UNIVERSITY OF PITTSBURGH
Engineering Science
Undergraduate Academic Program Manual
Dr. Minking Chyu
Chairman
Dr. John A. Barnard
Program Director
Dr. William S. Slaughter
Undergraduate Coordinator
University of Pittsburgh
Swanson School of Engineering
Mec
Exam 1
Math 0240
6/11/2012
Name: JulianBean Delphiki II
Directions (READ THIS): Bean needs no directions.
1. (10 pts) True or False: Simply write the word True if true, and False otherwise.
You will recieve 1 point for a correct answer and 1 for an incor
Engineering 0711/0016  Fall, 2013
Assignment 1
Due: Wednesday, September 4, 2013
Part 1
Open a telnet session and create a .plan file using PICO/NANO. The file should have at least 6
lines of text. You are free to have any content to the file that you wi
R2137
Engineering Science Program
Area of Concentration: Engineering Physics
Sample Curriculum
First Term
CHEM 0960
MATH 0220
PHYS 0174
ENGR 0011
ENGR 0081
Gen. Chem. For Engr.1
Anal. Geometry & Calc. 1
Phys. For Sci. & Engr. 1
Intr. Engr. Analysis
H/SS E
Practice Exam Instructor: Jared Barber
Important Notes (youll see this on the actual test too): No calculators allowed.
Throughout this test, use the methods or reasoning learned in class or in the textbook.
Using alternative outside methods will not rece
Review, things you should know about/know how to do for the finalChapter 13Vector Calculus
Section 13.1: Vector fields
A. Be able to draw and/or match (equation with graph) simple vector fields
B. Know what conservative/potential/incompressible fields ar
Review, things you should know about/know how to do for the test:
I)
II)
III)
IV)
V)
VI)
Section 11.5: Chain rule
A. Given a scalar function of one, two, or three intermediate variables where those
intermediate variables are themselves functions of one, t
Quiz 8, M ath 0240
J uly 23, 2012
Name:
A(l.f'PII
Show all work clearly. You have 25 m inutes t o t ake this 20 p oint quiz. No calculators.
Jf
1. (7 points) Evaluate t he line integral
c = cfw_(t2 ,1)
1
 1:; t:; 2.
I
"2.
 Sf(rCf) I r ' C+) J f

c
ds w
Quiz 7, M ath 0240
J uly 16, 2012
Show all work clearly. You have 25 minutes to
ta~e
t his 20 p oint quiz. No calculators.
a) L etS= cfw_(u,v) I 0:; u:; 1,0:; v:; 1. F ind t he set R = T (S) in t he x y plane,
t hat is, find out where T sends S.
b) Use t
Exam 2
Math 0240
7/9/2012
Name: Garrett, the Thief
Directions (READ THIS): There are 8 problems on this exam. You are required to solve
problems 1, 2, 3 and 4. You are required to solve any two problems from numbers 5,
6, 7 and 8. On the heading of these
9. E xtra C redit ( + 5 p ts)
Let h : R 3 ~ 'R, l et (a, b, c) E R 3 a D.xed p oint, a nd \ et U = cfw_ a\ u nit vectm:s < x, y , z > .
Prove t hat t he m aximum value o fthe directional derivative ~h(a, b, c) < x, y , z > occurs
in the direction of ~h(a,
Practice Problems E1 Solns
For Exam 1 on 6/11
Math 0240
6/5/2012
Additional Problems: These are about as hard as they come.
1. List ve points in the set S = N R cfw_0, 1, 2. Let T = Z R cfw_0. List ve points
in the set S T . Lastly, S T = ?
Solution: For
Practice Problems E2
For Exam 2 on 7/9
Math 0240
7/2/2012
1. Find the volume of the solid bounded between (both parts of) the cone z 2 = x2 + y 2
and the sphere x2 + y 2 + z 2 = 1 using double integrals.
Solution: Turns out, the region here is a bit ambig
Quiz 1, Math 0240
May 21, 2012
Name: Calculus Itself
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
(They wont help anyways.)
1. (5 points) A quiz can be viewed as a function. What are its domain and codomain?
Dene
Quiz 2, Math 0240
May 30, 2012
Name: Tyrion Lannister
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
(They wont help anyways.)
1. 1. (6 points) Let B be a box with dimensions length = k , width = k , height = 2k
whe
Quiz 3, Math 0240
June 4, 2012
Name: Paul MuadDib Atreides
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
1. (6 points) Find lim r(t) and T(1) where r(t) =< t lnt, t2 , cos(t) >.
+
t0
Solution: lim r(t) amounts to <
Quiz 4, Math 0240
June 18, 2012
Name: Kaiser Sze.
o
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
1. (6 points) Let f : R2 R, f (x, y ) = x2 + 2xy + y 2 + 5x 5. Find the equation of the
tangent plane to the graph o
Quiz 5, Math 0240
June 25, 2012
Name:
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
1. (8 points) Let f : R2 R, f (x, y ) = x4 4xy + y 4 + 2. Find all critical points of f
and determine whether they are local maxim
Quiz 6, Math 0240
July 3 , 2012
Name: Gordon Freeman
Show all work clearly. You have 25 minutes to take this 20 point quiz. No calculators.
1
0
1. (6 points) Evaluate the double integral
Solution: .
y
0
2
ey dxdy
y
1
1
y2
=
0
2
ey y dy
dy =
ex
0
0
Now, le
Review, things you should know about/know how to do for the test:
I)
II)
III)
IV)
Section 10.2: Vectors
A. Look at properties of vectors in this section
B. Be able to add, subtract, rescale/multiply vectors by a scalar
C. Find vector given two points
D. F