Please plan to attend the review session. More complete information
will be given there.
Exam III covers sections 5.4 - 5.7 on series solutions at regular
singular points, and Chapter 6 on Laplace transform methods.
Important skills include the following.
For 2nd order linear homogeneous equations Py'' + Qy' + Ry = 0,
where P(0) = 0, so 0 is a singular point, classify 0 as regular or
not
Solve equations and IVPs of Euler type
For more general equations where 0 is a regular singular point,
find the indicial equation
If r1 >= r2 are real roots of the indicial equation, there is
always a solution of the form x^r1 times a power series. Find it.
Identify piecewise continuous functions
Use the (supplied) table of Laplace transforms to pass back and
forth between f(t) and F(s)
Use the theorems on transforms of f " and f ' to find their
transforms in terms of the transform of f.
Solve IVP's where the transform F(s) is actually in the table.
Be acquainted with unit step function u-sub-c(t) and the
translation of a function f(t) to c.
Use the inverse transforms of (e^-cs)F(s) and F(s - c) to solve
IVPs
Use the above to solve IVPs Ly = g(t) where g(t) involves step
functions.
Understand modeling using the Dirac delta "function", delta(t -
a) = unit impulse instantaneous force at t = a
Know transform of delta
Solve undamped IVPs of form Ly = g(t), where g(t) involves
delta.
Same for damped IVPs
Compute convolution f*g of f(t) and g(t)
Know properties of transforms and inverse transforms in
connection with *
Express solution of Ly = g(t), y(0)=., y'(0) = . in terms of the
convolution of g(t) with some other function.
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