Summer I 2017 Math 2341
Test 2
Name:
Show your work!
1. (6 points) Rewrite the following as an augmented matrix, find its row-echelon form, and give the solution.
x1 + 2x2
+ x4 = 3
2x1 + 3x2 + 2x3
=1
2. (6
0
1
B0
@
0
0
points) The matrix below is in reduc
Summer I, 2017 Math 2341
Test 2 Review - Answers
1. Solve the following using Laplace transforms:
a) x0 + 9x = et with x(0) = 0
e9t ).
1
t
10 (e
x(t) =
b) x00 + 7x0 + 12x = cos(2t) with x(0) = 0, x0 (0) = 0
x(t) = 15 e4t
c) x00 + 6x0 + 13x = 0 with x(0)
MATH 2341 Dierential Equations and Linear Algebra: Quiz 8
Name:
This quiz is worth 20 points. Show all your work to justify your solutions.
1. [13 pts] Write the following system as Ax = b, then find A
1
and the solution x:
x1 + x2 + 5x3 = 5
x1 + 4x2 + 13
Summer I 2017 Math 2341
Test 2 Review
1. Solve the following using Laplace transforms:
a) x0 + 9x = et with x(0) = 0
b) x00 + 7x0 + 12x = cos(2t) with x(0) = 0, x0 (0) = 0
c) x00 + 6x0 + 13x = 0 with x(0) = 2, x0 (0) = 1
d) x00 + 5x0 + 6x = 0 with x(0) =
MATH 2341 Dierential Equations and Linear Algebra: Quiz 7
Name:
This quiz is worth 20 points. Show all your work to justify your solutions.
1. [10 pts] Solve the second-order initial value problem
y 00 + 4y = (t
3),
1
y(0) = 1, y 0 (0) = 0.
2. [10 pts] Fo
MATH 2341 Dierential Equations and Linear Algebra: Quiz 5
Name:
This quiz is worth 20 points. Show all your work to justify your solutions.
1. [10 pts] Solve the following initial value problem using the Laplace transform.
y 00
y(0) = 1, y 0 (0) = 2.
4y =
Summer 1 2017 Math 2341
Test 1
Name:
Show your work to justify your answers!
1. (14 points) Solve the following. Give the complementary, particular, and full solution.
y 00 + 5y 0 + 4y = 16x with y(0) =
1
5, y 0 (0) = 5
2. (6 points) Set up the dierential
Summer I, 2017 Math 2341
Test 1 Review - Answers
1. Solve the following:
a) y 0 + xy = y x with y(0) = 10
3/2
separable; y(x) = 10e2/3x
b) y 0 +
1/2x2
3
2
y = e(x ) with y(1) = 2
x
3
2 e/3
ex
use integrating factor; y(x) = 2 +
3x
x2
c) (x + 1)y 0 + 3y = x
Summer I, 2017 Math 2341
Test 1 Review
1. Solve the following:
a) y 0 + xy = y x with y(0) = 10
b) y 0 +
3
2
y = e(x ) with y(1) = 2
x
c) (x + 1)y 0 + 3y = x2 + 2x + 1
d)
dy
+ 3y 2 x = 2y 2
dx
e) xy 0 + 2xy = 3xe3x with y(0) = 3
2. A piece of paper is pla
Dare 1
Deforestation
This course focuses on functions with a special focus on exponential functions. Functions
are used to represent real life phenomenon to show how the real world works and forecast future
behaviors or numerical values. Since there are d
The Graduate School of Travel Management
Kaohsiung Hospitality College
Thesis for the Master Degree
The Role of Customization on the Relationships
between Tourist Knowledge and GPTs Travel Intention
Lee Chia-En
Lin Jo-Hui
June, 2008
iii
GPT
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subject
The roller coaster needs to meet certain parameters and you will (probably) have to make
adjustments to your equation. Your coaster must:
I.
II.
