Instructor: Patrick
Roberts
E-mail: 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 2-Dimensional 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 6.1-6.2, 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 1-3 |
| May 21 Random Variables & Distributions |
Class
Notes, MatlabDemoCode14.zip |
| May 23 Uncertain Dynamics |
Class
Notes, MatlabCode15.zip Reading: Rozanov, Chapters 7-8 |
| 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, 15:30-17:20 |
| 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.