If you wish your grade, please send me an email and I will reply with your final exam score and your semester grade. Please note there may be a slight security risk in having your grade sent by email. Unless you're a rock star hounded by tabloids, or you have nosy relatives/neighbors that are expert hackers, I don't think it could be much of an issue. Nevertheless I will assume that if you ask me to email your grade, then you are willing to assume this risk.

Your exam paper is yours to have, if you wish it. I'll probably toss them out around January 2004, maybe sooner.

The University of Colorado

Boulder, Colorado

Mathematics 4650, Spring 2003

Intermediate numerical analysis

• Location: ECCR 118
• Schedule: MWF 2:00PM-2:50PM
• Professor: Walter Taylor
  • Email address: walter.taylor@colorado.edu
  • Office Phone: (303) 492-8344 (Please email if at all possible)
  • Office : Mathematics Building 255
• Office hours:
  • Regular hours: (none -- semester over)
  • Or please email me; I almost always can find a time to see you, or possibly I can answer your question directly on email.
• Attendance: To be considered properly enrolled in the course, you must have this hour free on all MWF-days. At no time will I accommodate anyone who has registered for the class with a schedule conflict, academic or otherwise, or anyone who attempts to do so.

  You are expected to be in class every day. On the other hand, if you need to miss one class, on a day when there is no exam, just do it. (In such a case, permission from me is irrelevant.) I am happy to tell you in general terms what we covered in a class you missed. Nevertheless, I really cannot begin to recreate a class situation for you, since much of the material is spontaneous, and depends on student participation.

• Class decorum: No eating. No drinking. No reading of newspapers, etc. No conversation or talking, except with the prof. No headphones. No use of laptops or any other electronic gadgetry. Cell phones and pagers off. No exceptions. If you need to do any of these things, please leave the room; I will not be offended. (The one exception is if a calculation is before the class and you wish to work out the answer on a hand calculator; this however will never be required.)
• Computer decorum: All work must be submitted along with source code and with a signed statement that it is your own work (or with collaborative efforts clearly identified). This is true even though I usually don't grade code as such, and do not always read it in detail (unless I am helping you to locate a problem). Moreover I consider you responsible for taking reasonable care in assuring that your work is not used by anyone else. (In practice this means taking some care in erasing your source when you walk away from a shared PC -- while retaining it on a diskette, of course -- discarding source printout away from the lab, and so on.)

This page pertains only to Professor Taylor's section of Mathematics 4650, for the spring semester of 2003. As far as I know, this is the only section occurring this semester. For other sections or other semesters, other details and regulations will no doubt apply.

An attempt will be made to keep this page up-to-date, but this is not guaranteed. Students are responsible for every assignment made in class, whether or not it ultimately appears on this page.

Prerequisites

• Mathematical
  • Calculus -- three semesters is about right, although those three semesters surely covered more than we need for 4270. We do differentiate and integrate, but extreme prowess is not at issue.
  • Linear Algebra -- one semester (or possibly part of a combined calculus-linear-algebra course). The general idea of a matrix and how it represents a linear transformation. The necessary material will be reviewed, but not in depth.
• Computing This is not a computation-intensive class, nor a class about computing per se. Some principles of numerical analysis will be illustrated by small sample programs, which the students will write more or less from scratch. Although it is a small part of the class, it is an important part, and one should enter the class ready to compute. The following are definitely pre-requisites; the professor will not engage in any systematic remediation of deficiencies in these areas.
  • General -- a basic understanding of files, printing, web, and so on. This should include adequate familiarity with some system that is available to you -- such as computer labs on campus, or with a unix system (also available on campus), or your own personal system.
  • Programming -- Basic, but current, reliable, and reasonably fluent, knowledge of a programming language. (If you occasionally look up a fine point of syntax, that is fine; if you really don't know what to write next, this is not fine.) I recommend C (or C++), for the following reasons: the most thoroughly available language on campus is C, both through various unix versions and through Borland C++; I am really fluent only in C, and my illustrative examples (if any) will be in C. However, if you want to use a closely-related language like fortran, this is possible, so long as a compiler exists on rtt. We are not concerned with fancy or sophisticated styles of programming.
  • Implementation and equipment - A working knowledge of compiling (when necessary) and running programs in your chosen language. You can use any machine you like, but there are two reasons to recommend using university machines:
    • On a random basis your submitted code will be test-driven on one of the compilers on rintintin, or (in the case of Matlab) on the PC's in Math 217. Your program must run properly on one of these machines with no further editing.
    • No allowance will be made for any breakdowns or malperformance of systems other than rintintin or the computers in Math 217.
  • Personal computing equipment - None required, except perhaps a diskette, or zip-disk, or whatever, to hold your programs.

