Office hours: Monday 1:00 - 2:00 PM, & Wednesday, 6:00 - 7:00 PM, Harder House -Room 03.
Time and Location:
PSU, Harder House - Room 104
04/02/07 - 06/15/07, Monday & Wednesday, 4:00 - 5:50 PM
|Text:|| There will
be 3 texts, one for each section of the course:
Dynamical Systems with Applications using MATLAB (2004) Stephen Lynch, Birkhauser Boston.
(Supplementary MATLAB files from Lynch)
Probability Theory: A Concise Course (1977) Y.A. Rozanov, Dover.
Optimization Theory with Applications (1987) Donald A. Pierre, Dover.
|Software:||The numerical exercises can be solved using your favorite software, but
the supported package will be Matlab (Tutorial by
Octave is a free alternative to Matlab with similar syntax.
|Section A: Dynamics|
Introduction to course
2-Dimensional flow geometries
Discrete linear dynamics & Mappings
Diagonalization & eigenvalues
Homework 1 review
Higher dimensional dynamics & linearization
Readings: Lynch, Chapter 12, 13
Matlab code: plot_3dDEq.m; Java applet: Hopf Bifurcation
Homework 2 due, Homework 3
Readings: Lynch, Chapter 11
|Section B: Optimization|
Dynamics of Optimization
Notes, Practice Midterm Solutions
Readings: Pierre, Chapters 6.1-6.2, 6.6
|Homework 3 solutions (hw3_1.m, hw3_2.m)
|Section C: Uncertainty|
Probability & Bayes rule
Notes (coinFlip.m, DeMere.m)
Reading: Rozanov, Chapters 1-3
Random Variables & Distributions
Reading: Rozanov, Chapters 7-8
Statistics: Hypothesis testing, likelihood, Monte Carlo
|Homework 6 due
Class Notes, NetLogo Demo (Central Limit Theorem), hypothTest.m (stixbox)
Estimation & information
Notes, Dayan & Abbott, Chapter 3
Reading: Rozanov, Appendix 1
Review & course evaluation
Practice Exam, Practice Exam Solutions
|Jun 11 Final exam.||Mon, June 11, 15:30-17:20|
Homework 1: Mathematical graphics and linear algebra.
Homework 2: Dynamical Systems.
Homework 3: Linear Algebra Review.
|May 2||Homework 4: Optimization.|
|May 16||Homework 5: Discrete optimization.|
|May 28||Homework 6: Uncertainty.|
|Jun 4||Homework 7:|
|May 2||Midterm Exam: Dynamics & Optimization|
|Jun 11||Final Exam|
Homework 1/3, Midterm 1/3, Final 1/3
Exercises will be due every two weeks. Homework assignments will be graded pass/fail. Students are expected to complete all homework assignments successfully. Late assignments will be accepted only with prior approval.
The grade in the course will be based on successful completion of the homework, and the result of both exams (midterm and final). Each exam will be graded based on its completeness, clarity, and demonstrated depth of understanding.
An introduction to the quantitative representation and investigation of systems with an emphasis on mathematical tools and their applications to systems. Topics include linear dynamics, optimization, and uncertainty. The level of presentation assumes familiarity and fluency with calculus. Notions from linear algebra unify the topics and will be presented. Required course work includes both calculations to be done on a computer (we will mostly use MATLAB) and calculations to be done by hand.
Prerequisites: Calculus, familiarity with probability or statistics, computer literacy, exposure to matrix calculations, and graduate standing.