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.




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。
關鍵字 待補
課程要求
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.
面談時間