ENM510 - Advanced Engineering Mathematics I (Homework #9)
Fall Semester, 2015
M. Carchidi
Problem #1 (20 points)
a.) (5 points) While solving a regular Sturm-Liouville Problem a student found
eigenvalues n satisfying the equation
1
100n sin
n
= 1.
What is

ENM510 - Foundations of Engineering Mathematics I
(Practice Problems for the Midterm)
Fall Semester, 2010
M. Carchidi
Problem #1
Consider all real values of for which there are nonzero solutions (x) to
the problem consisting of the ordinary dierential equ

ENM510 - Foundations of Engineering Mathematics I (Homework #2)
Fall Semester, 2016
M. Carchidi
Problem #1 (12 points)
We have seen in class that a general solution to the partial dierential equation (PDE)
2 w(x, t)
2 w(x, t)
T0
=
0
x2
t2
for 0 < t, 0 <

ENM510 - Foundations of Engineering Mathematics I (Homework #3)
Fall Semester, 2016
M. Carchidi
General Solutions to the Wave and Heat Equations
We have seen that
X
w(x, t) = A0 + B0 t +
(An cos(n t) + Bn sin(n t)n (x)
n=1
with
n = n
s
T0
0
is a general s

ENM510 - Foundations of Engineering Mathematics I (Homework #4)
Fall Semester, 2016
M. Carchidi
Problem #1 (20 points)
Consider the vector space of all n1 columns Rn under the usual operations
of column addition and scalar multiplication:
[ai ]n1 + [bi ]n

ENM510 - Advanced Engineering Mathematics I (Homework #7)
Fall Semester, 2016
M. Carchidi
Problem #1 (20 points)
a.) (5 points) While solving a regular Sturm-Liouville Problem a student found
eigenvalues n satisfying the equation
1
100n sin
n
= 1.
What is

ENM510 - Foundations of Engineering Math I (Midterm Exam)
Fall Semester, 2016
M. Carchidi
Problem #1 (30 points)
Let V be the 4-dimensional subspace of the space of all continuous functions
of x, spanned by the basis
B = cfw_ex , e2x , e3x , e4x ,
and let

ENM510 - Foundations of Engineering Mathematics I (Homework #5)
Fall Semester, 2016
M. Carchidi
Problem #1 (25 points)
Consider the vector space of all n1 columns Rn under the usual operations
of column addition and scalar multiplication:
[ai ]n1 + [bi ]n

ENM510 - Foundations of Engineering Mathematics I (Homework #6)
Fall Semester, 2015
M. Carchidi
Problem #1 (20 points)
a.) (10 points) Let f (x) be periodic with period T = 2a, and let
f (x) = a0 +
X
an cos
n=1
2nx
2nx
+ bn sin
T
T
be the Fourier series

ENM510 - Foundations of Engineering Mathematics I (Homework #5)
Fall Semester, 2015
M. Carchidi
Problem #1 (25 points)
Consider the vector space of all n1 columns Rn under the usual operations
of column addition and scalar multiplication:
[ai ]n1 + [bi ]n

ENM510 - Foundations of Engineering Mathematics I (Homework #7)
Fall Semester, 2015
M. Carchidi
Problem #1 (25 points)
Consider the second-order, linear, homogeneous ordinary dierential equation,
y 00 (x) + P (x)y 0 (x) + Q(x)y(x) = 0.
a.) (7 points) Show

ENM510 - Advanced Engineering Mathematics I (Homework #8)
Fall Semester, 2015
M. Carchidi
Problem #1 (20 points)
The Legendre Polynomials Pn (x) satisfy the dierential equation
(1 x2 )Pn00 (x) 2xPn0 (x) + n(n + 1)Pn (x) = 0
for 1 < x < 1. Use this dierent

Class Notes For Advanced Engineering
Mathematics I
(ENM510)
Michael A. Carchidi
September 12, 2014
Chapter 2 - Groups, Fields and Linear Vector Spaces
The following notes are written by Dr. Michael A. Carchidi at the University
of Pennsylvania for the pur

Class Notes For Advanced Engineering
Mathematics I
(ENM510)
Michael A. Carchidi
August 25, 2014
Chapter 1 - The Boundary-Value, Initial-Value Problem
The following notes are written by Dr. Michael A. Carchidi at the University
of Pennsylvania for the purp

Class Notes For Advanced Engineering
Mathematics I
(ENM510)
Michael A. Carchidi
August 25, 2014
Chapter 1 - The Boundary-Value, Initial-Value Problem
The following notes are written by Dr. Michael A. Carchidi at the University
of Pennsylvania for the purp

Class Notes For Advanced Engineering
Mathematics I
(ENM510)
Michael A. Carchidi
September 12, 2014
Chapter 2 - Groups, Fields and Linear Vector Spaces
The following notes are written by Dr. Michael A. Carchidi at the University
of Pennsylvania for the pur