Course Announcements

5/3/22: 1. An anonymous grade distribution for the Final Exam has been posted.; 2. An anonymous grade distribution for the semester has been posted.
4/21/22: 1. An anonymous grade distribution for Exam 2 has been posted.; 2. The solution of Problem 1 on Exam 2 has been updated.
4/19/22: 1. Solutions for Exam 2 have been posted.
4/11/22: 1. Exam 2 will held in the usual classroom, 106 LOV.
4/5/22: 1. A final slide with the block version of the Cooley-Tukey radix 2 FFT wiring diagram has been added to Set 25.; 2. The block version of the Cooley-Tukey radix 4 FFT wiring diagram for n=16 has been added to the solutions for Study Question Set 4.; 3. Sets 32 and 33 have been posted.; 4. Solutions for Study Question Set 5 have been posted.
4/4/22: 1. Study Question Set 5 has been posted.; 1. Solutions for Study Question Set 4 have been posted.
4/1/22: 1. Sets 28, 29, 30, and 31 on numerical methods for ODEs have been posted.; 2. A paper by Strang on the DCT has been posted along with many papers on numerical methods for ODEs. These are all for your reference. You are not responsible for their content.
3/30/22: 1. Set 24 slides 42, 43, 44 and 45 have been modified to make the change of index, shift in basis, and permutation and the equivalence of their use here with that in the interpolation discussion earlier in the set..; 2. Exam 2 information has been posted.
3/28/22: 1. Study Question Set 4 has been posted.; 2. Graded Homework 4 has been posted.
3/26/22: 1. Sets 26 and 27 have been posted.; 2. Set 22 has been updated. Based on the discussions in Friday's class I have updated the derivation of the step halving error estimates (slides 25, 26, 27 in the new set) and the alternative derivation of extrapolation (slides 16 and 17 in the new set). The new versions are more detailed but make the approximation clearer and are good examples of manipulating expressions with unspecified higher order terms using "big O" notation. Download and read the new set before Monday's lecture.
3/25/22: 1. Set 25 has been posted.
3/24/22: 1. Set 24 and associated papers have been posted.
3/21/22: 1. Typos fixed on slide 35 Set 21 have been fixed.
3/17/22: 1. Set 23 has been updated to add some clarifications to the use of the polynomial-based differencing. In particular, slides 33 to 36 are modified.
3/11/22: 1. An anonymous grade distribution for Exam 1 has been posted.; 2. As requested, solutions for Exam 1 have been posted.
3/8/22: 1. Solutions for Study Question Set 3 have been posted. The Study Question Set 3 has also been reposted after a bit of cleanup on the notation in the problems.
3/4/22: 1. Study Question Set 3 has been posted.; 2. Sets 22 and 23 of the class notes have been posted along with a paper on adaptive quadrature. The paper is for your reference and is not required reading for the class..
3/4/22: 1. The due date for graded homework 3 has been extended to Friday at 11:59PM.; 2. Papers by Salzer and Mason on the derivation of the Barycentric 2 coefficients for Chebyshev points have been posted. (near the line with Set 5); 3. Set 21 of the class notes has been posted.; 4. Several papers on Gaussian quadrature and related methods have been posted. They are for your reference and are not required reading for the class.
3/2/22: 1. Set 20 of the class notes has been posted.
2/25/22: 1. Graded Homework 3 has been posted.
2/24/22: 1. Set 19 of the class notes have been posted.
2/23/22: 1. Exam 1 will be in the normal classroom.
2/22/22: 1. Sets 17 and 18 of the class notes have been posted.
2/21/22: 1. Set 16 of the class notes and some related papers have been posted.
2/17/22: Exam 1 is scheduled for next week Thursday 2.24.22. For those that have TA conflicts (I have heard from only 1 so far), contact me so we can arrange for you to take the exam on Wednesday (assuming you have no conflict on that day)
2/11/22: 1. The subscripts indicating the local interval and the associated polynomial have been made consistent in Set 11.; 2. Graded Homework 2 has been posted.; 3. Exam 1 information has been posted.
2/10/22: 1. Solutions for Study Questions Set 2 have been posted.
2/7/22: 1. Sets 13, 14 and 15 of the class notes have been posted.; 2. Multiple papers on splines have been posted. These are for reference and are note required reading. They contain the proofs of the theorems on convergence and error stated in the class notes.
1/31/22: 1. The due date on Graded Homework 1 has been corrected.
1/28/22: 1. Sets 11 and 12 of the class notes have been posted.
1/27/22: 1. Graded Homework 1 has been posted.; 2. The two typos on page 31 of Set 5 have been fixed.; 3. The solutions for Study Questions Set 1 have been posted.
1/26/22: 1. The typo on page 17 of Set 4 has been fixed.; 2. A typo on page 18 of Set 5 has been fixed and a clarifying line has been added to page 32 of Set 5.
1/21/22: 1. Sets 9 and 10 have been posted.
1/20/22: 1. Set 5 has been posted.; 2. Reading ahead carefully in Set 5 in preparation for the related lectures is required.; 3. Two papers discussing topics that include, but are not limited to, the third approach to computing divided differences have been posted. They are not required reading for class but you are encouraged to read them at some point .; 4. Sets 6, 7 and 8 have been posted.; 5. A paper by Reichel and a second by Calvetti and Reichel have been posted. They are not required reading for the class but are for your reference and further study on stability related to polynomials and approximation. You are also encouraged to read Higham's text on evaluation and conditioning of polynomials.
1/14/22: 1. Study Question Set 1 has been posted.
1/14/22: 1. Set 4 has been posted.; 2. You are strongly encouraged to read ahead carefully in Set 4 in preparation for the related lectures.; 3. A paper by Higham and a paper by Berrut and Trefethen have been posted. These are required reading.
1/7/22: 1. Set 3 has been posted.; 2. You are strongly encouraged to read ahead carefully in Sets 2 and 3 in preparation for the related lectures.; 3. A paper by Bjorck and Pereyra discussing the solution of Vandermonde linear systems has been posted. The algorithm was mentioned in Set 2. This paper is for your reference and you are not required to read it for the class.
1/6/22: 1. Set 2 has been posted.
1/5/22: 1. The class syllabus has been posted.; 2. Set 1 has been posted.; 3. A description of the format for submitting program solutions has been posted.; 4. Example program solutions have been posted.; 5. Note that we will cover nonlinear relaxation for systems before starting the second semster material. This is Set 19 of FCM 1 notes and the website is still available on my departmental page using the Teaching button on the top line.; 6. Also note that Set 16 of the FCM 1 notes has been updated with a reorganization and modification of the convergence theorems associated with contraction mappings and related iterations. This clarifies the theory and corrects some difficulties with Theorem 16.5 in the old version of the set.

