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Courses: SYSC 512: Quantitative Methods of Systems Science -- Spring 2007
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. |
Class Syllabus
Class notes, slides, and code:
| Section A: Dynamics |
Apr 2
Introduction to course
2-Dimensional flow geometries |
Slides(pdf)
Homework 1
Readings: Strogatz88
Matlab code: plot_1dDEq.m, plot_2dDEq.m, vectorfield.m
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Apr 4
Discrete linear dynamics & Mappings |
Slides(pdf)
Readings: Lynch, Chapter 2
Matlab code: henon_map.m; Java applet: Logistic Cobweb
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Apr 9
Diagonalization & eigenvalues |
Slides(pdf)
Homework 2
Readings: Lynch, Chapter 8, 10
Matlab code: eigenvalues.m, IODE
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Apr 11
Homework 1 review
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Matlab code: hw1_1.m, hw1_2.m, hw1_3.m
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Apr 16
Higher dimensional dynamics & linearization
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Slides(pdf)
Readings: Lynch, Chapter 12, 13
Matlab code: plot_3dDEq.m; Java applet: Hopf Bifurcation |
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Apr 18
Stability & Gradient systems
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Slides(pdf)
Homework 2 due, Homework 3
Readings: Lynch, Chapter 11 |
| Section B: Optimization |
Apr 23
No class |
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Apr 25
Unconstrained optimization |
Slides(pdf) , Class Notes
Homework 3 due
Readings: Pierre, Chapters 1, 2.1-2.4
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Apr 30
Dynamics of Optimization
Practice Midterm |
Class Notes, Practice Midterm Solutions
Readings: Pierre, Chapters 6.1-6.2, 6.6 |
May 2
Midterm |
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May 7
Review midterm
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Homework 3 solutions (hw3_1.m, hw3_2.m)
Homework 4 |
May 9
Constrained optimization
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Class Notes,
Readings: Pierre, Chapters 2.5-2.10
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May 14
Dynamic programming |
Class Notes,
Readings: Pierre, Chapters 7
Homework 4 due
Homework 5, (gradientDescent.m, grad.m)
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| 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
Reading: Rozanov, Chapters 4-6
Homework 5 due
Homework 6
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May 23
Uncertain Dynamics |
Class Notes, MatlabCode15.zip
Reading: Rozanov, Chapters 7-8 |
May 28
No class
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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.
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| Apr 16 |
Homework 2: Dynamical Systems.
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| Apr 25 |
Homework 3: Linear Algebra Review.
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| 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.
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