Instructor: Patrick
Roberts
Email: robertpa@ohsu.edu
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
Mark Goldman). Octave is a free alternative to Matlab with similar syntax. 
Section A: Dynamics  
Apr
2 Introduction to course 2Dimensional flow geometries 
Slides(pdf) 
Apr 4 Discrete linear dynamics & Mappings 
Slides(pdf) 
Apr 9 Diagonalization & eigenvalues 
Slides(pdf) 
Apr 11 Homework 1 review 

Apr 16 Higher dimensional dynamics & linearization 
Slides(pdf) Readings: Lynch, Chapter 12, 13 Matlab code: plot_3dDEq.m; Java applet: Hopf Bifurcation 
Apr 18 
Slides(pdf) Homework 2 due, Homework 3 Readings: Lynch, Chapter 11 
Section B: Optimization  
Apr 23 No class 

Apr 25 Unconstrained optimization 
Slides(pdf) , Class Notes 
Apr 30 Dynamics of Optimization Practice Midterm 
Class
Notes, Practice Midterm Solutions Readings: Pierre, Chapters 6.16.2, 6.6 
May 2 Midterm 

May 7 
Homework 3 solutions (hw3_1.m, hw3_2.m) Homework 4 
May 9 Constrained optimization 
Class
Notes, 
May
14 Dynamic programming 
Class
Notes, 
Section C: Uncertainty  
May 16 Probability & Bayes rule 
Class
Notes (coinFlip.m, DeMere.m) Reading: Rozanov, Chapters 13 
May 21 Random Variables & Distributions 
Class
Notes, MatlabDemoCode14.zip 
May 23 Uncertain Dynamics 
Class
Notes, MatlabCode15.zip Reading: Rozanov, Chapters 78 
May 28 No class 
Memorial Day 
May 30 Statistics: Hypothesis testing, likelihood, Monte Carlo 
Homework 6 due Class Notes, NetLogo Demo (Central Limit Theorem), hypothTest.m (stixbox) 
Jun 4 Estimation & information 
Class
Notes, Dayan & Abbott, Chapter 3 Reading: Rozanov, Appendix 1 
Jun 6 Review & course evaluation 
Review
Slides(pdf) Practice Exam, Practice Exam Solutions 
Jun 11 Final exam.  Mon, June 11, 15:3017:20 
Due  Assignment 

Apr 9  Homework 1: Mathematical graphics and linear algebra. 
Apr 16  Homework 2: Dynamical Systems. 
Apr 25  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: 
Due  Exam 

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.