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MATH 2413 Honors Differential Equations


Syllabus

GT Catalog description of the course.

Schedule
Topics       Chapter/Section       Lectures

A Single First Order Equation:       1       11
Some comments on modeling       1.1       1.5
Mathematical introduction to ODE;
Integrating equations;
the simplest equations
      1.2       1
Geometry of solution space       1.3       1
Euler's method       1.4       1
Some comments on existence and uniqueness       1.5       1
Equilibrium points       1.6       1
Bifurcation       1.7       1
First order linear ODE       1.8       1
           
Autonomous Systems of
Two First Order Equations
      2       7
Examples       2.1       2
Direction fields in the phase plane       2.2       1
Explicit solutions       2.3       2
Euler's method; comment on existence and uniqueness       2.4       1
Lorenz equations       2.5       1
           
Linear autonomous systems
of two equations
      3       10
           
Non-homogeneous and
non-autonomous equations;
Forcing and Resonance
      4       5
           
Nonlinear systems       5       6
           
Laplace Transforms       6       4

      43
Textbook 
  Differential Equations, by Blanchard, Devaney, and Hall;
  Brooks/Cole Publishers, 1998