# Math/CS 375. Introduction to Numerical Computing. Fall 2023.

## Books:

Section 002. TR 08:00-09:15. Room: Tuesdays: Zoom (passcode in e-mail); Thursdays: MECH 214 SMLC 356 F2F.
Syllabus for Math/CS 375 (76721/76720)
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:

Room: Tuesdays 12:30-13:45: Zoom; Thursdays 11:00-12:15: SMLC 220.

## 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: Thursday, December 14th, 2023, 7:30-9:30am, usual classroom.
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, time step etc.
-
12 Extra points Homework 12.
Help with analytical solution.
December 7 9th, 2023, end of day noon.
11 Homework 11HW11 Solution.
December 1st, 2023, end of day.
9-10 Homework 09-10.HW09 Solution HW10 Solution.
November 10th 11th, 2023, end of day.
- Midterm: October 19th, 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.
You are allowed to have one page one side of Letter size paper with any formulae you like,
BUT it is prohibited to have solutions of the problems there!
You will need to submit this page with you Midterm.
October 19th, 2023, class time.
7-8 Homework 07-8 HW07 Solution HW08 Solution. October 17th 18th, 2023, end of day 22:30.
5-6 Homework 05-6 HW05 Solution HW06 Solution. October 6th 7th, 2023, end of day.
3-4 Homework 03-4 HW03 Solution HW04 Solution. September 20th 22nd 23rd, 2023, end of day.
2 Homework 02 HW02 Solution. September 8th, 2023, end of day.
1 Homework 01 HW01 Solution. August 25th 28th, 2023, end of day.

Below you can find additional material.
Week # Lectures Notes and scripts (by courtesy of Prof. Lau)
14 TS 5.5, Gaussian Quadratures
Thanksgiving.
13 Lecture 23 (quad2) , (quad3) , TS 5.2
NewtonCotesClosedWeights.m
Lecture 24 (quad3) TS 5.2
12 Lecture 20 (linalg5) , TS 4.2-4.3 Lecture 21 (root4) TS 2.7. Lecture 21 (root4) TS 2.7,
Lecture 22 (quad1) , TS 5.2
11 Lecture 18 (splines1), TS 3.4
Lecture 19 (linalg4) , TS 4.1-4.2
Lecture 20 (linalg5) , TS 4.2-4.3
10 Lecture 17 (interp4), TS 3.3. TS 3.3,
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.
9 Lecture 14 (interp2), TS 3.2
hornernewt.m Calculation of Newton's method coefficients using
Horner's rule for polynomials. Lecture 15 (interp3), TS 3.3
Midterm.
8 Lecture 14 continued (interp2), TS 3.2
Fall break.
7 Lecture 12,
Sources of error, PLU factorization, TS 2.3-4, (linalg3),
iterative methods. TS 2.5.
Lecture 13 (interp1) , TS 3.1 Lecture 14 (interp2), TS 3.2
6 Lecture 11 (linalg3), TS 2.3-2.5
Extra Lecture (linalg4),
Extra Lecture (linalg5),
GE.m LU factorization without pivoting (unstable!).
Sources of error, condition number, TS 2.3, 2.4
5 Sensitivity of root finding problem to input errors. TS-1.3.2-1.3.3.
Lecture 09 (linalg1) 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 (root2), TS 1.2-1.3
Lecture 08 (root3), TS 1.4-5
newton.m Newton's method script.
3 Lecture 05, Textbook TS 0.3-0.4 Lecture 06, (root1), TS 1.1
part 2 (root2), TS 1.2
bisection.m Bisection algorithm very similar to the one given by Sauer.
2 Lecture 03, Textbook TS 0.1-0.2 Lecture 04, Textbook TS 0.3
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.