Course Announcements

12/15/20

1. Anonymous grade distributions for the Final Exam and the Semester have been posted.

12/10/20

1. The solutions for the Final Exam have been posted.

12/8/20

1. An anonymous list of Exam 2 grades have been posted on the Grade information page. Your personal grades have been added to you canvas record and you should be able to view them. In order for me to send you a grade summary and the marked up pdf file of your solutions, you must send me an email specifically granting me permission to do so.

12/2/20

1. Some slides have been added to Set 28. Examples of P(EC)mE methods and another comment on error estimation have been added.

Comment on remaining lectures:

Due to the period of adjustment at the beginning of the semester to the all-remote format, the early lectures were slower than usual and as a result we are approximately 3 lectures behind.

Therefore, I will lecture longer than 50 minutes for all three lectures this week in order to make up some of that time. These lectures will be recorded and available via canvas. As usual, there is no attendance requirement and those students that must leave the lectures for other appointments may so do.

I will cover Set 28 on linear multistep methods and then Set 32 on stiffness first. This is the last material for which you will be responsible this semester.

If there is time in the extended three lectures this week I will begin the discussion of Runge Kutta methods beginning with explicit RK methods. This will not be on the final this semester and the first topic next semester will be a review of the material covered on RK this week and completion of the material on implicit RK methods.

11/30/20

1. Sets 30 and 31 on Explicit and Implicit Runge Kutta methods respectively have been posted.
2. Set 32 on stiffness in ODE integration has been posted.
3. Set 33 on the computation of the coefficients of the coefficients in the GFS by numerical quadrature and the relationship to interpolation has been posted.
4. Study Questions Homework 6 and its solutions have been posted.
5. Final Exam information and a proposal for those not in the Eastern time zone have been posted on the exam information page.

11/24/20

1. The solutions for Exam 2 have been posted.

11/22/20

1. An anonymous list of Exam 1 grades have been posted on the Grade information page. Your personal grades have been added to you canvas record and you should be able to view them. In order for me to send you a grade summary and the marked up pdf file of your solutions, you must send me an email specifically granting me permission to do so.
2. A minor error was fixed in the posted solution to problem 3 on Exam 1.

11/20/20

1. A typo in the sign of the first in N1 (x) solution to study question 4.7 has been fixed. Also, the solution for 4.9 that was inadvertently left out has been added.

11/16/20

1. Sets 27, 28 and 29 of the class notes have been posted.
2. Several papers on the numerical integration of ODE IVP's have been posted. These are for your reference.

11/13/20

1. Set 25 has been reposted after fixing typo mentioned in class on slide 35.
2. Graded Homework 4 has been posted.

11/12/20

1. Solutions for Study Questions Homework 5 have been posted.
2. Typos in the Chebyshev polynomial recurrence fixed on slides 19 and 20 of Set 20 of the class notes.

11/10/20

1. The times for Exam 2 have been posted.

11/9/20

1. Typos fixed in Set 23 of the class notes.
2. Sets 25 and 26 of the class notes have been posted.

11/6/20

1. Two dates have been proposed for Exam 2 on the Exam Information page. Respond with any comments by email immediately.

11/5/20

1. The input data template for use when running Program 3 for Joshua has been posted.

11/4/20

1. The due date of Graded Homework 3 has been modified on the Homework page.
2. Set 24 of the class notes has been posted.
3. Several papers on numerical quadrature have been posted. They are for your further reading and not of immediate concern for this class.

11/3/20

1. Set 23 of the class notes has been posted.

11/1/20

1. Set 22 of the class notes has been posted.

10/28/20

1. The solutions to Exam 1 have been updated at 11:55AM
2. Graded Homework 3 has been posted.

10/27/20

1. Set 21 of the class notes has been posted.
2. Solutions for Study Questions Homework 4 have been posted. Note Problem 4.4 derives the s' boundary conditions when using the s" parameterization equations.
3. The solutions to Exam 1 have been posted. You are encouraged to read them carefully.

10/26/20

1. Set 20 of the class notes has been posted.

10/22/20

1. Study Question Homework 4 has been posted. Some of the material is covered in slides that will be posted next week.

10/22/20

1. Set 19 of the class notes has been posted.
2. Two papers on computation associated with Chebyshev and orthogonal polynomials have been posted along with a link to a repository of Matlab code for orthogonal polynomials related to the classic book 'Orthogonal Polynomials: Computation and Approximation', Clarendon Press, Oxford, 2004 by Gautschi.

10/21/20

1. Zoom meetings have been added to the class meeting schedule for the two Exam 1 sessions. Pdf files of the exam will be distributed immediately before the exam begins. Make sure therefore to join the meeting at least 15 minutes before the exam's starting time.

