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
kabedini@csupomona.edu
Office 172639
Phone: (909) 862569
Fax: (909) 8692564
SCHEDULE
Date
621
6/23
6/28
6
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
Course
Units
Fundamentals of Human Factors Engineering
Eleme
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 (4, 5, 7) minutes per barrel. The barrels
go to a fillin
1. It is believed some psychtropic meds cause endocrine problems. Synthroid 0.15 mg is ordered
for a client. Available is Synthroid 150 mcg/tablet. How many tabs will you administer?
2. Dr. Order: Administer 1000 units of heparin IV every hour. Solution a
Math 105
College Algebra Worksheet #8
Section 4.3, 4.4, 4.5
Review 2.4 if necessary.
4.3 Exercises 2, 3, 14, 16, 24, and 30. All these exercises were done in class with the
exception of number 30, which is on DesCartes rule of signs.
4.4 Exercises 8, 12,
Mat 105
College Algebra
Worksheet #3
Sections 2.7 and 3.2
Solve the inequality, and express the solutions in terms of intervals whenever possible.
1. (2  3x)(4 x  7) 0
2. x +12 x 2
4. x 4 +15 x 2 <16
5.
3. 25 x 2  9 x <0
2x
<0
16  x 2
6.
2
2
2 x +3 x
College Algebra, Math 105
Midterm 1
California State Polytechnic University Pomona
Name
Winter Quarter 2004
Instructor: Bill Edwards
Score:
Please write neatly, clearly indicate your answers in the spaces provided. Calculators are not needed,
show your wo
Mat 105 Final Exam Draft
Solve the equation.
1) x 2 2 x 1 35 0
2)
3)
2x 9
4 x 4 10 x3 6 x 2 15 x
1
3
x 2 2 x 1 35 0
4 x 4 10 x3 6 x 2 15 x
Express the inequality as an interval and sketch its graph
4)
( a, b)
( a, )
( , b]
Solve the inequality, and expre
College Algebra, Math 105
Midterm 1
California State Polytechnic University, Pomona
Name:_
Spring Quarter 2004
Instructor: Bill Edwards
Score:
Please write neatly, show your work and clearly indicate your answers in the space provided.
1.
a) Express the i
Math 105
3.8
College Algebra Worksheet #6
Inverse Functions
monotone functions
Section 3.8 and 3.9
One to one functions
horizontal line test
domain and range of functions and their inverses
finding
inverses.
One way to think of one to one functions is tha
Math 105 College Algebra Worksheet #5
Sections 3.6 and 3.7
3.6 Quadratic functions
Sketching the graph of a quadratic function
Equation of a parabola with vertical axis and vertex .
ffd8ffe000104a4649460001020100c800c80000ffe20c584943435f50524f46494c45000
Study Guide for Exam 1
1. Be able to carefully and completely state the definition of a function.
2. Derive the quadratic formula showing the details of your work.
3. Solve applications of quadratic functions
4. Solve radical equations
5. Solve absolute v
Exam problems:
could be incomplete, certainly overcomplete.
Worksheet #6: 1,2,5,6,7
Worksheet #7: 4.1 p. 270 #30, 4.2 p. 279 #10, 14, 32, 49
Worksheet #8: 4.3 p.291 # 2, 3, 4.4 p. 301 # 8, 18, the example not in book
4.5 p. 318 something from 110, 4144.
Math 105
College Algebra
Worksheet #4 Sections 3.4 and 3.5 (3.3 is review)
Definition of Function: A function f from a set D to a set E is a correspondence that
assigns to each element x of D exactly one element y of E .
Vertical line test
Graph of a func
MAT 401  FALL 2011
Homework 4
Ryan Szypowski
Due December 1, 2011
1. Let
x1 x2 + 1
x3 + x3
2
1
F(x) =
.
Perform 3 iterations of Newtons method to solve F(x) = 0 using
x(0) =
1
0
.
