MAT 425 HW 4
MAT 425.
Due April 7, 2011
Homework 4
Solutions.
Computational problems are marked with an *.
1. It is possible. For example the exact solution to the ODE
y = 100y
is y(t ) = y(0)e100t which is asymptotically stable. But if we apply the forwa
Newtons Divided
Difference Polynomial
Method of Interpolation
Major: All Engineering Majors
Authors: Autar Kaw, Jai Paul
http:/numericalmethods.eng.usf.
edu
Transforming Numerical Methods Education for STEM
Undergraduates
http:/numericalmethods.eng.usf.e
Homework 2: CS537, Spring 2015
Due Date: 11:00am, February 13, 2015
Please show all steps in your work. Please be reminded that you should do your homework
independently.
1. (10 points) There exists a unique polynomial p(x) of degree 2 or less such that
p
Honors Algebra 4, MATH 371 Winter 2010
Solutions 1
1. Let R be a ring. An element x of R is called nilpotent if there exists an integer m 0 such
that xm = 0.
(a) Show that every nilpotent element of R is either zero or a zero-divisor.
(b) Suppose that R i
! ) 1 + n(
1
) x( w
) x( P
x
x
x
x
) x( f ) ( ) 1 + n ( P ) ( ) 1 + n ( f = ) ( ) 1 + n ( = 0
,ecneH
! )1 + n(
)1+n(td
) n x t ( ) 1 x t ( ) 0 x t( (
1+n(d
)1+n(td
1+n(d
) )t( w(
) x( w
) x( f )t( ) 1 + n ( P )t( ) 1 + n ( f
)x ( P
) x( w
)t( ) 1 + n (
MAT 425 HW 3
MAT 425.
Solutions
Homework 3
Solutions
Computational problems are marked with an *.
2. No. The Newton-Cotes quadrature can be derived from integrating the polynomial
1
interpolation of the integrand f (t ) = 1+25x2 . Since, for Newton-Cotes
Math 425 Numerical Analysis
Homework 2. Solutions
Total points 100 = 25 + 25 + 50
1. Textbook, page 336, problem 7.15
Solution. There are n knots and thus n 1 subintervals. On each subinterval,
we need 3 coecients to determine a quadratic polynomial. Ther
Math 425 Numerical Analysis
Homework 1. Solutions
Computational problems are marked with .
Total points 100=254.
1. The centered dierence for approximating 1st derivatives of f (x) is
h
f (x) D0 f (x) :=
f (x + h) f (x h)
.
2h
(a) If one uses D0 f (x) to
MAT 425
Final Exam: Review
9:40am Thursday May 5, 2011 at the usual room
Open book. Open notes. No electronic device is allowed.
Sections to be covered in the Final.
7.17.4
8.18.7
9.19.3
10.1-10.6
11.1-11.2
No Chapter 1, Chapter 12
Distribution of point
MAT 425
MAT 425.
Midterm practice
March 24, 2011
Midterm Exam: practice problems
*
Honor Statement
By signing below you conrm that you have neither given nor received any unauthorized assistance on this exam.
Date:
Signature:
*
Open book. Open notes. No e
Lecture Notes on Introduction to Numerical Computation1
Wen Shen
Fall 2012
1
These notes are provided to students as a supplement to the textbook. They contain mainly
examples that we cover in class. The explanation is not very wordy; that part you will g