Math
5410/6840
Introduction to Ordinary
Differential Equations
M W 2:00-3:55 pm
JWB
208
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Text: Differential Equations, Dynamical Systems & Instructor: Prof. Elena Cherkaev |
Syllabus
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Assigned Homework Problems:
Aug 22 Ch 1 # 2, 3, 4, 9, 14
Aug 27 Ch 2 # 2ab, 7, 8 ; Ch 3 # 11
Aug 29 Ch 2 # 6 ; Ch 3 # 5, 6, 8, 13, 14
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Sept 10 Ch 4 # 1, 2, 3, 6, 7
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Sept 17 Ch 5 # 3, 5abc, 7, 8ab
Sept 19 Ch 5 # 12, 13, 14, 15
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Sept 24 Ch 6 # 2, 7 - 11
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Oct 1 Ch 6 # 2, 5, 12
Oct 3 Ch 6 # 15
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-------------------- Fall Break --------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------
Oct 17 Ch 7 # 1 - 7
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Nov 5 Ch 8 # 1, 2, 5, 6
Nov 7 Ch 8 # 7 - 10
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Nov 12 Ch 9 # 1 - 3, 6
Nov 14 Ch 9 # 7 - 11
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Nov 19 Ch 10 # 1 - 3
Nov 21 Ch 10 # 7
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Nov 28 Ch 15 # 1 - 4
Dec 3 Ch 15 # 5, 8, 9, 11, 15
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Dec 5 Ch 15 # 13, 14, 16, 17
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Computer lab set up: ODE toolkit
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: Course deals with the theory of linear and
nonlinear ordinary differential equations and dynamical systems. The
course gives an introduction to initial-value problems and behavior of
solutions, discusses existence, uniqueness, perturbations, and
continuous dependence of solution on initial conditions, gives
introduction to nonlinear dynamical systems and applications.
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: Linear
systems: Chapters 2 - 6
Part II:
Fundamentals: Chapters 7, 8, 17
Part III: Nonlinear
equations and dynamical systems: Chapters 9 -15
Exams: There will be three midterms and an optional
project or final exam. Tentative dates for the midterms: Sept 26
; Oct 31 ; Nov 28.
Grading: The grade will
be calculated as an average of the midterms and the project and/or final
Holidays: Labor Day holiday: Monday, September 3
Fall break: October 7-14
Thanksgiving break: Thurs.-Fri., Nov. 22-23
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.