Math 417: Qualitative Theory of Ordinary Differential Equations
T TH 11:15A - 12:30P 208 Willard
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Course instructor: Xiantao Li
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Office: 219C McAllister Building
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Phone: 3-9081
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Email: xli@math.psu.edu
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Office hours:
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Tuesdays 2:00 PM -- 3:00 PM
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Thursdays 2:00 PM -- 3:00 PM
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or by appointment.
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Textbook: A first course in the qualitative theory of differential equations By James Liu. (Has to be purchased at online stores).
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Reference: An Introduction to ordinary differential equations, by Ravi P. Agarwal and Donal O’Regan. (Available online).
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Main Topics
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Review of basis solution methods.
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Existence and uniqueness.
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Linear system with constant coefficients.
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Linear system with periodic coefficients.
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Nonlinear system; Linearization.
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Stability analysis; Linear analysis.
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Lyapunov function method.
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Perturbation method.
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Mechanical systems.
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Bifurcation theory and chaos. (6 lectures)
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Homework: homework sets will be assigned in class and collected every two weeks on Tuesdays.
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Exams: one in-class midterm, and a take-home final exam.
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Final grade: Midterm 20%; Final 30%; Homework 50%.