There will be a quiz roughly every few weeks.
The material covered in each quiz will be described in advance on this web page, sometimes very explicitly. Many quiz questions will cover basic material that you should know absolutely perfectly.
Quiz 1: Tuesday 30 January, beginning of class.
You should be able to sketch the direction field for the
first order differential equation y'=ky, both when k>0 and when k<0.
You should also be able to find the general solution of this equation
(that is, show that every solution has
the form y=Cekx for some constant C), using both
the First Order Linear method (like we did in class on the first day) and the
Separable method from Section 1.4.
There might also be some variant of this problem, or some other question
about direction fields.
Quiz 1 Solutions
Quiz 2: Monday 12 February, beginning of class.
There will be two problems, of which you should do one.
The first will be a substitution problem.
The second will ask you to find the phase line for a
differential equation of the form (dx/dt)=f(x), and to use the
phase line to determine the stability
of the equilibrium solutions, and to sketch solution curves.
Quiz 2 Solutions
Quiz 3: Thursday 15 March, beginning of class.
Sections 3.4 and 3.6. You need to know what the complementary and particular
solutions look like in each of the four cases (coming from undamped/damped,
unforced/forced), and what phenomena to expect as a result (e.g. damped
oscillations, beating, resonance, practical resonance). Know your "summary"
handout and your homework problems thoroughly, on these sections.
Quiz 3 Solutions
Quiz 4: Thursday 19 Aprill, beginning of class.
Method of Eigenvector Decomposition for first and second order linear constant
coefficient nonhomogeneous systems. (See class notes and homework for
Section 5.6.)
Quiz 4 Solutions