Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 2
Ryan Szypowski
Due April 17, 2014
1. Show that the following equations are not exact, then nd an integrating factor that
make them exact, then nd the general solution:
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2013
Homework 7 Solutions
Ryan Szypowski
Due Never
Find the solution to the following systems of dierential equations:
1.
x
y
= 5x + 3y
= 9x + 7y
Solution: The matrix
5 3
9 7
A=
has e
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2013
Homework 7
Ryan Szypowski
Due Never
Find the solution to the following systems of dierential equations:
1.
x
y
= 5x + 3y
= 9x + 7y
2.
y1 = 7y1 y2
y2 = 4y1 + 2y2
3.
y1 = 7y1 + 7y2
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2012
Homework 4
Ryan Szypowski
Due Feb 21, 2013
1. Find an annihilator for each of the following functions.
(a) 4 + 7x e3x
(b) 8xe4x cos(2x) e4x sin(2x)
(c) 2e2x + 2e2x cos(2x)
2. Fin
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  FALL 2012
Ryan Szypowski
Method of Undetermined Coecients with Annihilators
In order to solve P (D)y = f (x) where P (D) is a linear dierential operator with constant
coecients (and hence P
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  FALL 2012
Worksheet 2
Ryan Szypowski
1. Answer the following word problems.
(a) A tank is originally lled with 1L of solution with a concentration of 1g/L salt. If
a new solution with concen
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224 WINTER 2013
Name:
Test #1 Solutions
Please show all of your work. Answers without justifaction may be worth 0.
Please make your answers easy to read. This means it should be clear what you are
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
IE429Simulation
Course ProjectSpring 2016
3. At the Pilot Pen Company, a molding machine produces pen barrels of two different colorsred
and bluein the ratio of 2:3. The molding time is triangular (
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
California State Polytechnic University, Pomona
Degree Curriculum Sheet
Plan (Major) INDUSTRIAL ENGINEERING
Subplan/Option
20132014
Catalog Year
Minimum Units Required
198
Required Core Courses
Cours
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2013
Homework 6
Ryan Szypowski
Due March 7, 2013
1. Consider the following linear system of equations:
2x1 + 3x2 + 4x3 = 3
4x1 + 2x2 + x3 = 3
2x1 + x2 + 3x3 = 4.
(a) Write down the au
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2012
Homework 5
Ryan Szypowski
Due Feb 28, 2013
1. Find the general solution to the following dierential equation
y + y = sec x.
2. First prove that
y1 = 1, y2 = x2
is a fundamental s
Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 2 Solutions
Ryan Szypowski
Due April 17, 2014
1. Show that the following equations are not exact, then nd an integrating factor that
make them exact, then nd the general
Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 1
Ryan Szypowski
Due April 10, 2014
1. Determine the general solution to the following dierential equations:
(a) xy dx + (x + 1) dy = 0
(b)
dy
dx
=
(c) y +
y 2 +2xy
x2
1
Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 3
Ryan Szypowski
Due April 24, 2014
1. For each of the following autonomous dierential equations do each of the following:
(i ) nd and classify all equilibria, (ii ) pro
Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 1 Partial Solutions
Ryan Szypowski
Due April 10, 2014
1. Determine the general solution to the following dierential equations:
(a) xy dx + (x + 1) dy = 0
Solution: We be
Elementary Linear Algebra and Dierential Equations
MAT 224

Spring 2014
MAT 224  SPRING 2014
Homework 5
Ryan Szypowski
Due May 15, 2014
1. For each of the following sets, determine if the functions are linearly dependent or
independent.
(a) cfw_1, ex , sin x
(b) cfw_1 x,
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  WINTER 2012
Homework 3 Additional Problems
Ryan Szypowski
Due Feb 5, 2013
1. Sketch the phase line diagram for the following autonomous ODEs and then discuss
the behaviour as t for the given
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
MAT 224  FALL 2012
Worksheet 1
Ryan Szypowski
1. Show that the functions given below are solutions to the given dierential equations
or initial value problems.
1
, y + 2yy = 0, y(1) = 1
x
(b) y = x2
Elementary Linear Algebra and Dierential Equations
MAT 224

Winter 2013
CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
INDUSTRIAL AND MANUFACTURING ENGINEERING
Production Planning and Control
IME 3261
Dr. K. Abedini
[email protected]
Office 172639
Phone: (909) 86