Math 527/CSCE 561 Homework Assignments

MATH 527/CSCE 561
Numerical Analysis

Homework Assignments

No. Assignment Due Page and No.'s Solutions

#1 Thursday
Jan. 19. Section 1.1 (Page 8-11): 1, 2, 3,10, 11 d, 12 a, 14
Section 1.1, 'computer' (Page 12-16): 7, 15, 20
Only problem # 15 really requires a computer algebra application. Solutions for HW #1

#2 Thursday
Jan. 26. Section 2.2 (Page 66): (single precision only!) 2b, 5h, 5e, 5b
Section 2.3 (Page 82): 1,3,7* (#7 will be used for extra credit)
Additional Homework: #11 on page 83
Read Example 2 on page 77 and be sure to understand it. Solutions for HW #2

#3 Tuesday
Jan 31 Click here (not to be turned in)

#4 Tuesday
Feb 7

Page 32: 10, 14, 26, 39 (square roots can be used!)
Read through the Matlab Tutorial and write a Matlab program for the bisection method based on your notes (or the pseudo-code on p. 94 of the text). This will be used for your homework due Thursday, and you will not need to turn this in today.
Solutions for HW #4

#5 Thursday
Feb 9

Page 101: 1, 3, 8
Page 103: 1, 3
Page 117: 1,4,6 E.C. #9
Solutions and Remarks for HW #5

#6 Thursday
Feb 23

Page 133: 2,5
Page 135: 1
Page 161: 1,2,3, 7a
Solutions for HW #6

#7 Friday (4 pm)
Mar 3

Page 164-167: 15,19,23,26,27,34-37,47
Page 168 (computer problem): 3
Solutions for HW #7, Maple Worksheet

#8 Wednesday (1 pm)
Mar 22
LC 418

[Section 4.3] Page 191-192: 1,3,16,17
(10 pts each)
Using the matlab or excel codes provided to you, modify and run experiments similar to those in class to observe the behavior of the errors. Apply the Richard extrapolation of the central difference approximation to the functions

f(x) = arctan(x) at x=1.
f(x) = x |x|, at x=0, then at x=1. Print off the results and in about 1/2 page, describe what you have observed and how it is predicted by the theory. This is a good candidate for a test question.
(30 pts)

#9 Tuesday
Mar 28

Use the matlab code (here) for Romberg integration to experimentally verify convergence rates applied to the example of the intergral form 0 to 1 of 1/(1+x²). You will need to provide the appropriate function fun.m. [Not to be turned in.]

#10 Thursday
Apr 13

[Section 9.1] Page 393-4: 10, 11, 17, 20 a,b
[Section 9.2] Page 413-4: 2, 6, 7

CAS Computer Account Information

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Worksheets

Matlab Tutorials and Documentation

"demo"

You can find helpful tutorials and quick-start documents at the following links:

Manual of basics to get started (University of Florida): MatLab Primer
"Getting Started with Matlab" from MathWorks in hyperlinked, cross-referenced PDF document format [Getting Started] and on-line at the URL [On-Line]
Official Matlab source PDF documents for technical information from MathWorks.

Minimalist Matlab m-files

Title	Brief Descripton
bisect.m	Simple bisection algorithm.
Newton.m	Simple Newton algorithm.
my_function.m	Sample functions for use in bisect and Newton.
der_my_function.m	Derivative of my_function.
deriv_approx.txt	Code fragments for experimentally observing the error behavior of the derivative approximation algorithms.


This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Jan. 31, 2006. This page ©2005-2006, The Board of Trustees of the University of South Carolina. URL: http://www.,math.sc.edu/~sharpley/math527

Return to Math 527/CSCE 561 Home Page

No.	Assignment Due	Page and No.'s	Solutions
#1	Thursday Jan. 19.	Section 1.1 (Page 8-11): 1, 2, 3,10, 11 d, 12 a, 14 Section 1.1, 'computer' (Page 12-16): 7, 15, 20 Only problem # 15 really requires a computer algebra application.	Solutions for HW #1
#2	Thursday Jan. 26.	Section 2.2 (Page 66): (single precision only!) 2b, 5h, 5e, 5b Section 2.3 (Page 82): 1,3,7* (#7 will be used for extra credit) Additional Homework: #11 on page 83 Read Example 2 on page 77 and be sure to understand it.	Solutions for HW #2
#3	Tuesday Jan 31	Click here (not to be turned in)
#4	Tuesday Feb 7	Page 32: 10, 14, 26, 39 (square roots can be used!) Read through the Matlab Tutorial and write a Matlab program for the bisection method based on your notes (or the pseudo-code on p. 94 of the text). This will be used for your homework due Thursday, and you will not need to turn this in today.	Solutions for HW #4
#5	Thursday Feb 9	Page 101: 1, 3, 8 Page 103: 1, 3 Page 117: 1,4,6 E.C. #9	Solutions and Remarks for HW #5
#6	Thursday Feb 23	Page 133: 2,5 Page 135: 1 Page 161: 1,2,3, 7a	Solutions for HW #6
#7	Friday (4 pm) Mar 3	Page 164-167: 15,19,23,26,27,34-37,47 Page 168 (computer problem): 3	Solutions for HW #7, Maple Worksheet
#8	Wednesday (1 pm) Mar 22 LC 418	[Section 4.3] Page 191-192: 1,3,16,17 (10 pts each) Using the matlab or excel codes provided to you, modify and run experiments similar to those in class to observe the behavior of the errors. Apply the Richard extrapolation of the central difference approximation to the functions f(x) = arctan(x) at x=1. f(x) = x \|x\|, at x=0, then at x=1. Print off the results and in about 1/2 page, describe what you have observed and how it is predicted by the theory. This is a good candidate for a test question. (30 pts)
#9	Tuesday Mar 28	Use the matlab code (here) for Romberg integration to experimentally verify convergence rates applied to the example of the intergral form 0 to 1 of 1/(1+x²). You will need to provide the appropriate function fun.m. [Not to be turned in.]
#10	Thursday Apr 13	[Section 9.1] Page 393-4: 10, 11, 17, 20 a,b [Section 9.2] Page 413-4: 2, 6, 7