ENM 251 - Analytic Methods in Engineering (Homework #8)
Spring Semester, 2014
M. Carchidi
Problem #1 (20 Points)
Determine all real values of for which there are nonzero solutions to the
boundary-value problem consisting of the ordinary dierential equatio

ENM 251 - Analytic Methods in Engineering (Homework #9)
Spring Semester, 2014
M. Carchidi
Problem #1 (15 Points) - The Eight Roots of One
Determine all values of (1+i0)1/8 and use your results to determine an exact
exact closed-form expression for
X
x8n
.

The Deection of Beams
Portonovo S. Ayyaswamy and Michael A. Carchidi
February 5, 2010
1. The Statement Of The Problem
Consider a horizontal beam as shown in the gure below.
Side View of a Straight
Uniform Horizontal Beam
We assume that the beam is uniform

Complex Numbers and Complex
Algebra
Michael A. Carchidi
April 12, 2010
1. The Complex Unit i and its Properties
The complex unit i is dened by
i=
1.
(1)
and it satises the equation
i2 = 1
and hence
(2a)
1
= i
i
and in fact, it is not hard to show that
1
i

ENM 251 - Analytic Methods in Engineering (Final Exam)
Spring Semester, 2013 Ayyaswamy & Carchidi
Problem #1 (20 Points) - Steady-State Temperature in a Cylinder
Consider a cylinder of nite length L and radius R, with its principle axis
along the z axis b

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