Math 128A, Numerical Analysis, Spring 2008.
 Class Information
 DSP students: The exam will be between 11:00AM and
5:00PM on May 19 in Room 939 Evans.

Sample Final ; the actual final exam might have fewer
questions, though.
 Jeff will have reviews on Wed. 5/14 2:305:00PM in
3106 Etcheverry, and Sat. 5/17 3:005:30PM in 102
Wurster. He has also prepared a list of practice problems
at his website
http://www.math.berkeley.edu/~jdonatel/128A.html.
 Final will be cumulative, covering all matrials
covered in class, through Section 7.3. Monday May 12 will be
the last lecture on Chapter 7.
 Last homework set is for Chapter 7. It will not be
collected, though.
 I will have a review on Wed. 5/14. Time is
Noon2:PM. Room will be 247 Cory Hall.
 Midterm II will cover all the materials up to and
include Friday's lecture (March 14). But the emphasis will
be on material since Midterm I.
 Special announcement for students in the
Wed. 11:00AM12:00Noon section: Please bring your midterms
in to section next week.
 General information about the course can befound
here .
 A syllabus can be found
here . This document is where weekly homework and
reading assignments can be found. Homeworks are collected
Wednesdays during discussion. For those who can not make it,
homework can be handed in on Friday before class.
 For problem 4 of section 4.8 in the homework set due
4/7, only do 3a as the integral, and only use an upper bound
on the quadrature error to find values of m and n.
 Exams and Solutions
 DSP students: the upcoming midterm II will take place at
12:30PM in 961 Evans and finish at 2:30PM, March 17, 2008.
 DSP students: the upcoming midterm will take place at
11:30AM in 961 Evans and finish at 1:30PM, Feb. 20, 2008.
 For the upcoming midterm, there will not be any cheat
sheet allowed, nor will be any calculators. There will be a
brief review on Friday, Feb. 15. The exam will cover all
material through 3.2.

Sample Midterm II and
Solutions .

Sample Midterm I and
Solutions .
 Here is a
Grade Curve for Midterm I. The average is 73.4 and
median 73. The top 1/3 scored 84 and above, and the middle
1/3 scored between 6684.
 Here are the
Midterm Solutions.
 Programming Homework
 Pictures
 Here are temperatures downloaded from www.weather.com , for
the City of Berkeley, on Monday, Feb. 29.
The daily temperatures are from 00:00AM to 23:00PM.
We use numerical differentiation schemes in the book to
compute temperature changes on the hour
temperature changes on the hour. Note the higher order
scheme works better, but covers fewer hours for lack of
data. You can
his is a
download matlab program to see how it works.
 The wellknown Gibbs Phenomenon can be illustrated with
interpolating the function f(x) = 1/(1+x^2) with a high
degree polynomial. In the following experiment, we
interpolate f(x) over 81 points on interval [2,2].
this picture illustrates the accuracy on the interval [1.5,
1.5] . It is clear that interpolation accuracy is quite
satisfactory here. However, the interpolate actually swings
wildly near end points (2 and 2), as can be seen in
this picture . Of course, this problem completely goes
away with
splines
 Here are pictures obtained from interpolating daily
temperatures downloaded from www.weather.com , for
the City of Berkeley, on Monday, Feb. 11.
The daily temperatures are from 6AM (6:00) to 9PM
(21:00) on 3hour intervals, a grand total of 6 data
points. We use these data to compute
an interpolating polynomial of degree $5$ that
approximates the temperatures throughout the day from 6AM
(6:00) to 9PM. We verify the accuracy of this interpolation
by
comparing the approximate temperatures with the hourly
temperatures downloaded from www.weather.com . The
interpolation works well during the day. But the error is
quite big around 7AM (when the Sun arises) and 9PM,
indicating that interpolation sometimes does not do as well
as we would hope.
 Here is an example of
Newton's method dancing in cycles without convergence.
However, the same method will converge to the root for a
slightly different initial guess p0=1.
 Newton's Method slows down and becomes less accurate in
the case of multiple roots. Here is an example of
Newton's method accurate only to 8 digits on the double
root x = 0.
 Matlab Codes
 Web Links