Syllabus Detail

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

Learning Goals:
AS A CAPSTONE: The second course of the MAT 119 sequence includes an in depth study of advanced topics in ordinary differential equations. Such topics include Lorentz attractors, phase space analysis, chaos, and fractals. Students will gain mastery over technical aspects of the field, and develop their ability to communicate at a capstone level, commensurate with that expected of an undergraduate degree in mathematics.