Perform 3 iterations of Broydens method to solve F(x) = 0 using
x(0) =
1
0
MAT 401 FALL 2011
Name:
Test #2 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 doing
from one step to the next and your work should be
MAT 401 FALL 2011
Name:
Test #1
ID #:
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 doing
from one step to the next and your work should be legi
MAT 401  FALL 2011
Homework 3
Ryan Szypowski
Due November 15, 2011
1. Chapter 3.4 # 12 from the textbook.
2. The Frobenius norm of an n n matrix is dened as
A
F
n
1
2
n
a2 .
i,j
=
i=1 j=1
This is not a natural norm associated with any vector norm. Prove
MAT 401  FALL 2011
Computer Homework 1
Ryan Szypowski
Due October 27, 2011
I have provided some basic Matlab code to perform most of the rootnding methods
discussed in class as well as a test driver to show you how to call the routines. Each
one returns
MAT 401  FALL 2011
Homework 4
Ryan Szypowski
Due December 1, 2011
1. Let
x1 x2 + 1
x3 + x3
2
1
F(x) =
.
Perform 3 iterations of Newtons method to solve F(x) = 0 using
x(0) =
1
0
.
Perform 3 iterations of Broydens method to solve F(x) = 0 using
x(0) =
1
0
MAT 401  FALL 2011
Homework 2 Partial Solutions
Ryan Szypowski
Due October 13, 2011
1. Justify the approximation
g (p)
pn pn1
pn1 pn2
used in the stopping criterion for xed point iteration when it is converging only linearly. This should not require muc
MAT 401  FALL 2011
Homework 1
Ryan Szypowski
Due October 6, 2011
1. Recall the following fact about alternating series: the absolute error made
in truncating a convergent alternating series is bounded by the magnitude
of the following term. That is,
n1
(
MAT 401  FALL 2011
Homework 3 Solutions
Ryan Szypowski
Due November 15, 2011
1. Chapter 3.4 # 12 from the textbook.
2. The Frobenius norm of an n n matrix is dened as
A
=
F
1
2
n
n
a2
i,j
.
i=1 j=1
This is not a natural norm associated with any vector n
MAT 401  FALL 2011
Homework 2
Ryan Szypowski
Due October 13, 2011
1. Justify the approximation
g (p)
pn pn1
pn1 pn2
used in the stopping criterion for xed point iteration when it is converging only linearly. This should not require much work.
2. Show th
MAT 401  FALL 2011
Homework 1 Partial Solutions
Ryan Szypowski
Due October 6, 2011
1. Recall the following fact about alternating series: the absolute error made in truncating
a convergent alternating series is bounded by the magnitude of the following t
MAT 540  Spring 2012
Homework 3 Solutions
Ryan Szypowski
Due May 8, 2012
1. Suppose we take two independant measurements, y1 and y2 , of a single RV x with
variance 2, where the measurement variances are 1 and 4. What is the weighted leastsquares estimat
MAT 540  Spring 2012
Homework 1 Solutions
Ryan Szypowski
Due April 17, 2012
1. Let
A=
a b
b c
be a 2 2 real, symmetric matrix. Show that all eigenvalues of A are real. What values
of b guarantee that it is positive denite.
Solution: The eigenvalues of A
MAT 540  Spring 2012
Homework 3
Ryan Szypowski
Due May 8, 2012
1. Suppose we take two independant measurements, y1 and y2 , of a single RV x with
variance 2, where the measurement variances are 1 and 4. What is the weighted leastsquares estimate of x in
MAT 540  Spring 2012
Homework 2 Solutions
Ryan Szypowski
Due April 26, 2012
1. Prove that (, F, P ) dened below is a proper probability space:
= [0, 1),
F = cfw_, [0, 0.5), [0.5, 1), [0, 1),
P ([a, b) = b2 a2 .
Solution: In order to show that (, F, P )
MAT 540  Spring 2012
Homework 2
Ryan Szypowski
Due April 26, 2012
1. Prove that (, F, P ) dened below is a proper probability space:
= [0, 1),
F = cfw_, [0, 0.5), [0.5, 1), [0, 1),
P ([a, b) = b2 a2 .
2. Prove the following statements (for any probabili