2009, 5/20-30
史峻平

2A栋(电子信息大厦)13层1312室, 参见地图

(作业: 工大同学交给方健, 师大同学交给赵宇华; MATLAB问题答疑: 苏颖（工大), 崔仁浩（师大)，王金凤(师大,工大）)

 日期 时间(上午) 内容 时间(下午) 内容 5/21(四) 9-11 没有课 2-5 Darwin, Genetics, Hardy-Weinberger law, Differential/difference equations, bifurcation, stability,, biological models (1-D), bistability, hysteresis, Matlab, Differential/difference equations, bifurcation of maps, phase portrait (Dfield), linear algebra(eigenvalue/eigenvector),  生物数学综述(pdf)      Fisher方程的由来 (ppt) 5/22(五) 9-11 Systems of equations, phase portrait, competition, predator-prey models,  nondimensionalization, phase plane analysis, Poincare-Bendixson theory,  Pplane 2-5 Bifurcation in competition, predator-prey models, paradox of enrichment, competition exclusion, Lyapunov functional, limit cycles, Hopf bifurcation, relaxation oscialltion, limit cycle, bifurcation/continuation, higher-dimensional models (competition, food-chain, etc), MatCont,  神经传导的方程 (pdf)   神经传导(中文科普)(pdf)   Age structure model(pdf) 5/23(六) 休息 休息 5/24(周日) 9-11 Diffusion, random walk, linear diffusion equation, eigenvalue problems, Fourier series, fundamental solutions, Fisher equation, traveling wave, minimal patch size, biological invasion, simulation of diffusion equations in Maple Mississippi Bifurcation Lecture 1, Lecture 2, Lecture 3 5/25(一) 9-11 Reaction-diffusion systems in biology, chemistry, and physics, linearization/stability, Turing instability, Hopf bifurcation, Numerical schemes, discrete diffusion model/patch model, Survey Paper on Frontier of Math in China 2-4 PDE  Matlab solver, numerical solutions of R-D systems PDE in Matlab by P. Howard 5/26(二) 9-11 Implicit function theorem, Bifurcation theory in infinite dimensional space, Sobolev/Holder spaces, Fisher equation, competition, predator-prey models, 5/27(三) 9-11 休息 休息 5/28(四) 9-11 Maximum principle, a priori estimates, Degree theory, application of degree theory, global bifurcation theorem 5/29(五) 9-11 Variational/energy methods, Lyapunov functional, Hamiltonian systems, Gradient systems, Dissapative systems 5/30(六) 9-11 Dynamical system approach (monotone dynamical system)

1. 作业1: (5/24上课交)  第一章1,2,4,5,6,7,8,  第二章 1,2,3,4,5
2. 作业2: (5/28上课交) 待定
3. 作业3: (不用交, 将提供答案)
4. 阅读报告:  从下面生物数 学综述文章生物 数学经典论文中, 选读一篇文章, 用中文介绍文章的观点内容, 并谈谈对你自己学习的启发 (请用MS-WORD 或LATEX打印, 不超过5页, 将最后PDF文件在5/29下午6点前用电子邮件发给苏 颖（工大) , 王金凤(师大）).
5. 个人研究小课题(选做): 第一章9,  第二章 6, 其他待定 (请用LATEX打印, 用电子邮件 苏颖（工大), 王金凤(师大）).

1. Google Scholar (免费, 但是检索精度可能不高)
2. Science Citation Index (不免费但是大学里一般可用, 引用数仅限于SCI收录杂志, 1990年后)
3. MathSciNet (不免费但是大学里一般可用, 仅为数学有关文章,引用数仅限于某些杂志, 1940年后)
4. 常用 生物数学/非线性科学杂志

Matlab, Pplane(a Matlab package for phase plane), MatCont (a Matlab package for bifurcation/continuation), AUTO, XPPAUT