2009winter

2009Winter

Academic Calendar

Winter '09 Schedule

AMS 206-01 (41107) MoWeFr 11:00AM - 12:10PM Cowell Clrm 131

AMS 212A-01 (43809) TuTh 12:00PM - 1:45PM Porter Acad 241

AMS 216-01 (43810) TuTh 6:00PM - 7:45PM J Baskin Engr 169

AMS 214-01 (43808) TuTh 8:00AM - 9:45AM J Baskin Engr 165 ???

Seminars

AMS 280A-01 (43348) Th 4:00PM - 5:45PM J Baskin Engr 330 M. Mangel 2.00

AMS 280B-01 (41721) Mo 4:00PM - 6:00PM Engineer 2 180 A. Rodriguez 2.00 ???

Magazines

http://ics.org.ru/rus?menu=mi_publish&publish=all

http://ics.org.ru/rus?menu=mi_pubs&subj=all

http://www.mathnet.ru/

AMS 212A Applied Mathematical Methods I

http://www.soe.ucsc.edu/classes/ams212a/Winter09/

http://www.ams.ucsc.edu/~pgaraud/Lectures.html

http://www-sbras.nsc.ru/rus/textbooks/akhmerov/ode_unicode/index.html Ахмеров ODE

http://ocw.mit.edu/OcwWeb/Mathematics/18-306Spring2004/LectureNotes/index.htm MIT

http://ocw.mit.edu/OcwWeb/Mathematics/18-305Fall-2004/LectureNotes/index.htm

http://ocw.mit.edu/OcwWeb/Mathematics/18-303Fall-2006/LectureNotes/index.htm

http://ocw.mit.edu/OcwWeb/Mathematics/18-152Fall-2004/LectureNotes/index.htm

http://ocw.mit.edu/OcwWeb/Mathematics/18-152Fall-2005/LectureNotes/index.htm

AMS 206 Bayesian Statistics

http://www.soe.ucsc.edu/classes/ams206/Winter09/

http://en.wikipedia.org/wiki/Checking_if_a_coin_is_fair

http://www.maths.bath.ac.uk/~masss/ma40189.html

http://www.markirwin.net/stat220/lecture.html

http://web.thu.edu.tw/wenwei/www/bayesmarginpdf.htm

http://www.stat.uiowa.edu/~kcowles/s138_2007/node2.html

http://www.stat.uiowa.edu/~kcowles/s138_2008/node2.html

Metropolis-Hastings

http://www.mas.ncl.ac.uk/~ndjw1/teaching/sim/metrop/

http://en.wikipedia.org/wiki/Metropolis-Hastings_algorithm

http://xbeta.org/wiki/show/Metropolis-Hastings+algorithm

AMS 216: Stochastic Differential Equations

http://www.soe.ucsc.edu/classes/ams216/Winter09/ Local lecture Notes

http://www.soe.ucsc.edu/~hongwang/AMS216/

http://www.ifp.uiuc.edu/~hajek/Papers/randomprocesses.html

MIT opencources

http://cnx.org/content/m10235/latest/

http://ocw.mit.edu/OcwWeb/Mathematics/18-366Fall-2006/LectureNotes/index.htm

http://ocw.mit.edu/OcwWeb/Sloan-School-of-Management/15-070Fall-2005/CourseHome/

http://ocw.mit.edu/OcwWeb/Sloan-School-of-Management/15-098Spring-2006/CourseHome/

http://en.wikipedia.org/wiki/Stochastic_process

AMS 214: Applied Dynamical Systems

http://www.soe.ucsc.edu/classes/ams214/Winter09/

Local files: 1D chaos

http://en.wikipedia.org/wiki/Hyperbolic_fixed_point

http://www.egwald.ca/nonlineardynamics/index.php

http://www.scholarpedia.org/article/Limit_cycle

http://www.egwald.ca/nonlineardynamics/limitcycles.php

http://www.maths.qmw.ac.uk/~klages/teaching/mas424/

http://www.ams.ucsc.edu/~pgaraud/Lectures.html

Local Files ivanovDoublePendulum

YouTube: Steven Strogatz:

http://www.youtube.com/results?search_query=Steven+Strogatz&search_type=

Kuznetsov http://sgtnd.narod.ru/publ/rus/main.htm

Fixed point

saddle (hyperbolic) fixed point: eugenvalues have different signs

Conservative system cannot have any attracting fixed points, only saddles and centers.

Reversible Systems

x' = f(x, y) odd regarding y->-y

y' = g(x, y) even regarding y->-y

t->-t if x. = 0 is a linear center for a reversible system,

then all trajectories are closed curves near the origin

Bifurcations: phase portrait changes its topological structure as parameter varies

saddle-node bifurcation normal form: a (+-) x^2 creation and destruction of fixed points

transcritical bifurcation normal form: ax (+-) x^2

pitchfork bifurcation: ax (+-) x^3

pitchfork supercritical

pitchfork subcritical.

Supercritical Hopf bifurcation occurs when stable spiral changesinto unstable spiral surrounded by small limit cycle.

No closed orbits criteria:

1) Gradient systems cannot have periodic orbits

2) Dulac criterion: Let x' = f (x) defined on a simply connected subset R.

If there exists function g(x) such that div (gx') has same sign in R, then no closed orbits lying entirely in R.

I No algorithm for finding g(x). Try g = 1, 1/(x^a)*(y^b), exp(ax), exp(ay)

YES closed-orbits criteria: Poincare-Bendixson Theorem

If R contains no fixed points and exists a trajectory of X starting in R which stays in R for all future times. Then, either is a closed orbit or asymptotically approaches a closed orbit; in other words,

there exists a limit cycle in R

TA AMS 20: Mathematical Methods for Engineers II

http://www.soe.ucsc.edu/classes/ams020/Winter09/

http://www.ams.ucsc.edu/courses/course?ams020a/

Instructor: Qi Gong qigong@soe.ucsc.edu office: BE 143

TA: Chan dchan@soe.ucsc.edu