Math/CS 466/666

466/666 NUMERICAL METHODS I (3+0) 3 credits

Instructor  Course Section                       Time
------------------------------------------------------------------------
Eric Olson  Math/CS 466/666 Numerical Methods I  MW  10-10:50am DMS105
                                                   F 10-10:50am DMS106

Course Information

Instructor:: Eric Olson
email:: ejolson at unr edu
Office:: Monday, Tuesday and Wednesday 1pm DMS 238 and by appointment.
Homepage:: http://fractal.math.unr.edu/~ejolson/466/
Assistant:: Jordan Blocher
Jordan's email:: jordanblocher at gmail.com
Jordan's Office:: Monday 11am to 4pm in SEM 207 and by appointment.
Jordan's Homepage:: http://www.cse.unr.edu/~jblocher/
Required Texts:: James McDonough, Basic Computational Numerical Analysis, lecture notes, University of Kentucky, 2007
Supplementary Resources:: Germund Dahlquist, Ake Bjorck, Numerical Methods, Dover Books on Mathematics, 2003; ISO/IEC 9899:TC3 Standard for the C Programming Language, final committee draft, 2007; Brian Kernighan, Rob Pike, The Unix Programming Environment, Prentice-Hall Software Series, 1983; Brian Kernighan, Dennis Ritchie, The C Programming Language, 2nd Edition, Prentice-Hall, 1988; David Kincaid, Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, American Mathematical Society, 2002; Attila Mate, Introduction to Numerical Analysis with C Programs, lecture notes, Brooklyn College, 2004; William Press, Saul Teukolsky, William Vetterling, Brian Flannery, Numerical Recipes 3rd Edition, The Art of Scientific Computing, Cambridge university Press, 2007; Anthony Ralston, Philip Rabinowitz, A First Course in Numerical Analysis, Second Edition, Dover Books on Mathematics, 2001; Francis Scheid, Schaum's Outline of Numerical Analysis, Second Edition, McGraw-Hill, 1989; Endre Suli, David Mayers, Introduction to Numerical Analysis, Cambridge University Press, 2003

Programming Projects and Homework

Homework 1 Vectors, Matrices and Condition Number (solutions).
Project 1 Adaptive Quadrature (solutions).
Project 2/Homework 2 Three Stage Runge-Kutta Methods.
Project 3/Homework 3 Two-point Boundary Value Problems.

The ECC Ubuntu Virtual Machine

If you want to transfer files between the Ubuntu VM at UNR and your home computer, this may be done by connecting to remote.ecs.unr.edu using the FileZilla Client. You may also use PuTTY and PSFTP, which accomplish the same thing in a simpler way. As always, please excercise caution when downloading software to your personal computer. The above links point directly to the developer websites and should be fine; however, malware has been found on third-party websites.

Ubuntu is free software and can be installed on your personal computer. The ECC lab staff have provided specific instructions (local copy) for downloading and configuring a copy of the ECC Ubuntu VM. Students can bring their laptops to the ECC for assistance. The best times to find one of the ECC Linux experts at the desk is MW afternoons and most Fridays. General help with installing an Ubuntu virtual machine may also be obtained by asking for Michael at the Knowledge Center.

Computing Labs

Lab 1 Introduction to Computing I
Lab 2 Introduction to Computing II
Lab 3 Spectral Radius
Lab 4 Newton's Method (advanced version)
Lab 5 Numerical Quadrature
Workshop 1 Gram–Schmidt Orthogonalization (handout)
Lab 6 Lorenz Equations
Quiz 1 Programming Solutions
Exam 1 Review Euler's Method
Lab 7 Runge-Kutta Methods
Lab 8 Two-point Boundary Value Problems
Lab 9 Adaptive RK Methods
Lab 10 Partial Differential Equations

Exams and Quizzes

Announcements

[07-Dec-2014] Changes to Programming Project 3

I have made a small change in programming project/homework 3 that affects two students. For jganska and pwhite the original table of customized problems had f(x)=A=B=0 which leads to y=0 being the solution. This is not a particularly good test problem, so please use the following instead:

netid          p(x)    f(x)     A     B
---------------------------------------
jganska       sin x       0     0     6
pwhite      -sin 2x       0     0     6

Please let me know if there are any problems.

[14-Nov-2014] Quiz 2

There is an quiz Friday in the computer lab. The first part of the quiz will be without computers; the second part you will use a computer. Do not type or use the mouse until the first part of the quiz has been collected. I have prepared a review sheet to help focus your studying.

[12-Nov-2014] Correction to Lecture

There was an error in the Maple worksheet I presented at the end of class. The differentiation rule for y'(t) = f(t,y(t)) was entered into Maple without the chain rule. The correct worksheet is

restart;
`diff/y`:=proc(s,t) f(s,y(s))*diff(s,t) end proc;
y1:=y(t)+h*(3/2*f(t,y(t))-1/2*f(t-h,y(t-h)));
series(y(t+h)-y1,h=0,4);

which now produces the expected O(h³) answer. In Reduce the equivalent statements are

load_package "dfpart";
load_package "taylor";
operator y;
generic_function f(t,y);
for all x let df(y(x),x)=f(x,y(x));
y1:=y(t)+h*(3/2*f(t,y(t))-1/2*f(t-h,y(t-h)));
taylor(y(t+h)-y1,h,0,3);

Note that the chain rule doesn't need to be explicitly stated in Reduce.

