Contour integration / Hankel functions

Problem attached.

Past Exam Question, Sets, Functions and Permutations

I have an extremely crammed exam timetable and had to hand in a large report last week. Having just finished an exam today, I have one the next day and the day after and not much time to revise. I would be extremely grateful if someone could give me solutions to the attatched past exam paper, as it would help tremendously.

Eigenvalue problem: axially symmetric wave propagating in a cylinder

Problem attached.

Properties of Neumann functions of integral order

Show that For Neumann function of the n'th order: N_[-n] = (-1)^n*N_[n]

Eigenvalue problem: circular coordinates

On Circular disk of radius a find the orthonormal set of eigenfunctions for the system defined by the eigenvalue problem: -Del^2 Psi = (k^2) *Psi dPsi/dr (r=a)=0 psi(0)=finite

Cutoff frequency for a wave propagating in a cylinder

Problem attached.

Determining Reach and Frequency for an Ad Buy

2. A company plans to use the following media to communicate with its target audience of 1.5 million people. Compute the reach, average frequency, total impressions, and total GRP's if this media mix is implemented. What do you conclude regarding the reach and frequency allowed by this schedule? What would you suggest if the fir ...continues

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Logarithms See attached files

Numerical Integration

Numerical Integration. See attached file for full problem description.

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Complex numbers Please find attched files Thank you