University of California, Davis Department of Applied Science
Fall 2005 David M. Rocke
Numerical Methods
EAD 115 November 28, 2008
Homework Assignment 7 Due December 5, 2005
1. Do problem 25.125.5 from the text. 2. Do problem 25.11 and 25.12 from the text
University of California, Davis Department of Applied Science
Fall 2005 David M. Rocke
Numerical Methods
EAD 115 November 16, 2005
Homework Assignment 6 Due November 28, 2005
1. Do problem 21.4 and 21.5 from the text. 2. Do problem 22.1 and 22.4 from the
University of California, Davis Department of Applied Science
Spring 2005 David M. Rocke
Numerical Methods
EAD 115 November 9, 2005
Homework Assignment 5 Due November 16, 2005
1. Do problems 17.4, 17.8, and 17.15 from the text. You may use Excel or Matlab
University of California, Davis Department of Applied Science
Spring 2005 David M. Rocke
Numerical Methods
EAD 115 October 26, 2005
Homework Assignment 4 Due November 2, 2005
1. Do problems 13.213.6 from the text. Note that concave means that the second d
University of California, Davis Department of Applied Science
Fall 2005 David M. Rocke
Numerical Methods
EAD 115 October 19, 2005
Homework Assignment 3 Due October 26, 2005
1. Do the following problems from the text: 9.8, 10.210.4, 10.16. 2. Write a progr
University of California, Davis Department of Applied Science
Fall 2005 David M. Rocke
Numerical Methods
EAD 115 October 12, 2005
Homework Assignment 2 Due October 19, 2005
1. Write a program in a language of your choice to implement Newtons method. Assum
University of California, Davis Department of Applied Science
Fall 2005 David M. Rocke
Numerical Methods
EAD 115 October 5, 2005
Homework Assignment 1 Due October 12, 2005
1. Determine machine epsilon in both double and single precision for Excel Visual B
EAD 115
Numerical Solution of Engineering and Scientific Problems David M. Rocke Department of Applied Science
Taylor's Theorem
Can often approximate a function by a polynomial The error in the approximation is related to the first omitted term There are
14.7 Newton Method The first and second derivatives can be expressed as:
= 3.5 + 2 - 4 3 - 2 , = 2 - 2 - 2 , =
2 -2 , -2 -2
2
2
2
From this the Hessian Matrix is expressed as: = and it follows that
2
= -2 .
2
2
=2,
= -2 ,
. 25 -.25 -1 = . -.25
EAD 115
Numerical Solution of Engineering and Scientific Problems David M. Rocke Department of Applied Science
Multidimensional Unconstrained Optimization
Suppose we have a function f() of more than one variable f(x1, x2, ., xn) We want to find the value
University of California, Davis Department of Applied Science
Fall 2009 David M. Rocke
Numerical Methods
EAD 115 October 28, 2009
Homework Assignment 5 Due November 9, 2009
1. Do problem 14.7 on page 385 in the text. 2. Using the function from problem 14.
University of California, Davis Department of Applied Science
Fall 2009 David M. Rocke
Numerical Methods
EAD 115 October 21, 2009
Homework Assignment 4 Due October 28, 2009
1. Do the following problems from the text: 10.210.4, 10.20 on pages 293294. 2. Us
University of California, Davis Department of Applied Science
Fall 2009 David M. Rocke
Numerical Methods
EAD 115 October 14, 2009
Homework Assignment 3 October 21, 2009
1. Do the following problems from the text: 6.3, 6.5, 6.6 on pages 171172. 2. Do the f
University of California, Davis Department of Applied Science
Fall 2009 David M. Rocke
Numerical Methods
EAD 115 October 7, 2009
Homework Assignment 2 Due October 14, 2009
1. Write a program in a language of your choice to implement the bisection method o
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 May 27, 2004
Homework Assignment 6 Due June 3, 2004
1. Do problem 25.125.5 from the text. 2. Do problem 25.11 and 25.12 from the text. 3. Wr
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 May 18, 2004
Homework Assignment 5 Due May 27, 2004
1. Do problem 21.8 and 21.9 from the text. 2. Do problem 22.1 and 22.4 from the text. 3.
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 May 6, 2004
Homework Assignment 4 Due May 18, 2004 1. Do problems 13.213.6 from the text. Note that concave means that the second derivative
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 April 22, 2004
Homework Assignment 3 Due May 4, 2004
1. Do the following problems from the text: 9.8, 10.210.4, 10.16. 2. Write a program in
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 April 15, 2004
Homework Assignment 2 Due April 22, 2004
1. Write a program in a language of your choice to implement Newtons method. Assume
University of California, Davis Department of Applied Science
Spring 2004 David M. Rocke
Numerical Methods
EAD 115 April 8, 2004
Homework Assignment 1 Due April 15, 2004
1. Determine machine epsilon in both double and single precision for Excel Visual Bas
13.2 (a) The function can be plotted
40 0 -2 -1 -40 -80 -120 0 1 2
(b) The function can be differentiated twice to give
f " ( x) = -45 x 4 - 24 x 2 Thus, the second derivative will always be negative and hence the function is concave for all values of x.
9.8 (a) The system is first expressed as an augmented matrix:
27 10 2 - 1 - 3 - 6 2 - 61.5 1 1 5 - 21.5
Forward elimination: a21 is eliminated by multiplying row 1 by 3/10 and subtracting the result from row 2. a31 is eliminated by multiplying row 1 by 1
method program to find a root of f ( x ) = e - ( x SOLUTION: Option Explicit Function Newton(xi, es, imax)
Write a program in a language of your choice to implement Newtons method. Assume that you have functions f(x) and fp(x) to return the function value
EAD 115
Numerical Solution of Engineering and Scientific Problems David M. Rocke Department of Applied Science
Least Squares Regression
Curve Fitting
Given a set of n points (xi, yi), find a fitted curve that provides a fitted value y = f(x) for each val