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
ENM 503 - Probability and Statistics (Take-Home Exam #1)
Fall Semester, 2016
M. Carchidi
Instructions:
1.) You must do all of the following three take-home problems worth 8, 9 and
8 points, respectively, for a total of 25 points.
2.) You are to do these w
ENM 503 - Probability and Statistics (Homework #2)
Fall Semester, 2016
M. Carchidi
Problem #1 (10 points)
Two cards are randomly selected from an ordinary deck of 52 playing cards.
Compute the probability that they form a blackjack. A blackjack occurs
whe
ENM 503 - Probability and Statistics (Take-Home Exam #1)
Fall Semester, 2016
M. Carchidi
Instructions:
1.) You must do all of the following three take-home problems worth 8, 9 and
8 points, respectively, for a total of 25 points.
2.) You are to do these w
ENM 503 - Probability and Statistics (Exam #1)
Fall Semester, 2015
M. Carchidi
Problem #1 (20 points)
Consider a bias coin having a fixed probability p (0 p 1) of coming up
heads on a single flip of this coin. You want to flip this coin n times and
record
ENM 503 - Probability and Statistics (Homework #1)
Fall Semester, 2016
M. Carchidi
Problem #1 (10 points)
Consider a binary word (i.e., a word containing zeroes and ones) of length
n. Let sn equal the number of binary words of length n that do not contain
ENM 503 - Probability and Statistics (In-Class Exam #1)
Fall Semester, 2016
M. Carchidi
Problem #1 (15 points)
Consider a couple that is starting a family. In the interest of promoting a
diverse family, they decide to have children until they have one of
ENM 503 - Probability and Statistics (Homework #6)
Fall Semester, 2016
M. Carchidi
Problem #1 (20 points) - Computing Average Distance
Suppose that X U[0, L) and Y U[0, L), compute (as a number times L)
the average distance between the point (X, Y ) and t
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 (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
ENM 503 - Probability and Statistics (Homework #4 )
Fall Semester, 2016
M. Carchidi
Problem #1 (30 points) - An Independent Sum of Geometrics
Suppose that X1 is geometric with parameter p1 and X2 is also geometric
but with perhaps a dierent parameter p
ENM 503 - Probability and Statistics (Homework #2)
Fall Semester, 2016
M. Carchidi
Problem #1 (10 points)
Two cards are randomly selected from an ordinary deck of 52 playing cards.
Compute the probability that they form a blackjack. A blackjack occurs
whe
ENM 503 - Probability and Statistics (Homework #1)
Fall Semester, 2016
M. Carchidi
Problem #1 (10 points)
Consider a binary word (i.e., a word containing zeroes and ones) of length
n. Let sn equal the number of binary words of length n that do not contain
1
Name (Print)_ Penn I.D.#_
Please read carefully and sign the following statement:
I agree to abide by the provisions of the Code of Academic Integrity and I certify that I have
complied with the Code of Academic Integrity in taking this examination.
NOT
Preston Eni
ENM 321
HW 2
1.
Cx = n! / [x! *(nx)!]
a) n = 9students, x = 4, nCx =9C4 =126
b) n = 5students, x = 2, nCx =5C2 = 10
n = 4 students, x = 2, nCx =4C2 = 6
5C2 * 4C2 = 10 * 6= 60
c) A = #of ways to get 4 students: 9C4 =126
B = # of ways to get all
1
Name (Print)_ Penn I.D.#_
Please read carefully and sign the following statement:
I agree to abide by the provisions of the Code of Academic Integrity and I certify that I have
complied with the Code of Academic Integrity in taking this examination.
NOT
1
Name (Print)_ Penn I.D.#_
Please read carefully and sign the following statement:
I agree to abide by the provisions of the Code of Academic Integrity and I certify that I have complied with
the Code of Academic Integrity in taking this examination.
NOT
ENGINEERING MATHEMATICS
(EG) cfw_ENM
375. Biological Data Science I - Fundamentals of Biostatistics. (C) Prerequisite(s): Sophomores
and Juniors only.
The purpose of this course is to provide students with skills to analyze and interpret small and large
b
1
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
ENM 321 ENGINEERING STATISTICS
INSTRUCTOR:
Dr. Wen K. Shieh, 347 Towne, 8-4634.
shieh@seas.upenn.edu.
CLASS HOURS: Tuesday/Thursday 4:30PM 6:00PM (311 TB).
OFFICE HOURS: Tuesday/Thursday 10:30AM 12:00N (370 Town
Preston Eni
ENM 321
HW 1
1.
1 - they get view Paris without running out of money but have bad time
2 - they get to view Paris and have good time and still have money
3 - Still have a good time without seeing Paris and dont spend all of their money
4 no mo
1
ENM 321 First Exam Solution Keys (2016)
1 (pc)2
p p(pc)2
1 (pc)2(1 +
ppc)2
R = p p(pc)2(1 +
ppc)2
2
1.
1 1
1
dydx c dydx c (1 x)dx
f ( x, y)dydx c
R
R
0 x
0
2
x 1 c
0 1 c 2.
c x
2
2
2.
0.51 x
P( X Y 1)
f ( x, y )dydx 2 dydx
R'
0 x
0.5
2 (1 2 x)dx 0