Computing Resources

Experience in a structured programming language is highly desirable. I prefe r helping you in C, just because I am more familiar Generally speaking, the computing part of this course will not go beyond the abilities of any student with university-level computing experience.

Your main programming work can take place either on a university unix machine, such as rintintin, or on a PC (your own, or the university's). To use any university machine, unix or PC, you will need an identikey . (See this page). Here you can also set up an account on rintintin.

The unix machine rintintin (also abbreviated rtt) is a remote-access machine, which can be accessed from almost any computer on campus (using ssh). It can also be contacted from your home PC, if you have a modem and an available phone line. rtt has several compilers, and all the tools you need.

If you elect to use unix machines, it is imperative to make sure that you have noclobber set at all times. (Ask me what this means.) On a unix account, your work is theoretically saved for your next login. (Accidents do happen - most frequently user mistakes, much less often system breakdowns. I would make copies of your precious files on disk or on other machines, or something!)

On the ITS page about printing,, and on a second ITS page about printing, you can find out about printing from a unix machine such as rtt.

You may use your own PC, or a university PC, but the code you submit must compile and run, with no editing, on one of the compilers on rintintin. (I will ask for the "math library, -lm", but beyond that it must run with no further assistance.) There are many PC-labs on campus. According to the ITS computer lab list, the following rooms in Engineering have PC's with Borland C++: ECCH 107, ECCR 235, ECCR 239, ECCR 252, ECME 107.

Remember that when you use your identikey to access a PC on campus, from the operating system's point of view you are only a temporary guest, and none of your work is protected against deletion by another user . (In fact, to protect class security, you are asked to delete at least your source-code before leaving a shared machine on campus.) Therefore, it is imperative to save your work on diskette at the end of every session. If you have Borland at home, you can of course carry work back and forth between home and CU on a diskette.

Textbook

ISBN 0-534-38216-9

To see the cover of the text, click here .

The book comes with a CD that contains various computational materials. We will not use this CD, although you might gain something by browsing through it and playing with it a bit. (In any case, the CD files are available here, if you're missing the CD.)

About homework

When homework involves computing, you will submit results of calculation in writing (computer output fine), and will submit code by email. Please send it as ordinary text, no fancy encodings. Both should include a statement of your sole authorship of the material. Code submitted will be subjected, on a random basis, both to performance testing and to scrutiny to see that it really looks like it's doing the right thing. So please keep it simple. All of our problems will have simple solutions. A few more things will be said in class.

Exams

• You must be present at all exams.
• No books, calculators, cards or other aids.
• The final examination will be Monday, May 5th, 1:30pm - 4:00pm. You must keep this time free for the exam. Unless announced otherwise, the final is to be in the regular classroom.
• Hour exams are in the usual classroom, at the usual class time, and are limited to the usual fifty-minute hour.
  • First Hour Exam: Wednesday, February 19
  • Second Hour Exam: Wednesday, March 19
  • Third Hour Exam: Wednesday, April 23
• Final Exam: Monday, May 5th, 1:30pm-4:00pm, (as announced in the course schedule (corrected version)). Due to storm-induced compression of the semester, the final exam has been made completely optional. The optional final will allow two and a half hours for completion. A good calculator will be necessary.

  If you wish your grade, please send me an email and I will reply with your final exam score and your semester grade. Please note there may be a slight security risk in having your grade sent by email. Unless you're a rock star hounded by tabloids, or you have nosy relatives/neighbors that are expert hackers, I don't think it could be much of an issue. Nevertheless I will assume that if you ask me to email your grade, then you are willing to assume this risk.

  Your exam paper is yours to have, if you wish it. I'll probably toss them out around January 2004, maybe sooner.

Homework.