Course Announcements

5/3/22

1. An anonymous grade distribution for the Final Exam has been posted.

2. An anonymous grade distribution for the semester has been posted.

4/21/22

1. An anonymous grade distribution for Exam 2 has been posted.

2. The solution of Problem 1 on Exam 2 has been updated.

4/19/22

1. Solutions for Exam 2 have been posted.

4/11/22

1. Exam 2 will held in the usual classroom, 106 LOV.

4/5/22

1. A final slide with the block version of the Cooley-Tukey radix 2 FFT wiring diagram has been added to Set 25.

2. The block version of the Cooley-Tukey radix 4 FFT wiring diagram for n=16 has been added to the solutions for Study Question Set 4.

3. Sets 32 and 33 have been posted.

4. Solutions for Study Question Set 5 have been posted.

4/4/22

1. Study Question Set 5 has been posted.

1. Solutions for Study Question Set 4 have been posted.

4/1/22

1. Sets 28, 29, 30, and 31 on numerical methods for ODEs have been posted.

2. A paper by Strang on the DCT has been posted along with many papers on numerical methods for ODEs. These are all for your reference. You are not responsible for their content.

3/30/22

1. Set 24 slides 42, 43, 44 and 45 have been modified to make the change of index, shift in basis, and permutation and the equivalence of their use here with that in the interpolation discussion earlier in the set..

2. Exam 2 information has been posted.

3/28/22

1. Study Question Set 4 has been posted.

2. Graded Homework 4 has been posted.

3/26/22

1. Sets 26 and 27 have been posted.

3/25/22

1. Set 25 has been posted.

3/24/22

1. Set 24 and associated papers have been posted.

3/21/22

1. Typos fixed on slide 35 Set 21 have been fixed.

3/17/22

1. Set 23 has been updated to add some clarifications to the use of the polynomial-based differencing. In particular, slides 33 to 36 are modified.

3/11/22

1. An anonymous grade distribution for Exam 1 has been posted.

2. As requested, solutions for Exam 1 have been posted.

3/8/22

1. Solutions for Study Question Set 3 have been posted. The Study Question Set 3 has also been reposted after a bit of cleanup on the notation in the problems.

3/4/22

1. Study Question Set 3 has been posted.

2. Sets 22 and 23 of the class notes have been posted along with a paper on adaptive quadrature. The paper is for your reference and is not required reading for the class..

3/4/22

1. The due date for graded homework 3 has been extended to Friday at 11:59PM.

2. Papers by Salzer and Mason on the derivation of the Barycentric 2 coefficients for Chebyshev points have been posted. (near the line with Set 5)

3. Set 21 of the class notes has been posted.

4. Several papers on Gaussian quadrature and related methods have been posted. They are for your reference and are not required reading for the class.

3/2/22

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

2/25/22

1. Graded Homework 3 has been posted.

2/24/22

1. Set 19 of the class notes have been posted.

2/23/22

1. Exam 1 will be in the normal classroom.

2/22/22

1. Sets 17 and 18 of the class notes have been posted.

2/21/22

1. Set 16 of the class notes and some related papers have been posted.

2/17/22

Exam 1 is scheduled for next week Thursday 2.24.22. For those that have TA conflicts (I have heard from only 1 so far), contact me so we can arrange for you to take the exam on Wednesday (assuming you have no conflict on that day)

2/11/22

1. The subscripts indicating the local interval and the associated polynomial have been made consistent in Set 11.

2. Graded Homework 2 has been posted.

3. Exam 1 information has been posted.

2/10/22

1. Solutions for Study Questions Set 2 have been posted.

2/7/22

1. Sets 13, 14 and 15 of the class notes have been posted.

2. Multiple papers on splines have been posted. These are for reference and are note required reading. They contain the proofs of the theorems on convergence and error stated in the class notes.

1/31/22

1. The due date on Graded Homework 1 has been corrected.

1/28/22

1. Sets 11 and 12 of the class notes have been posted.

1/27/22

1. Graded Homework 1 has been posted.