[17-Oct-2014] Exam 1

Exam 1 will be in the DMS106 computer lab. The first part of the quiz will be without computers; the second part you will use a computer. Do not type or use the mouse until the first part of the quiz has been collected. I have prepared a review sheet to help focus your studying.

[24-Oct-2014] Programming Project 1

Programming project 1 on adaptive quadrature will be due October 24. Solutions are now available.

[03-Oct-2014] Quiz 1

Quiz 1 will be in the DMS106 computer lab. The first part of the quiz will be without computers; the second part you will use a computer. Do not type or use the mouse until the first part of the quiz has been collected. I have prepared a review sheet to help focus your studying.

[29-Sep-2014] Homework 1

Homework 1 is due in class on Monday, September 29. You may find Gaussian Elimination and LAPACK helpful when implementing the inverse power method for finding the smallest eigenvalue.

[28-Sep-2014] Programing Workshop

We will meet Saturday at 1pm in the DMS106 computer lab to discuss programming techniques. This session is optional and will not cover material which is core to the course. We wrote a Gram–Schmidt elimination routine and examined the performance difference between a simple linear algebra solver and an optimized LAPACK routine.

[19-Sep-2014] Reduce Computer Algebra System

In today's computer lab we used the Reduce Computer Algebra System which can be downloaded free of charge for most computers. For more information see the Reduce User's Manual or the more up-to-date online documentation. There is also a comprehensive guide to the GENTRAN automatic code generator and translator.

[10-Sep-2014] Correction to Lecture

It has been pointed out that a term was missing in the update rule for h_k written on the board at the end of class. The corrected update rule is

Please mind the +h_k−1 terms added in blue at the end of each line.

[25-Aug-2014] Room Changes

The rooms for our class have been changed. We will be Monday and Wednesday in DMS 105 and Friday in DMS 106.

[29-Aug-2014] Friday in Computing Lab 106

Every Friday class will be held in the computing lab on the first floor of the Davidson Mathematics and Science Building in room 106.

[03-Sep-2014] Preliminary Survey

This survey contains calculus and computer literacy questions of wide ranging and varying difficulty designed to gauge both undergraduate and graduate student backgrounds. The results will be used to direct each student towards specific resources and to shape the focus of the lectures. The results will not affect your grade or the overall content of the course.

Grading

     2 Quizzes                 10 points each
     1 Exam                    30 points
     1 Final Exam              50 points
     3 Homework Assignments    10 points each
     3 Programming Projects    10 points each
    ------------------------------------------
                              160 points total

Calendar

    August 25 Section 1.1 Solution of Linear Systems
    August 27 Section 1.1 Solution of Linear Systems (continued)
    August 29 Introduction to Computing Part I

    September 1 (no class)
    September 3 Computer Literacy Survey
    September 5 Introduction to Computing Part II

    September 8 Section 1.2 The Algebraic Eigenvalue Problem 
    September 10 Section 1.2 The Algebraic Eigenvalue Problem (continued)
    September 12 Computing Lab on Eigenvalues

    September 15 Section 2.1 Fixed-Point Methods for Nonlinear Equations
    September 17 Section 2.2 Modifications to Newton's Method
    September 19 Computing Lab on Newton's Method

    September 22 Section 3.1 Approximation
    September 24 Section 3.2 Numerical Quadrature
    September 26 Computing Lab on Quadrature

    September 29 Section 3.3 Finite-Difference Approximations
    October 1 Section 3.4-3.5 Richardson Extrapolation
    October 3 Quiz 1 (review)

    October 6 Section 4.1 Initial Value Problems
    October 8 Section 4.1 Initial Value Problems (continued)
    October 10 Computing Lab on Initial Value Problems

    October 13 Summary
    October 15 Review
    October 17 Exam 1

    October 20 Section 4.1 Runge-Kutta Methods
    October 22 Section 4.1 Runge-Kutta Methods (continued)
    October 24 Computing Lab on Runge-Kutta Methods

    October 27 Section 4.2 Boundary Value Problems
    October 29 Section 4.2 Boundary Value Problems (continued)
    October 31 (no class)

    November 3 Section 4.3 Nonlinear Boundary-Value Problems
    November 5 Section 4.4 Singular Boundary-Value Problems
    November 7 Computer Lab on Boundary-Value Problems

    November 10 Summary
    November 12 Review
    November 14 Quiz 2

    November 17 Adams-Bashforth multistep methods 
    November 19 Section 5.1 Introduction to PDEs
    November 21 Computing Lab on Adaptive RK Methods

    November 24 Section 5.2 Parabolic Equations 
    November 26 Section 5.2 Parabolic Equations (continued)
    November 28 (no class)

    December 1 Section 5.2 Parabolic Equations (continued)
    December 3 Section 5.2 Parabolic Equations (continued)
    December 5 Computer Lab on Parabolic Equations

    December 8 review
    December 10 (no class)

Final Exam

The final exam will be held on Friday, December 12 from 10:15am-12:15pm in DMS106.

Equal Opportunity Statement

The Mathematics Department is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to contact instructors during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't talk or pass notes with other students during an exam. Don't read notes or books while taking exams given in the classroom. You may work on the programming assignments in groups of two if desired. Homework may be discussed freely. If you are unclear as to what constitutes cheating, please consult with me.

Last Updated: Wed Mar 5 05:38:03 PST 2014