Math/CS 375. Introduction to Numerical Computing. Fall 2020.


Sections:

Books:
Section 002. TR 09:30-10:45. Room: BANDE 105 Remote Scheduled. Syllabus for Math/CS 375 (60786/60787) Timothy Sauer
Numerical Analysis
2nd Edition, Pearson.

Additional material (by courtesy of Prof. S. Lau) can be found at the bottom of the page.
Additional Matlab tutorial by Prof. M. Nitsche.

Office hours:


TR 12:30-13:45. Room: SMLC 220 Remote Scheduled.

How grades are assigned?

All homeworks: 250 points.
Midterm exam: 125 points.
Final exam: 125 points.
Total: 500 points.
Lowest boundaries for grades (not higher than):
A = 450, B = 400, C = 350, D = 300.

Homework regulations

HW has to be typed in what ever editor you like.
If you were asked to produce any output from Matlab - it has to be copied in the HW text.
If you were asked to prepare a script and use it, every Matlab script has to be printed.
If you were asked to plot something, this plot has to be printed.
Essentially, it is recommended to type all HW together with plots and cut-and-paste scripts and Matlab outputs.
Week # Homework problems Due date
- Final Exam: Tuesday, December 8th, 2020, 7:30-9:30am, through UNM Learn.
What is covered: all topics.
You need to understand and be able to use definitions and algorithms.
Training set of problems:
Sauer, p. 19: 0.4.1;
Sauer, p. 59: 1.4.5;
Sauer, p. 101: 2.4.3;
Sauer, p. 198: 4.1.2, 4.1.7-9;
Sauer, p. 224: 4.3.1, 4.3.2 (Using both Gramm-Schmidt process and Givens' rotations (see lectures linalg4-5));
For linear algebra in general: you need to be able to estimate number of operations
necessary to complete the problem, understand sources of errors (condition number),
similar to problems in Midterm;
Sauer, p. 156: 3.2.1-3 (also work through problems in the Midterm);
Sauer, p. 164: 3.3.1, 3.3.5, 3.3.7-8;
Sauer, p. 176: 3.4.7, 3.4.12;
Sauer, p. 263: 5.2.1-3 (also you shall need understanding of error dependence on a grid step);
Sauer, p. 278: 5.5.1-3 (work through HW#11);
Sauer, p. 252: 5.1.1, 5.1.5;
Sauer, p. 321: 6.4.3 (you need to be able to use all methods we studied);
In all methods which we studied you need to understand
errors dependence on the parameters of methods like grid step etc. 		-
11 Homework 11 HW11 Solution.
 December 1st, 2020, end of day.
9-10 Homework 09-10.HW09 Solution HW10 Solution.
 November 5 10th, 2020, end of day.
- Midterm: October 15th, class time. (Solution published).
What is covered: all topics up to and including interpolation.
You need to understand and be able to use definitions and algorithms.
Training set of problems:
HW 2: 1, 2;
HW 3: 1, 4;
HW 4: 1-3;
HW 5: 1, 2;
HW 6: 1;
HW 7: 3;
HW 8: 1, 4;
anything else from what we studied also can be included. 		October 15th, 2020, class time.
7-8 Homework 07-8 HW07 Solution HW08 Solution. October 13th, 2020, end of day.
5-6 Homework 05-6 HW05 Solution HW06 Solution. October 6th, 2020, end of day.
3-4 Homework 03-4 HW03 Solution HW04 Solution. September 17th, 2020, end of day.
2 Homework 02 HW02 Solution. September 1st 3rd, 2020, class time.
1 Homework 01 HW01 Solution. August 25th, 2020, class time.
Below you can find additional material.
Week # Lectures Notes and scripts (by courtesy of Prof. Lau)
YouTube playlist for lectures' recordings.
14 TS 6.1, Numerical Differentiation
TS 6.2, Analysis of IVP solvers. 		TS 6.3-5, Systems of ODEs, Variable time step.
14 TS 5.5, Gaussian Quadratures
 Thanksgiving.
13 Lecture 23 (quad2) , (quad3) , TS 5.2
NewtonCotesClosedWeights.m 		Lecture 24 (quad3) TS 5.2
12 No lectures day. Lecture 21 (root4) TS 2.7,
Lecture 22 (quad1) , TS 5.2
11 Snow day. Lecture 20 (linalg5) , TS 4.2-4.3
10 Lecture 19 (linalg4) , TS 4.1-4.2 Lecture 20 (linalg5) , TS 4.2-4.3
9 Lecture 18 (splines1), TS 3.4
pwchermite_coeffs.m Compute coefficients defining piecewise cubic (PWC) Hermite spline.
eval_pwpoly.m Evaluate piecewise defined polynomial with Horner's rule. 		Midterm
8 Lecture 15, (interp3), TS 3.2 Lecture 16 (interp4), TS 3.3
7 Lecture 12 (interp1) , TS 3.1 Lecture 13 (interp2), TS 3.2
hornernewt.m Calculation of Newton's method coefficients using
Horner's rule for polynomials. 		Lecture 14 (interp3), TS 3.3
6 Lecture 11 (linalg3), TS 2.3-2.5
Extra Lecture (linalg4),
Extra Lecture (linalg5),
GE.m LU factorization without pivoting (unstable!).
 Lecture 11 (linalg3), TS 2.3, 2.4
5 Lecture 09 (linalg1)(linalg2), TS 2.1
LTriSol.m Forward substitution for general lower triangular system.
UTriSol.m Backward substitution for general upper triangular system. 		Lecture 10 (linalg2).
TriDiLU.m Tridiagonal LU factorization.
LBiDiSol.m Forward substitution for unit lower bidiagonal system.
UBiDiSol.m Backward substitution for upper bidiagonal system.
4 Lecture 07 (root3), TS 1.4-5
newton.m Newton's method script. 		Lecture 08, TS 1.3
3 Lecture 05 (root1), TS 1.1
Lecture 06, part 1 (root2), TS 1.2
bisection.m Bisection algorithm very similar to the one given by Sauer. 		Lecture 06, part 2 (root2), TS 1.2
Lecture 06, part 3 (root3), TS 1.4-5
2 Lecture 03, Textbook TS 0.1-0.2 Lecture 04, Textbook TS 0.3-0.4
nest.m Evaluates a polynomial with shifts by Horner's method.
1 Where to get MATLAB
Lecture 01 (matlab1-2)
explot.m Formats the plots in Matlab so they are easily viewable
on a smaller screen or when exported ("ex" stands for "export"). 		Lecture 02 (matlab1-2), TS 0.1.
exsemilogy.m Analogous to explot.m, but provides larger semilogy (semi Log(y)) format.