III.
cross/touch the x-axis at the location that the guests get on the ride
cross/touch the x-axis at the loc
Indicates an action in progress-
Sports match, competition-
Download-
Ball game-
At the same time- .
Song-
Some-
Know how to-
Guitar-
France-
Cello-
Play violin-
Harp-
Violin-
(4 Questions)
Domain, Range, End Behavior
Set & Interval Notations
(2 Questions)
Graphing Absolute Value Functions
Solving Absolute Value Functions
(10 Questions)
Completing the Square
Quadratic Vertex Form
Writing Quadratic Functions
Solving Quadratic Fu
Sabin, A. B. "Vaccine control of poliomyelitis in the 1980s." The Yale Journal of Biology and
Medicine. Yale Journal of Biology and Medicine, 1982. Web. 30 Jan. 2017.
Vaccine Control of Poliomyelitis in the 1980s, a scholarly article from The Yale Journal
1.) Do nothing.
2.) Line of symmetry: A line that divides the figure into a mirror-image. Ive seen quadratic
functions, which have an axis of symmetry because they create a parabola.
3.) In the function, f(x) = a |xh| + k: h represents the x value coordin
Pros and Cons
Pros of Nathans:
- Big drop
- Shorter
- Looks cool ish
Pros of Jakes:
- Big drop
- Fun
Pros of Anikas:
- It looks realistic
- It has a start and an end
- It looks cool
- It looks safe
Pros of Zohras:
- Safer
- Shorter
Cons of Nathans:
- Shor
use
put, place
a
let, allow
originally
bring/take
for books, for notebooks
notebook
notebook
many
so
crayon
borrow, lend
pen
for pens
Ball point pen-
Buy-
For a handful-
Purple-
f - type, kind
Pencil-
For pieces-
Mp3 player- mp
File
LEARNER NAME: Zohra Ahmed
Application for Reassessment
In order to reassess, you must reflect on your performance. The reflection will be reviewed by your
facilitator, and a parent. This will be an opportunity for you to learn from what has occurred and p
MATH 2341
Makeup Test 2 Solutions
Spring 2017
1.
(35 pts) A 1 kg mass is attached to a spring with constant = 1 N/m. The undamped spring system, which is
initially at equilibrium is subject to a periodic external force () = 2 cos .
a)
(30 pts) Find the mo
MATH 2341
1.
Makeup Test 2
Spring 2017
Name _
(35 pts) A 1 kg mass is attached to a spring with constant = 1 N/m. The undamped spring system, which is
initially at equilibrium is subject to a periodic external force () = 2 cos .
a)
(30 pts) Find the motio
Math 2341
1.
2.
3.
4.
5.
6.
7.
Test 3 Review
Matrix method for solving a linear system
Construct an augmented coefficient matrix
Convert the augmented matrix to its row-echelon form (REF) or reduced REF (RREF)
Identify free variables and assi
Math 2341
Test 2 Review
Spring 2017
Test 2 covers Sections 2.5, 2.6, 3.1 to 3.4 in the book. To prepare for the test, you should do all homework problems,
review all examples done in class, and Quizzes 4 to 6, and make sure you thoroughly understand the c
Math 2341
I.
II.
Review
Integration techniques
Substitution, By parts, Partial fractions
ote: It is extremely important that when you integrate, you do not omit the integration constant.
First-order differential equations and initial value problems
1.
Se
Math 2341
1.
Test 4 Review
Spring 2017
You are allowed to bring one piece of 8.5x11 paper with notes written on only one side.
Wronskian , , =
If , , 0 for at least one point , then , , are linearly independent
If , , = 0 for all , find a non-zer
MATH 2341
Test 4 Solutions
Spring 2017
1.
(15 pts) Determine if the following functions are linearly independent on , .
= sin
= cos ,
cos sin
, , =
= cos + sin = 1 0 The functions are linearly independent.
sin cos
2.
(15 pts) Consider a two-tank