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   WF   9-9:50am EJCH205
                                                 M     9-9:50am DMS106

Course Information

Instructor:: Eric Olson
email:: ejolson at unr edu
Office:: Monday, Wednesday and Friday 11am DMS 238 and by appointment.
Homepage:: http://fractal.math.unr.edu/~ejolson/466/
Assistant:: Jordan Blocher
Jordan's email:: jordanblocher at gmail.com
Required Texts:: Richard Burden and Douglas Faires, Numerical Analysis, 7th, 8th, 9th or 10th edition.; Do not purchase Numerical Methods by the same authors.
Supplemental Texts:: Simon Long, Learn to Code with C.

Programming Assignments

Homework Assignments

Announcements

[16-Dec-2016] Project and Homework 3

Please turn in Combined Programming Project and Homework 3 at the final exam or shortly afterwards on December 16. The final exam will cover topics from Quiz 1 and the Midterm as well as the proof of the convergence of Euler's method for solving ordinary differential equation initial-value problems.

[12-Dec-2016] Computer Quiz 2

There will be a quiz in the computer lab Monday covering the topics

2nd order Taylor's method for ODEs.
Newton's method for systems.

[10-Dec-2016] Convergence of Euler's Method

I have created lecture notes on the convergence of Euler's method for solving initial-value problems for ordinary differential equations that should help you study for the final exam. A similar proof may be found in Chapter 5.2 of our textbook.

[07-Dec-2016] Midterm Solutions

My solutions are now available for programming part and the written part of the midterm.

[02-Dec-2016] Programming Project 2

Please turn in Programming Project 2 in class or shortly afterwards on December 2. Note, there is now a code snippet hint for completing the LAPACK part of the project.

[23-Nov-2016] Midterm Part II

The second part of the midterm will be held in our regular classroom Wednesday and cover topics from Quiz 1 as well as the following additional topics:

Proof that the spectral norm |A|=ρ(A^tA)^1/2.
State the power method for finding ρ(B) for a symmetric matrix B.
Proof that the power method converges to the spectral radius.

[09-Nov-2016] Quiz 1 Solutions

My solutions for Quiz 1 are now available to help you study for the midterm. My solutions are now available for Midterm Part II.

[21-Nov-2016] Midterm Part I

The first part of the midterm will be held in the computing lab Monday and involve performing two practical computations out of a selection of four choices. My solutions are now available for Midterm Part I.

[26-Oct-2016] Quiz 1

The first quiz will cover the following topics:

State Newton's method.
Show Newton's method is quadratically convergent.
Explain why it is sometimes said the Newton's method doubles the number of significant digits at each iteration.
Complete a table of Newton's divided differences.
Use a table of divided differences to construct an interpolating polynomial through the given points.
State the method of Gauss quadrature.
1. Define the orthogonal polynomial P_n of degree n.
2. Define the points x_k and the weights w_k for k=0,2,...n.
Prove the Gauss quadrature method is exact for polynomials of degree 2n+1.
More to come discussed on Friday.

[24-Oct-2016] Programming Project 1

Please turn in Programming Project 1 in class or shortly afterwards on October 24.

[02-Oct-2016] Computing Workshop

We will have an optional computing workshop in DMS106 on Sunday from 1:30pm to 3:30pm to discuss issues related to Linux but not directly related to the subject of numerical analysis.

[30-Sep-2016] Programming Project 1

Programming Project 1 is now ready. If you find any errors or have questions please let me know.

[29-Aug-2016] First Day of Class

As the lab is not ready, the first day of class will be held in EJCH205 and not in the computer lab. Note there was a room change and this is a different room than appeared on the original schedule.

[24-May-2016] Information about Textbooks

The main textbook for the course is Numerical Analysis by Richard Burden and Douglas Faires. This book has gone through 10 editions since the first edition in 1978. I have ordered the 10th edition at the ASUN bookshop. If you have an earlier edition of the book, that would also be fine for the course. Please make your choice based on budget and availability. Warning: do not purchase the book entitled Numerical Methods by the same authors.

Sample Code

September 02: Print IEEE representation of double in binary.
September 12: Newton's method.
September 19: Trapezoid method and C Code Generation with Maple (pdf,mws).
September 26: Parallel trapezoid method (cilk_for, cilk_spawn, Makefile)
October 02: Latex Template, a Gnuplot Template and the finished tutorial.
October 03: Makefile and Mueller's Method.
October 05: Newton-Cotes Methods (mpl,mws).
October 07: Gauss Quadrature (mpl,mws).
October 10: Makefile, Adaptive Quadrature and another Maple worksheet (mpl,mws).
October 17: Makefile, Approximation of Derivatives.
October 21: Makefile, Multiprecision Newton's Method.
October 23: Timing routines (tictoc.c, tictoc.h)
October 24: Frobenious Norm
October 31: Makefile and partial code for power method.
November 07: Makefile, compute spectral norm, matrix library matlib.h, matlib.c.
November 13: Gaussian elimination (solveAx.c, solveAx.h).
November 14: Makefile and Inverse Power Method.
November 19: Code Snippet Hint for Programming Project 2.
November 28: Makefile and Euler's and a Convergence study of Taylor's method.
December 07: Solutions to programming part of the midterm.
December 09: Newton's Method for Systems, Makefile, Jacobian with Maple (pdf)
December 12: Solutions to Quiz 2.

Grading

     2 Quizzes                 20 points each
     1 Exam                    60 points
     1 Final Exam             100 points
     3 Homework Assignments    20 points each
     3 Programming Projects    20 points each
    ------------------------------------------
                              320 points total

Calendar

Final Exam

The final exam will be held on Friday, December 16 from 2:45-4:45pm in EJCH205.

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: Tue May 24 17:48:13 PDT 2016