Math6340 Winter 2017
Differential Equations



Course Information:

Instructor: Huaiping Zhu
Office: Ross Building, N618
Phone: (416)736-2100, Ext: 66095
Email: huaiping@mathstat.yorku.ca
Class meetings: Monday 2:30-5:30pm CB 120
Grade policy: Assignment 50% + Final exam 50%
Office Hours: TBA
Final Exam: TBA
Text Book Differential Equations and Dynamical Systems. by Lawrence, Perko

Formatted lecture notes will be distributed. If you are interested in the notes, contact me.



Lectures: (Updated weekly)


Syllabus

Math 6340 is a graduate course on ordinary differential equations and dynamical systems. Dynamical systems is a very active field of research that has a tremendous impact on our understanding of complicated, nonlinear phenomena in various systems of applied sciences. I will emphasize on both theoretical and applied aspects of differential equations and dynamical systems. We will cover most of the topics of the text book but the materials will be modified and reorganized.

Main topics


References:
  • H. Amann
    Ordinary Differential Equations: an introduction to nonlinear analysis, Berlin ; New York : W. de Gruyter, 1990.
  • V. I. Arnold
    Ordinary Differential Equations, Springer Verlag, 1992
  • G. Birkhoff, and G. C Rota
    Ordinary Differential Equations, 4th ed. Wiley, 1988.
  • Carmen Chicone
    Ordinary Differential Equations with Applications, 2nd Edition Texts in Applied Mathematics, New York: Springer-Verlag, 2006.
    Page from the author with Errata
  • J. Guckenheimer, P. Holmes
    Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences 42, Springer-Verlag, New York-Berlin, 1983.
  • J. K. Hale
    Ordinary Differential Equations, Krieger, Malabar, Florida, 1980.
  • J. K. Hale and H. Kocak
    Dynamics and Bifurcations, Springer 1991.
  • James Hetao Liu, A First Course in the Qualitative Theory of Differential Equations, Prentice Hall 2003.
  • M. W. Hirsch and S. Smale
    Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, 1974.
  • D. W. Jordan & P. Smith,
    Nonlinear ordinary differential equations, Oxford University Press 1977.
  • Luis Barriera and Claudia Valls, Ordinary Differential Equations: Qualitative Theory, American Mathematical Society Graduate Studies in Mathematics 137, 2010.
  • Y.A. Kuznetsov
    Elements of Applied Bifurcation Theory, Springer-Verlag, 2004.
  • Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd. ed., Springer Universitext, 2006.
  • Vladimir Arnold, Ordinary Differential Equations, 3rd. ed., Springer Universitext, 1992.
  • David Betounes, Differential Equations: Theory and Applications, 2nd. ed., Springer 2010.
  • Stephen Salaff and Shing-Tung Yau, Ordinary Differential Equations, 2nd ed., International Press, 1998.