Math 315,
Quiz 5
April 9, 2013.
1. Write down Newtons method for nding the pth root of any positive real number a.
Solution:
We have f (x) = xp a, f (x) = pxp1 , hence Newtons method becomes
xn+1 = xn
Math 315,
Quiz 1
January 22, 2013.
Consider the function
f (x) =
1x
1
.
1 + 2x 1 + x
(a) Explain why evaluating f (x) may give inaccurate results when |x|
1.
(b) Rewrite f (x) so as to avoid the probl
Math 315
5 March 2013
Test 1
Instructions: For full credit on each problem, you must show all work needed to obtain your
answers. You are expected to abide by all the provisions and spirit of the Emor
Math 315,
Quiz 2
February 7, 2013.
NOTE: You must show all details of your work to receive credit.
0 3 4
1. Let A = 0 4
4 .
20
4
(a) Use Gaussian elimination with partial pivoting to nd the P A = LU f
Math 315
5 March 2013
Test 1
Instructions: For full credit on each problem, you must show all work needed to obtain your
answers. You are expected to abide by all the provisions and spirit of the Emor
Math 315
11 April 2013
Test 2
Instructions: For full credit on each problem, you must show all work needed to obtain your
answers. You are expected to abide by all the provisions and spirit of the Emo
Math 315,
Quiz 1
January 22, 2013.
Consider the function
f (x) =
1 cos x
.
x
(a) Explain why evaluating f (x) may give inaccurate results when 0 = |x|
1.
(b) Rewrite f (x) so as to avoid the problem i
Math 315,
Quiz 2
February 7, 2013.
NOTE: You must show all details of your work to receive credit.
1. Consider the matrix
2 1
1
A=
0
0
0
2 1
0
.
1
2 1
0 1
2
0
Find the LU factorization of A, where L
Math 315,
Quiz 3
February 21, 2013.
NOTE: You must show all details of your work to receive credit.
1. Find the Newton form of the interpolation polynomial for the following points: (1, 0), (0, 1)
and
Math 315,
Quiz 3
February 21, 2013.
NOTE: You must show all details of your work to receive credit.
1. Find the Newton form of the interpolation polynomial for the following points: (1, 1), (0, 3)
and
Math 315,
Quiz 4
March 26, 2013.
1. Consider the function f (x) = 1 + 10x x2 and let S1,n (x) be its piecewise linear interpolant
at a set of n + 1 equidistant nodes 0 = x0 < x1 < < xn1 < xn = 1 on th
Math 315,
Quiz 4
March 26, 2013.
1. Consider the function f (x) = 2 cos(x) 5x + 1 and let S1,n (x) be its piecewise linear interpolant
at a set of n + 1 equidistant nodes 0 = x0 < x1 < < xn1 < xn = 1
Math 315,
Quiz 5
April 9, 2013.
1. Write down Newtons method for nding a root of a dierentiable function f (x).
Solution:
Newtons method is the iteration
xn+1 = xn
f (xn )
,
f (xn )
n = 0, 1, . . . ,
Math 315,
Quiz 6
April 23, 2013.
Consider the polynomial equation
an xn + an1 xn1 + + a1 x + a0 = 0 .
Answer the following questions:
1. True or false: Multiple roots are typically ill-conditioned.
2.
Chapter 4
Curve Fitting
We consider two commonly used methods for curve fitting, interpolation and least squares. For interpolation, we use first polynomials and later splines. Polynomial interpolatio
Chapter 2
Computing with Floating Point
Numbers
The first part of this chapter gives an elementary introduction to the representation of computer
numbers and computer arithmetic. First, we introduce t
Chapter 1
Getting Started with Matlab
The computational examples and exercises in this book have been computed using Matlab, which is
an interactive system designed specifically for scientific computa
Times.
Lectures: MW 11:30 AM - 12:45 PM, Math & Science Center, Room
W201
Lab: F 11:30 AM - 12:20 PM, Chemistry, Chem 260
First day of classes: August 25, 2016
Last day of classes: December 6, 2016
Re