Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Welcome to Math 101Section 202!
Integral Calculus with Applications to Physical
Sciences and Engineering
Information about this course
Area problem
Courseinformation
My name: Hexi Ye. Email: yehexi@
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Feb. 1, 2007
Marks
[2]
Math 101/206 Quiz 3
Dr. Haussmann
No aids allowed
Time: 15 min.
1. Sketch the region bounded on the left by the parabola x = y 2 and on the right by the
parabola x = 3
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Mar. 1, 2007
Marks
[2]
Math 101/206 Quiz 5
Dr. Haussmann
No aids allowed
x2 4
1. Compute
dx. Hint: tan2 + 1 = sec2 .
x
Let x = 2 sec so x2 4 = 4(sec2 1) = 4 tan2 . Then
x2 4
2 tan
dx =
2 se
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Jan. 18, 2007
Marks
[3]
Math 101/206 Quiz 1
Dr. Haussmann
No aids allowed
Time: 15 min.
1. If
n
lim
n
2
2i
5+
n
i=1 n
10
b
=
f (x) dx
a
nd a, b, f .
It looks like we should take f (x) = x10
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 8, 2007
Marks
[2]
Math 101/206 Quiz 6
Dr. Haussmann
No aids allowed
Time: 15 min.
1
2
1. Use Simpsons rule with n = 4 to approximate
0
sum of ve fractions.
1
1
h = ( 2 0)/4 = 8 , y0 =
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 15, 2007
Marks
Math 101/206 Quiz 7
Dr. Haussmann
No aids allowed
Time: 15 min.
[2]
dx
converges or diverges.
x2 + ln x
1
N.b. You will be unable to nd an antiderivative of the integran
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Feb. 15, 2007
Marks
[2]
Math 101/206 Quiz 4
Dr. Haussmann
No aids allowed
Time: 20 min.
1. Evaluate
t e3t dt.
(a)
Set u = t, dv = e3t dt to obtain
t e3t dt = t
(b)
e3t
3
e3t e3t
e3t
dt = t
+
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS April 5, 2007
Marks
[2]
Math 101/206 Quiz 9
No aids allowed
Dr. Haussmann
Time: 15 min.
1. A tank contains 1000 L of water with 10 kg of salt dissolved in it. Pure water enters
the tank at a
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 22, 2007
Marks
[2]
Math 101/206 Quiz 8
Dr. Haussmann
No aids allowed
Time: 15 min.
1. A trough is lled with water (density =1000 kg/m3 ).The ends of the trough are
equilateral triangle
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Jan. 25, 2007
Marks
[2]
Math 101/206 Quiz 2
Dr. Haussmann
No aids allowed
Time: 15 min.
1. Evaluate
1
x
(a)
+
1
x3
dx.
1
x
(b)
1
1
+
1
x3
1
dx = ln x + x3 dx = ln x 2 x2 + c
x cos x dx.
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Bonding and Properties
Materials and atoms
Materials are made of atoms (elements)
and mixtures of atoms (molecules or
compounds)
atom = the basic unit of a chemical element
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Electrical Properties II
Electrical Insulators
2
Energy Band Structures: Insulators vs. conductors
Schematics (a) and (b) for metals, (c) for insulator.
Understanding Insulators low electrical conduct
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Electrical Properties I
Examples of applications where electrical properties
are relevant
Conductive Concrete for Deicing
www.apple.com
www.conductiveconcrete.unomaha.edu/conductiveconcrete