The Wave Equation
1. Suppose f (t, x), dened for t > 0 and x in [0, ], is a function satisfying the boundary conditions
f (t, 0) = f (t, ) = 0.
(a) How can we use Fourier series to express f (t, x)?
S
Q1. Plato believed that the human soul consisted of the following three
fundamental parts:
a. id, ego, and superego.
b. appetite, moral courage, and reason.
c. psyche, intellect, and judgment.
d. memo
Problem Set 34 - The Wave Equation
1. Solve the wave equation
2f
2f
= c2 2
t > 0, 0 x
t2
x
with boundary conditions f (t, 0) = f (t, ) = 0 and initial conditions f (0, x) = 2 sin 3x 5 sin 4x,
f
(0, x
(*)
(*) We did not cover this property of symmetric matrices, so you dont need to know it. (Its not necessary
for this problem.)
Question 10. (6 points total)
Find a symmetric 2 x 2 matrix, A, with th
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the quest
1) The production possibilities frontier is
A) upward sloping and reflects tradeoffs in ch
2.
(10 pts) . Two sound sources, S1 and S2, a distance d = 4m apart as shown in the picture
above. Both sources vibrate in phase and emit auditory waves of equal amplitude and
wavelength .
L = 40 m
a.
Group 21: Abdulrahman Jamjoom, Yusuf Jailani, and Aurian Capart
Homework for Work and integration:
Harvard University is trying to beat the record held by the Burj Khalifa (829.8 meters) in Dubai
for
WORKSHEET: MANDATORY READING
1. communication in organizations goes far beyond training managers to be effective
speakers and to have good interpersonal communication skills Give an example
2. communi
Fourier Series
Recap
Recall that P C [, ] denotes the linear space of piecewise continuous functions on [, ]. As weve seen
in Bretscher 5.5, if we endow P C [, ] with the inner product
f, g =
1
f (x)g
Inner Product Spaces
1. Consider P1 , the linear space of all polynomials with degree 1. Suppose we give P1 the inner product
f , g = f (0)g (0) + f (10)g (10).
(a) Find 1, t .
Solution. If f (t) = 1
Trigonometric Polynomials and Fourier Analysis
1. Find the norm 1 .
Solution. We know that 1 is dened to be the square root of 1, 1 , so lets compute that inner
product:
1
1, 1 =
1 dt = 2.
So, 1 = 2
The Heat Equation and the Wave Equation
The Heat Equation
Imagine that we have a metal bar of length (1) which is thermally insulated (meaning that it doesnt lose
heat to its surroundings, except at t
Problem Set 30 - Trigonometric Polynomials and Fourier Analysis
1. When doing Fourier analysis, we work with the space P C [, ] of piecewise continuous functions on
1
f (x)g (x) dx.
[, ] and the inner
INTRODUCTION TO COMMUNICATION
DEFINITION OF COMMUNICATION
Communication is transfer of information from one person to another,whether or not it elicits
confidence. But the information transferred must
Physics 6B - Winter 2011
Homework 4 Solutions
Expansion and Compression of a Gas
Part A
In an adiabatic process, there is no heat transferred to or from the system i.e. dQ = 0. The
first law of thermo
Discussion Boards (please provide enough VALUABLE information)
1. Top commissioned salespeople can earn substantial compensation. In some situations,
the top salespeople can earn more in some months t
MAT 171
Writing Activity 1 - Algebraic Properties
For this activity, you will be discussing/explaining algebraic properties common to the course. All of these
properties have been used in prior math c
Overview
In this assignment you will be given a topic to research and will need to provide an in-depth analysis of how it
applies to you. The topic is Self-Efficacy.
Learning Outcomes Assessed
The fol
Running head: WAL-MART AND AMAZON CASE ANALYSIS
Wal-Mart and Amazon Case Analysis
Name
Professor
Course
Date
1
WAL-MART AND AMAZON CASE ANALYSIS
2
Wal-Mart and Amazon Case Analysis
According to Karlof
Assignment 1:
Format:
Submission Name:
Perception and Promotional Messages
Microsoft Word document, Delete this instructions page but use pages 2-3
Assignment # Last Name, First Name (e.g., Assignment
322
Applied Math
Mensuration of Solid
Chapter 15
Mensuration of Solid
15.1
Solid:
It is a body occupying a portion of three-dimensional space and
therefore bounded by a closed surface which may be cur
QBA 775 Assignment #2
Due during final exam period
Name _
1. Wheelers Containers has agreed to terms with Mountain Dew to produce 100,000
twelve ounce aluminum cans for their soda during the next mont
Paper: Marketing Mix Analysis
Select an innovative product. Consider these questions: How does this product fill a market need? What is
innovative about it? How is the company marketing the product?
T
Managerial Accounting : 2183
( I need these questions answered and solved ) I need this by the September 2
EX 18-5 Equivalent units of production
The Converting Department of Soft Touch Towel and Tiss
Problem Set 31 - Fourier Series
1. (Practice)
(a) Bretscher #5.5.26
(b) Bretscher #5.5.28
x2 sin kx 2x cos kx 2 sin kx
+C.
+
k
k2
k3
This integral can be evaluted by using integration by parts twice.)
2a.
Please note that there is a typo in the above solutions. As calculated in the first
line, a0 = pi/sqrt(2), not 0, as it says later in the thirdtolast lin