Math
5470/6440
Nonlinear Dynamics and Chaos
M W F 2:00-2:50 pm LCB
225
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Text: Nonlinear Dynamics and Chaos Instructor: Prof. Elena Cherkaev |
Feb 10 : Midterm 1 - Chapters 2, 3,
4.
Solutions to selected hw problems: Ch2, Ch3-4
March 26 : Midterm 2 - Chapters
5-7, 8 (1-2)
Solutions to selected hw problems: Ch6, Ch7-8
April 23 : Midterm 3 - Chapters 9-11
Solutions to selected hw problems: Ch10-11
Final: April 30,
1:00 -- 3:00 pm
Project is due on May 3 (or
morning of May 4, the latest).
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Assigned Homework Problems:
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Jan 13: Ex 2.4 # 2, 4, 7, 8, 9;
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Jan 18: Ex 2.7 # 1, 2, 4, 6, 7; Ex 3.1 # 1, 3
Jan 20: Ex 3.2 # 2, 4, 6; Ex 3.3 # 1, 2
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Jan 23: Ex 3.4 # 3, 8, 14, 15, 16
Jan 25: Ex 3.6 # 6, 7
Jan 27: Ex 3.7 # 5, 6
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Jan 30: Ex 4.1 # 4, 8; Ex 4.2 # 2; Ex 4.3 # 1, 2, 3 ;
Feb 1: Ex 4.5 # 1, 3; Ex 4.6 # 3
Steven Strogatz on synchronization
Feb 3: Ex 5.1 # 1, 2, 10 ;
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Feb 6:
Feb 8: Ex 5.2 # 2, 3, 7, 9, 12
Feb 10: Midterm 1
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Feb 15: Ex 5.2 # 13; Ex 5.3 # 2-6
Feb 17: Ex 6.1 # 1, 4, 6; Ex 6.2 # 2
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Feb 22: Ex 6.3 # 2, 3, 13, 14, 15
Feb 24: Ex 6.4 # 1, 2, 3
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Feb 27: Ex 6.5 # 1, 2, 8, 9
Feb 29: Ex 6.8 # 6, 7, 8 , 11, 13
Mar 2: Ex 7.1 # 1-5, 8; Ex 7.2 # 1-3, 6, 9
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Mar 5: Ex 7.3 # 6, 7;
Mar 7: Ex 7.5 # 4
Mar 9: Ex 8.1 # 1-4, 5, 6, 11 ; Ex 8.2 # 2, 8
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Spring Break
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Mar 19: Ex 8.2 # 1;
Mar 21: Ex 8.4 # 1, 2; Ex 8.6 # 1, 3
Mar 23: Ex 8.7 # 1, 3, 9
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Mar 26: Midterm 2
Mar 28: Ex 9.1 # 4; 9.2 # 3, 4, 6
Mar 30: Ex 9.3 # 1, 2-7, 8 , 9-10; Ex 9.4 # 2; play with lorenz attractor in maple
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Apr 2: Ex 10.1 # 11 ;
Apr 4: Ex 10.3 # 1, 2 , 4
Apr 6: Ex 10.3 # 7, 8, 9; Ex 10.4 # 3 ; Ex 10.5 # 2
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Apr 9:
Apr 11: Ex 11.1 # 4-7 ; Ex 11.2 # 2, 6
Apr 13: Ex 11.3 # 1-3, 5, 7-9
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Apr 16: Ex. 11.4 # 1-4, 6, 9
Apr 18:
Apr 20:
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Apr 23: Midterm 3
Apr 25:
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Computer lab set up:
Maple
example (slope field)
Maple: Lorenz attractor
For Matlab, download dfield8 and pplane8 from John C. Polking's
website:
http://math.rice.edu/~dfield/index.html#8.0
Java simulator: http://chaos.wlu.edu/106/programs/lorenzdes.html
Course description Chaos is
everywhere around us from fluid flow and the
weather forecast to the stock exchange and striking geometric images.
The
theory of nonlinear dynamical systems uses bifurcations, attractors and
fractals to describe the chaotic behavior of real world things. The
course
gives an introduction to chaotic motions, strange attractors, fractal
geometry.
The emphasis of the course is on applications:
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The course is addressed
to senior
undergraduate and graduate students in mathematics, science and
engineering. Prerequisites: Calculus and Differential Equations.
Tentative Course Schedule:
Part I: Jan 9 - Feb
1 -- Flows on the line: Jan 9-16. Bifurcations:
Jan 18-27. Flows on the circle: Jan 30-Feb 1.
Part II: Feb 3 -
Mar 9 -- Linear systems: Feb 3-6. Phase plane: Feb 8-17.
Limit Cycles: Feb 22-24. Bifurcations: Feb 27-Mar 9.
Part III: Mar 19
- Apr 25
-- Lorentz equations:
Mar 19-26. 1D Iterated maps: Mar 28-Apr 6. Fractals:
Apr 9-18. Strange attractors: Apr 20-25.
Exams: There will be three midterms and an optional
project or final exam. Tentative dates for the midterms: Feb 8 ;
Mar 21 ; Apr 20 .
Final test: April 30,
1:00 -- 3:00 pm
Grading: The grade will
be calculated as an average of the midterms and the project and/or final
Holidays: Martin Luther King Jr. Day:
Monday, January 16; Presidents' Day: Monday, February 20
Spring break: March 12-17
Maple/Matlab
webpage Lorenz attractor
-- Java simulator: http://chaos.wlu.edu/106/programs/lorenzdes.html
ADA statement: The
American with Disabilities Act requires that
reasonable accommodations be provided for students with physical,
sensory,
cognitive, systemic, and
learning, and psychiatric disabilities. Please contact me
at the beginning of the semester to discuss any such accommodations for
the
course.