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
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Lecture(s) 
Sections 
Comments/Topics 
Lorentz equations 
Phase space analysis; general properties; bifurcation; Lorenz map 

1d maps 
Phase space analysis: iterative diagram, fixed points & stability; unimodal maps: numerics & analysis; perioddoubling 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 