10/16/20

1. The coverage and rules for Exam 1 have been postedon the Exam Information page.

10/13/20

1. Sets 16, 17 and 18 of the class notes and some papers on polynomial splines have been posted.
2. Sets 16 and 17 are on cubic splines. It is strongly recommended you read ahead in these.
3. Set 18 is on parametric curves as an application of interpolation, splines and other related curves. It will not be covered in class.

10/9/20

1. Proposed times for Exam 1 are on the exam information page.

10/6/20

1. During your readings to prepare for the lectures, for Set 13 we will cover in the lecture Sections 3 and 5 of the slides that cover the definition of Hermite and Hermite-Birkhoff interpolation, and the Newton form of the interpolating polynomial respectively. The sections on the monomial basis and the basis for the Lagrange-like form are for your study. They are not required for any exam or graded homework this semester but you are encouraged to read them and some study questions homework problems use them to help reinforce the ideas.
2. Study Questions Homework 3 and their solutions have been posted. They use material in Sets 13, 14 and 15.
3. Set 15 of the class notes have been posted.

10/5/20

1. Graded Homework 2 has been posted. Due to the delay in posting I have made the due date next Wednesday (10/14) rather than Monday (10/12).
2. The solutions to the written problems of Homework 1 have been posted.

10/2/20

1. Exam 1 will be during the week of 19 October 2020. Details will be given next week.
2. Sets 10, 11, 12, 13 and 14 have been posted.
3.Study Questions Homework Set 2 and its solutions have been posted.
4. Calvetti and Reichel, "On the evaluation of polynomial coefficients" has been posted.
5. Reichel, "Newton Interpolation At Leja Points" has been posted. Set 11 describes the Leja ordering and one of the solutions for study questions in Homework 2 contains an algorithm to compute the ordering so this paper is not absolutely required for the Homework but it is recommended you skim it for the Homework.

9/23/20

1. Instructions for homework solutions have been posted.

9/20/20

1. Sets 5 through 9 of the class notes has been posted. They are all on the approaches to the basic function value based interpolation problem.
2. Sets 5 through 8 will be covered in class. It is imperative that you read ahead in these notes. Prepare questions for the lectures and any office hour meetings you schedule; and review the slides after the lectures and meetings.
3. Four papers related to polynomial interpolation have been posted. The first two should be read since they are directly related upcoming lectures and homeworks. The second two are important but not crucial reading for the course. The last is a classic paper on structured linear systems but not crucial reading for the course, i.e., the main relevant points have been made in the suplemental material on the mononial basis in the notes.

9/19/20

1. 12:30PM I have added some potential test sums to Graded Homework 1 and reposted the pdf file. These are suggestions and not requirements.
2. Graded Homework 1 has been posted.
3. Make up lecture: There is no single day that can handle all of the preferences so next week Monday during the regular class time (10:10 - 11:00) I will start the interpolation material. On Monday from 11:00 - 12:00, I will give the make up lecture that finishes discussing the stability material of use for the first program assignment. Both, of course, will be taped. For those that prefer a live make up lecture and cannot make Monday at 11:00, I will repeat the make up lecture on Tuesday at 11:00. For those that cannot attend either make up and do not want to use only the tape of the make up, contact me after listening to the tape and I will set up a separate discussion of the material. This should be done early enough to you can use the information in your work on the first program assignment.

9/18/20

1. Typos on p. 22 in half angle formula of Set 4 fixed.
2. Please send email to kgallivan@fsu.edu with your top two day preferences for the make up lecture next week. It can be 11:00 to noon any day next week. If necessary due to differing schedules between the degree tracks I can give two such lectures.

9/17/20

1. Typos on p23 of Set 3 fixed. FP vs Real addition notation fixed on pp. 23-24.

9/14/20

1. The solutions for Study Questions Homework Set 1 have been posted.

9/4/20

1. The link to Study Questions Homework Set 1 has been fixed.

9/3/20

1. Study Questions Homework Set 1 has been posted.

9/2/20

1. Typo fixed on p 24 of Set 2. The special pattern indicating subnormal and large numbers or NaN explanation has been clarified by added detail on pp. 22 and 23 for single precision and pp. 25 and 26 for double precision.

8/28/20

1. Sets 3 and 4 of the class notes have been posted.

8/26/20

1. Set 2 of the class notes has been posted.

8/24/20

8/24/20 10:45 Due to Canvas/Zoom problems, the FCM 1 class meeting for today is cancelled.
10:30 Canvas/Zoom is having problems this morning and is refusing to allow access by the hosts to start class meetings. Multiple attempts to start FCM 1 have failed. The myfsu portal is also having login problems.

8/18/20

1. The class syllabus has been posted.
2. A description of the format for submitting program solutions has been posted.
3. Two documents related to floating point representation and arithmetic have been posted.
4. Set 1 of the class notes has been posted.