• Exercises 1, Due Wednesday, January 22
  • Run this program sufficiently often (varying the parameters N, LARGER, SMALLER), to observe overflow and underflow in your computer. Write a brief report asserting that you have done this and summarizing your findings. Keep it short, please.
• Exercise set 2, Due Wednesday, January 29
  • 2.1, p. 53 -- 11, 10, 13
  • 2.2, p. 64 -- 4, 9, 10, 11ab
  • 2.3, p. 74 -- 6a, 12
• Program 1, Due Wednesday, January 29
  • Write and submit a program that implements Newton's method. Generally, you will have to hand-enter both the function and its derivative. Use your program to solve x^x = 100 and x + x²⁰ = 1.9. Submit printed code, whose first page is a report that summarizes what the code does and gives the output for the two test problems. (List the various approximate solutions obtained.)
• Exercise set 3, Due Wednesday, February 5
  • 2.3, p 74 -- 13, 16, 19
  • 2.4, p 85 -- 1, 2, 3, 4, 8
  • 2.5, p 90 -- 9

  • The function  g(x) = 2x - x2  has  1  as a fixed point, and
    one can easily see that, for certain starting values, the iteration
    method  pn+1 =  g(pn)  will approach  1.  Show that this convergence
    is quadratic.
    

• Program 2, Due Monday, February 10 -- extended to 2/12
  • Program to implement the Muller method. Some routines for complex numbers may be found here . (The syntax may be a little old, but you'll see the sort of thing that has to be done.) Use your method to find one solution to the equation

               x6  +  x4  +  3 x3  +  2 x2  +  1   =   0.
    

• Exercise set 4, Due Wednesday, February 12
  • 3.1, p 119 -- 3ac, 4ac, 7ac, 15a
  • 3.2, p 131 -- 1a, 2b, 4
• Exercise set 5, Due Wednesday, February 26
  • 3.3, p 139 -- 1bc, 4a
  • 3.3, p. 139 -- 3ab, 7ab (new)
  • 3.4, p. 153 -- 3d

  • Find a fifth-degree polynomial  p  such that
    
             p(-1)  = -2
             p'(-1) =  4
             p(0)   =  0
             p'(0)  =  3
             p''(0) =  4
             p(1)   =  6
         

• Exercise set 6, Due Wednesday, March 5
  • 4.1, p. 175 -- 3b, 4b, 5a
  • 4.3, p. 194 -- 1cd, 2cd, 3cd, 4cd, 5cd, 6cd
• Program 3, Due Monday, March 10 -- calculation of spline curves. Your program should use the method of the handout. (If you need another copy of the handout, it can be found here.) You should have subroutines for f, g and h. Then there should be subroutines for f₀, f₁, and so on. Finally you should accept seven values as input and be able to calculate function values that interpolate these seven values. I'd like to see graphic output of the following:
  • The basic functions f, g and h.
  • The function mentioned in the text that oscillates between 1 and -1.
  • A function that has f(0)=f(6)=0 and whose other five values f(1) ... f(5) are the digits of your favorite zipcode. (Your home, your friend, Disneyland, -- whatever interests you.)
  • I assume many of you have access to one way or another of displaying a curve. If you have no other way, here is a crude but serviceable way of making a .pdf file that will display your curve. First make a file that looks like this:

                             x1 y1  m
                             x2 y2  l
                             x3 y3  l
                                   ....  

    To this file, prepend this file and append this file. The result is a valid .pdf file (and may be viewed with an acrobat reader). The x and y values should be re-scaled to lie between 0 and 1. The x-values should be in increasing order. Each y-value should be f(x) for the corresponding x. For a more sophisticated compiler of .pdf files, see here.
• Exercise set 7, Due Wednesday, March 12
  • 4.4, p. 203 -- 1c
  • 4.5, p. 211 -- 1b
• Exercise set 8, Due Wednesday, April 2
  • 4.6, p. 219 -- 1ab, 2ab, 6
• Exercise set 9, Due Wednesday, April 9
  • 5.2, p. 263 -- 1cd, 2cd, 3a, 4a
  • 5.3, p. 271 -- 1a
  • 5.4, p. 280 -- 1a, 3a, 4a
  • 6.2, p. 368 -- 3c
  • 6.3, p. 378 -- 1f
• Exercise set 10, Due Wednesday, April 16
  • 6.4, p. 386 -- 1cd
  • 6.5, p. 396 -- 3a
  • 7.1, p. 428 -- 1, 2a, 4c
  • 7.2, p. 436 -- 1gh, 11
• Exercise set 11, Due Wednesday, April 30
  • 7.3, p. 451 -- 1a
  • 8.1, p. 493 -- 3, 8
  • 8.2, p. 506 -- 1bd, 2bd, 7, 9bd, 10bd