Write down Green’s Circulation Theorem. Explain when Green’s
Circulation Theorem applies and when it does not. Give an example
of Green’s Circulation Theorem showing the function, the integral
and drawing the region.
Determine the eigenvalues and the corresponding normalized
eigenfunctions of the following Sturm–Liouville problem: y''(x) +
λy(x) = 0, x ∈ [0;L], y(0) = 0, y(L) = 0,
Consider the Sturm-Liouville problem
X′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0.
Are the boundary conditions symmetric?
Do these boundary conditions yield negative eigenvalues?
Determine the eigenvalues and eigenfunctions, Xn(x). (It is
enough in some cases to provide the equation that determines the
eigenvalues rather than an explicit formula.)
Are the eigenfunctions orthogonal?
In this problem, you need to derive the block-pricing scheme
that maximizes profit in the case of 2nd-degree price
discrimination when a monopolist faces a consumer with high demand
PH = 80 − QH, a consumer with low demand PL = 50 − QL, and constant
marginal cost of $10. For your derivations, assume that the
monopolist serves both consumer types and use TL and TH to denote
the fixed fees (dollar amounts) charged to the consumers with low
and...
When calculating the market value of your bond, what
calculations do you need to complete?
Question 1 options:
Both present value of a lump sum and present value of an
annuity
Future value of an annuity
Future value of a lump sum
Present value of an annuity
Present value of lump sum
Both future value of a lump sum and future value of an
annuity
Why might a company issue bonds as opposed to stock?
Question 2 options:
To finance...
Derive the variation of parameters formula for the solution of
the initial value problem for a non-homogeneous, linear system of
first order, ordinary differential equations in terms of a
fundamental matrix of solutions of the corresponding homogeneous
problem.