Please plan to attend the review period. More complete information
will be given there.
The final covers chapter 7 on linear systems of DEs, sections 9.1
- 9.5 on nonlinear systems, and sections 10.1 - 10.4 on Fourier series.
Important skills include the following.
Although there are no direct questions on them, you will need to
know the material in 7.1 and 7.2. All systems are 2 by 2
Find all eigenvalues and eigenvectors of a matrix A
Check that two vector functions are linearly independent, and
compute their wronskian
Let r1 and r2 be the eigenvalues of *) x' = Ax. Find general
solution of *), specific solution of IVP in case r1 not = r2 real
Find solution of *) when r1 and r2 are a conjugate pair of
complex numbers
Same, in the case r1 = r2 = r real
Find general solution of non-homogeneous system using the method
of undetermined coefficients in the case where the trial xp does not
solve the reduced equation
Classify the type and stability of the critical point (0,0) of
the linear system x' = Ax, using (supplied) table
Find all critical points of an autonomous system
Classify the critical point (0, 0) of an almost linear system
Classify a critical point (a, b) not equal to (0, 0) of an almost
linear system by translating the system to (a, b)
Classify critical points for competing species equations
Same, for predator - prey equations
Although there are no direct questions on it, you need to be
familiar with section 10.1
Define Fourier series of a piecewise continuous function of
period 2pi
Know where it converges, and to what
Compute the fourier coefficients an and bn, being aware of the
effect of the parity of the function f on them
Extend functions on [0, pi] as even or odd to get Fourier cos or
sin series expansions
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