UC Davis Mathematics

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 119A: 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:





1-d systems

Phase space analysis, fixed points & stability, existence & uniqueness flow on the circle


1-d bifurcation theory

Saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, catastrophes


Linear systems with constant coeffients

Canonical form & classification, stability


2-d systems

Phase place analysis: fixed points, nullclines & limit set; existence & uniqueness; stability: linearization & Lyapunov function; special systems: conservative, gradient & reversible systems; index theory; coupled oscillators & quasiperiodic orbits; poincare map: stability of periodic orbit; iterative methods for solving equations


Limit cycles

Poincare-Bendixson theorem, lienard systems, weakly nonlinear oscillators, relaxation oscillators


2-d Bifurcation Theory

Saddle-node, transcritical and pitchfork bifurcations; hopf bifurcation; homoclinic bifurcation