課程資訊
課程名稱
數學建模
Mathematical Modeling 
開課學期
104-1 
授課對象
理學院  數學系  
授課教師
林太家 
課號
MATH5426 
課程識別碼
221 U6130 
班次
 
學分
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302 
備註
與洪子倫、鄧君豪合開
總人數上限:28人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1041MATH5426_ 
課程簡介影片
 
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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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):
Tai-Chia Lin is charged in methods of model derivation and techniques of mathematical analysis, which include the following topics (7 weeks):
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

洪子倫簡介奈米孔洞作為建模的基礎知識包含下列主題(上課3週):
1. General introduction to nanopore and its applications.
2. Governing equations used in nanopore: Poisson-Nernst-Planck and Poisson-Boltzmann type equations, Navier-Stokes equations.
3. Physics about nanopore: especially focusing on electric double layer and steric effect.

鄧君豪教授常微、偏微分方程式的數值模擬方法 (上課6週):
Chun-Hao Teng is charged in concepts and techniques of numerical methods for partial differential equations, which include the following topics:
1. Introduction to numerical partial differential equations (PDEs)
2. Introduction Fourier pseudospectral methods for PDEs
3. Introduction to polynomial pseudospectral methods for PDEs
4. Multidomain pseudospectral methods for PDEs
5. Constructing numerical schemes for ion flows in a nano-pore: An energetic variational approach
6. Pseudospectral schemes for Poisson-Nernst-Planck and Poisson-Boltzmann type equations (I)
7. Pseudospectral schemes for Poisson-Nernst-Planck and Poisson-Boltzmann type equations (II)
 

課程目標
Three abilities will be trained in this course. The first one is to derive mathematical models and use techniques of mathematical analysis to justify models. The second one is to do numerical simulations and the third one is to learn basic knowledge of nanoscience. Students may learn how to do research works by mathematical models in nanoscience. The course would be helpful for students to study problems of different fields of applied mathematics in the future. 
課程要求
Introduction to ordinary and partial differential equations, Computer programing 
預期每週課後學習時數
 
Office Hours
 
指定閱讀
 
參考書目
1. Brain J. Kirby, Micro- and Nanoscale Fluid Mechanics Transport in Microfluidic Devices, 2010
2. Sandip Banerjee, Mathematical Modeling: Models, Analysis and Application, 2014
3. Stein & Shakarchi: I Fourier Analysis: An Introduction
4. Spectral methods in MATLAB, Lloyd N. Trefethen, SIAM, 2000
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期末報告 
100% 
根據上課內容中有興趣的主題,蒐集相關資料、製作ppt檔並上台報告。 
 
課程進度
週次
日期
單元主題
第1週
9/18  洪子倫 
第2週
9/25  林太家 
第3週
10/02  林太家 
第4週
10/09  放假 
第5週
10/16  洪子倫 
第6週
10/23  洪子倫 
第7週
10/30  林太家 
第8週
11/06  林太家 
第9週
11/13  林太家 
第10週
11/20  鄧君豪 
第11週
11/27  鄧君豪 
第12週
12/04  鄧君豪 
第13週
12/11  鄧君豪 
第14週
12/18  鄧君豪 
第15週
12/25  鄧君豪 
第16週
1/01  放假 
第17週
1/08  林太家; analysis of ion-channel signal