):
Chun-Hao Teng is charged in concepts and techniques of numerical methods for partial differential equations with applications, which include the following topics:
1. Introduction to numerical partial differential equations (PDEs)
2. Introduction Fourier/polynomial pseudospectral methods for PDEs
3. Multidomain pseudospectral methods for PDEs
4. Pseudospectral schemes for advection-diffusion equations
5. Pseudospectral schemes for PDEs on spherical surfaces
6. Applications of numerical computations in weather predictions
洪子倫、陳仁祥教授離子通道模擬與應用 (上課2週)
Examples of mathematical models of biological systems
- Ecological models of population growth and species interaction
- Molecular model of enzyme kinetics
- Membrane excitability and H-H models
Unique opportunities of math models of ion channels: where biology meet meaningfully connects with physics and chemistry
(biologists' imaginary creativities is supported by natural reality)
Biological functions of ion channels
- membrane, transporter, and ion channel
- Why focusing on ion channels
- How are proteins synthesized in biological cells:
DNA/RNA/amino acids
transcription, translation, side-chain, back bone
Measurement of ionic currents through channels
- voltage and current clamp
- two major properties of ion channels: gating and permeation
- classical model of channel gating: Hodgkin-Huxley model
- gating schemes: experimental studies and models
- gating current/charge, models, copling gating current to channel opening
- Mechanisms of channel permeation, KcsA structure by Mackinnon, later structures and studies by Perozo, Miller, Nimigean...
- examples from my own experiments and recent studies on KcsA.
李勇達教授數值線性代數在數值模擬之應用 (上課2週)
Title: Decompositional approach to scientific computations
Abstract:
In 1951, Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations. The approach is selected as one of the top 10 algorithms with the greatest influence on science, numerical analysis, and engineering in the 20th century in the January/February 2000 issue of Computing in Science and Engineering. In this talk, we will discuss the motivations, ideas, and history of some matrix decompositions including LU decomposition and singular value decompositoin. Moreover, we will present a novel numerical algorithm for solving Poisson equation designed by taking advantage of a matrix decomposition associated with the Legendre polynomials. Finally, we use some numerical examples to show the necessity of designing a viable numerical algorithm with the aid of useful matrix decompositions.
王偉仲教授Mathematical Models in Computational and Data Sciences (上課1週)
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課程目標 |
學習數學建模,數學分析與數值模擬相關知識,培養跨領域研究能力。 |
課程要求 |
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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 |
待補 |
參考書目 |
1.Sandip Banerjee, Mathematical Modeling: Models, Analysis and Application,
2014
2. Stein & Shakarchi: I Fourier Analysis: An Introduction
3. Spectral methods in MATLAB, Lloyd N. Trefethen, SIAM, 2000
4. Spectral Methods for Time-Dependent Problems, Jan Hesthaven, Sigal Gottlieb,
and David Gottlieb, Cambridge University Press 2007.
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期末報告 |
100% |
繳交 ppt file |
|
週次 |
日期 |
單元主題 |
第1週 |
9/15 |
鄧君豪 |
第2週 |
9/22 |
林太家 |
第3週 |
9/29 |
林太家 |
第4週 |
10/06 |
林太家 |
第5週 |
10/13 |
林太家 |
第6週 |
10/20 |
林太家(林元堯) |
第7週 |
10/27 |
陳仁祥 |
第8週 |
11/03 |
鄧君豪 |
第9週 |
11/10 |
李勇達 |
第10週 |
11/17 |
李勇達 |
第11週 |
11/24 |
鄧君豪 |
第12週 |
12/01 |
鄧君豪 |
第13週 |
12/08 |
謝英恆 |
第14週 |
12/15 |
鄧君豪 |
第15週 |
12/22 |
鄧君豪(氣象局陳建河博士) |
第16週 |
12/29 |
鄧君豪 |
第17週 |
1/05 |
洪子倫 (楊啟伸) |
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