dy x
1) Let a 6 y( y _ 2) be the given initial value problem.
y(2) = 1
a) (10 pts.) Using Existence and Uniqueness Theorem show that the initial value
problem has a unique solution.
b) (7 pts. ) Find this unique solution.
c) ( 8 pts.) Determine the interv
Q.1
Grading: (a) 10, (b) 4, (c) 6
points
A uniform beam 9.00 m long, weighing
300 N, rests symmetrically on two
supports 5 m apart. A boy weighing
600 N starts at point A and walks
toward the right.
(a) Calculate the upward forces FA and FB exerted on the
BILKENT UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2011-2012
FOURTH HOMEWORK ASSIGNMENT
December 2, 2011
Due Date:
December 12, 2011
Name
:
.
Id. No.
:
.
Section
:
.
IMPORTANT
This homework consists of
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA: Final Exam: May 24, 2006
Final Exam Solutions
1.a) Let A be an n n matrix and k is a (constant) scalar. Show that
the set of all vectors v such that A v = kv is a subspace of Rn . (This means
that eigen
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
Second Midterm Exam Solutions
1. Prove the following statements: 1.a) Let A be an n n invertible matrix. Then
the homogeneous linear system Ax = 0 has only the trivial solution. Solution: Since
A has inv
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
Second Midterm Exam
April 25, 2006
17:40 - 19:40
Name
:
ID#
:
Department :
Instructor : Metin Grses
u
The exam consists of 4 questions of equal weight.
Please read the questions carefully.
Show all yo
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA
Solutions of First Midterm Exam
March 13, 2006
1.a) Show that the function y (x) = A + Bex + Ce2x satises the dierential
equation y 3y + 2y = 0, where A, B , and C are arbitrary constants.
Solution:
y (x
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
First Midterm Exam
March 13, 2006
17:40 - 19:40
Name
:
ID#
:
Department :
Instructor : Metin Grses
u
The exam consists of 4 questions of equal weight.
Please read the questions carefully.
Show all you
MATH225 - HW6
Q1
(a) Write a function TransMatrix that takes an n nx1 column vectors (v1 , v2 , .vn ) as input. If these vectors
are linearly independent, compute transition matrix from the standart basis of n to the ordered basis
(v1 , v2 , .vn ). Otherw
BILKENT UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2011-2012
FOURTH HOMEWORK ASSIGNMENT
December 2, 2011
Due Date:
December 12, 2011
Name
:
.
Id. No.
:
.
Section
:
.
IMPORTANT
This homework consists of
PHYS 101 General Physics-I, Final Exam
Duration: 125 minutes
January 15, 2009
NAME:. Section:.
Q.1 (20)
Q.2 (20)
Q.3 (20)
Q.4 (20)
Q.5 (20)
Total (100)
You must sign the Honor Code for your exam to be graded:
I pledge, on my Honor, not to lie, cheat, or s
MATH 225
2013 - 2014 Spring
Lab Assignment #1
Due date: March 3, Monday, for all sections.
IMPORTANT
Submit your homework as a hardcopy to your instructor.
Homework must be turned in to your instructor before 5:30 pm of the due date. Late
homework will be
4‘
. . m . A. by" ,_ 2 \I
13 COHSIdST the (hi erenual equauon :4 = ~er + 2x x 4. y t X E
at
4 _. , V . . . a. .1 . 2
a) {113 pts,) Solve th1s d1fferent1a1 equatlon by geangjﬁgmegmstaggtmn u = x + y.
M:><Z»er%§ =9
b){ 10 pts.) Verify that the
MATH 225 Linear Algebra and Differential Equations
Fall 2015
Homework 2
Due Date: November 10th, 2015
Name: .
ID Number: .
Department: .
Rules:
1. Include this page in your homework as the cover page. Otherwise, you
will lose 10 points.
2. H
Math 225
Differential Equations & Linear Algebra
Fall Semester 2014-2015
SECOND HOMEWORK ASSIGNMENT
October 23, 2014
Due Date: October 30, 2014
Name : .
Id. No. : .
Section : .
Department :.
IMPORTANT
This homework consists of 5 questions of equal weight.
Math 227: Introduction to Linear Alebra
Homework 1
Due: 14 October, 2016 at 13.30. Turn in to SA 140.
Instructions:
There are two sets of problems in this homework set.
Turn-in problems must be delivered to SA 140, or handed to me directly, by 13.30 on
Linear Algebra & Differential Equations
2015-2016 Fall Semester
THIRD HOMEWORK ASSIGNMENT
Due Date: December 1, 2015
Name: . gochquKEY
Id. No. : .
Section: .
Department: : .
IMPORTANT
0 This homework consists of 5 questions of equal weight. Homework that
Fla \
sou-kw to 45 Z
1 2 3 4 0 O
1) a) ( 15 pts.) Let B: O 1 2 and C = 3 g 0 be two 3x3 matrices.
O 0 1 5 0 1
Compute the following and write the necessary rules. Show your work.
i)( 3 pts.) dew; B 12)
ii) )( 3 pts.) det(3C)
iii) )( 3 pts.) det(B13C3)
iv)
3) a) (15 pts.) Let P2 be the vector space of all polynomials of degree less than or equal to
2. Find all values of a such that the polynomial x2 9x +1 6 P2 is 1_1_ot in the
subspace of P2 spanned by the polynomials 411(x)=x2 + 2x +1,
q2 (x): 2x2 3x + 1 a
MATH 225
2013 - 2014 Fall
Lab Assignment #2 Solutions
Q1) a)
dsolve('Dx = x - 1')
ans =
C2*exp(t) + 1
b)
dsolve('Dx = x - 1','x(1) = a')
ans =
(exp(t)*(a - 1)/exp(1) + 1
c)
t = -2 : 0.001 : 1;
a = 2;
x = (exp(t)*(a - 1)/exp(1) + 1;
plot(t,x);
2
1.9
1.8
1.
MATH 225
2013 - 2014 Fall
Lab Assignment #1
Solutions
BASICS
3) The workspace consists of the set of variables built up during a session of using the MATLAB
software and stored in memory. You add variables to the workspace by using functions, running
M-fi
MATH 225
2011-2012 Fall
HOMEWORK 2
Due date: October 24, 2011 for Sections 2 and 4,
October 25, 2011 for sections 1and 3.
IMPORTANT:
Homework must be turned in before the first lecture starts. You can turn in your
homework anytime before the deadline. Yo
Bilkent University Department of Mathematics
Math 225 Linear Algebra and Dierential Equations
Fall 2012
Homework 2
Assigned: Monday, 8 October 2012
Due: Monday, 15 October 2012
Name:
Student Number:
Section:
Instructions:
1. Print the homework on 6 A4-siz