1.
Q=M c T
T = 24-20 = 4
the c for aluminum is 900 J/kgK
and the c for water is 4190 J/kgK
Heat transferred to the water = 10* 4 * 4190 =167,600
Heat transferred from the Aluminum = 0.75 * (T - 24) * 900
(The trick is to realize that they both end up at 2
Math 270
Name: Dimitry Pigne
D40391722
Lab #4
The Taylor and Fourier Series are among the most important ideas in mathematics that you will
encounter during this class. Remember to SHOW ALL YOUR WORK TO EARN FULL CREDIT,
because providing only the answers
Math 270
Name: Dimitry Pigne
D40391722
Lab #7
This week, we study Laplace Transforms, one of the most useful transforms in all of mathematics, because it
allows us to move from the differential domain to an algebraic domain, operate algebraically to a sol
MATRH260Week 7 Lab
Name:
Dimitry Pigne
D40391722
Logarithmic Integrals
Examine each example below then answer questions 13.
Integral:
1
x dx
Solution: ln |x|
Integral:
Integral:
+C
2x
x2 + 4 dx
Solution: ln |x 2+ 4|+C
1) What is the formula for findi
Math 270
Name: Dimitry Pigne
D40391722
Lab #5
Solutions of Diff. Eqns., Separation of Variables, 1 st order Linear Diff. Eqns., Elementary
applications
SHOW ALL WORK TO EARN FULL CREDIT. Note that providing only an answer earns
approximately 1/3 credit .
Math 270
Name: Dimitry Pigne
D40391722
Lab #6
Higher order homogeneous and non-homogeneous Differential Equations, with distinct,
repeated, or complex roots
Show all work for full credit.
1.)
y + 7y+ 12y = 0
The characteristic equation for this homogeneou
a R1 , R2 ,E areseries because they are all connected ;That leaves R3 , R4 ,R 5 are
1.
b)
R1 ,E are series they are the only 2connect ; R2 , R3 , R4 are.
c)
R1 ,E are series they are the only 2connect ; R2 , R3 , R4 are.
R=
2. a)
b)
R '=
RT =
3.
( 1 )( 10
1 4 8 12 32 15
1. a)
I1 =
R2 I
(8 )(6 A) 8
=
= ( 6 A)=4.8 A
R2 + R1 8 + 2 10
I2 =
R1 I
(2 )(6 A ) 2
=
= (6 A)=1.2 A
R1 + R2 2 +8 10
b) V s=I 1 R 1=( 4.8 A )(2 )=9.6 V
4. a)
8.
V s= E=24 V
b)
I2 =
c)
I s=
a)
R1 I
(1 )(2 A) 2
=
= (2 A)=1 A
R1 + R2 1 +3 4
E
Chapter 3
44. Why do we never apply an ohmmeter to a live network? The reading will be meaningless and
may damage the instrument.
Chapter 4
1. What is the voltage across a 220 resistor if the current through it is 5.6 mA?
E=v R =IR=(5.6 A)(220 )=1232 V
2.
Chapter 6
3,5,9,28,31,36, 10
3. Find the total resistance for each configuration in Fig. 6.73. Note that only standard value
resistors were used.
a)
b)
c)
RT =
RT =
RT =
3
d)
e)
f)
1
1 1
+
R1 R2
RT =
1
1
= =12
1
1
1
+
36
18
12
1
1
= =0.652k
1
1
1
23
+
+
Math 270
Name Rohan Smith
Lab #2
Week 2 Topics: Trigonometric Identities and powers of trigonometric functions, inverse trigonometric
functions, integration by parts, trigonometric substitution, Partial Fraction decomposition, and
integration using tables
Math 270
Name Rohan Smith
Lab #3
Topics: Series, Operations, and Computations with Series, Maclaurin, Taylor
SHOW ALL OF YOUR WORK AND highlight your answers. Note that an answer
without supporting steps earns approximately 1/3 credit.
1.)
Find the first
Math 270
Name Rohan Smith
Lab #4
The Taylor and Fourier Series are among the most important ideas in mathematics that you
will encounter during this class. Remember to SHOW ALL YOUR WORK TO EARN FULL
CREDIT, because providing only the answers will earn ap
Math 270
Name Rohan Smith
Lab #6
Higher order homogeneous and non-homogeneous Differential
Equations, with distinct, repeated, or complex roots
Show all work for full credit.
1.)
y + 7y+ 12y = 0
2
r +7 r +12=0
r=16
x
6 x
y=C 1 e +C 2 e
2.)
y - 25y = 0
2
r
Math 270
Name: Samuel Swapp
Lab #2
Week 2 Topics: Trigonometric Identities and powers of trigonometric functions, inverse trigonometric
functions, integration by parts, trigonometric substitution, Partial Fraction decomposition, and
integration using tabl
[Type text]
Math 270
Name: Samuel Swapp
Lab #3
Topics: Series, Operations, and Computations with Series, Maclaurin, Taylor
SHOW ALL OF YOUR WORK AND highlight your answers. Note that an answer
without supporting steps earns approximately 1/3 credit.
1.)
F
Math 270
Name_Samuel Swapp_
Lab #1
While the integral fills an area with an infinite number of rectangles and sums the areas to get
an exact area under a curve, there are many methods for finding an approximate area under a curve
as well. We will look at
f} I}. ,1, Week 2 Lab
Name
Part 1: Rules for integrating trigonometric functions
I sin 3: cos" x dx
There are three rules governing how we deal with integrals of this form.
1. If the power of the sine is odd and positive, save one sine fact
N... i a" (2W3
Part I Directions: For the function I: f (x) : (x - 2)2 + 2 dx we are going to estimate the area under
the curve using the trapezoidal rule where n = S by doing the following:
1. Divide the interval into 5 equal pieces. How lo