Notes on content coverage:

The general rule is that you are responsible for all content
in all sections that are listed on the website 

   http://www.math.upenn.edu/ugrad/calc/m114/05-06Math114Syllabus.pdf ,

with five exceptions, listed below.  You are responsible for 
knowing the material well enough to do the core problems, 
WHETHER OR NOT EVERY ASPECT OF THIS MATERIAL HAS BEEN ADDRESSED 
IN YOUR LECTURE AND RECITATION.  The five excluded sections are:

	Sections 13.6, 16.5, 10.5, 10.7 and Appendix G. 

The course will still give you some exposure to these topics, 
through lectures and homework problems, but these topics will not 
be covered to as great a depth as the topics for which you are 
responsible on the examinations.  

----------------------------------------------------------------------------

Here are further details on coverage of topics in chapters 10 and 18.


First and foremost, be sure to understand qualitative aspects of 
first-order differential equations!  This includes: 

	sketching (direction fields)
	approximation (Euler iteration; series solutions)
	being able to tell which of several sketches might be a solution

Other big-picture concepts:

	know how to tell qualitative behavior of separable equations (see:
	   http://www.math.upenn.edu/~pemantle/114-html/classification.pdf ).
	know how to distinguish uner/critical/over damping
	know how to recognize resonance
	recognize exponential growth/decay/convergence

Be able to solve: 

	separable first-order equations
	linear first-order equations
	homogeneous second-order equations with constant coefficients
	some non-homogeneous ones, via variation of parameters 
		or undetermined coefficients

Not covered:

	Logistic equation
	Predator-prey equations
	Orthogonal trajectories 
	Complex numbers (but do know how to use them in second order DE's)