Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 119B: Ordinary Differential Equations
Approved: 2003-01-01, A. Schwarz

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
S. H. Strogatz, Nonlinear Dynamics and Chaos, 1st Edition, ($49.00)
Search by ISBN on Amazon: 0738204536

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

Lorentz equations

Phase space analysis; general properties; bifurcation; Lorenz map

1-d maps

Phase space analysis: iterative diagram, fixed points & stability; unimodal maps: numerics & analysis; period-doubling bifurcation; Lyapunov exponent; Sarkovskii theorem: period three implies chaos; chaos & symbolic dynamics

Fractals

Cantor set, Sierpinski triangle and Koch snowflake; contraction mapping theorem; iterative function systems; algorithms of generating fractals; fractal dimension