# Math 375. Introduction to Numerical Computing. Fall 2014.

## Books:

Section 001. TR 12:30-13:45. Room: SMLC B81. Syllabus for Math 375 (18211) 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:

Wednesday 12:45-14:00, Tuesday 11:00-12:15. Room: SMLC 220.

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: December 11th, 2014, 10am-12pm, the same room as class. (Solution published). No calculators.
One page (one side) of records is allowed with definitions and algorithms only.
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.
-
12 Extra (20) points homework 12.
Help with analytical solution.
December 8th, 2014, 12pm, electronic version by e-mail.
11 Homework 11.
December 2nd, 2014, class time.
9-10 Homework 09-10.
November 6th, 2014, class time.
- Midterm: October 21st, class time. (Solution published). No calculators.
One page (one side) of records is allowed with definitions and algorithms only.
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;
to be continued...
October 21st, 2014, class time.
7-8 Homework 07-8.
October 21st, 2014, class time.
5-6 Homework 05-6. October 7th, 2014, class time.
3-4 Homework 03-4. September 18th, 2014, class time.
2 Homework 02. September 9th, 2014, class time.
1 Homework 01. September 2nd, 2014, class time.

Below you can find additional material.
Week # Lectures Notes and scripts (by courtesy of Prof. Lau)
12 Lecture 21 (interp5) , TS 3.3 Lecture 22 (root4) TS 2.7, (quad1) , TS 5.2
11 Lecture 19 (linalg4) , TS 4.1-4.2 Lecture 20 (linalg5) , TS 4.2-4.3
10 Midterm 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 16 (interp3), TS 3.2 Lecture 17 (interp4), TS 3.3
8 Lecture 15, TS 2.5 Fall Recess.
7 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, 2.4
TriDiLU.m Tridiagonal LU factorization.
LBiDiSol.m Forward substitution for unit lower bidiagonal system.
UBiDiSol.m Backward substitution for upper bidiagonal system.
GE.m LU factorization without pivoting (unstable!).
LTriSol.m Forward substitution for general lower triangular system.
UTriSol.m Backward substitution for general upper triangular system.
Lecture 12 (interp1) , TS 3.1
5 Lecture 09 (linalg1), TS 2.1 Lecture 10 (linalg2), TS 2.1
4 Lecture 07 (root3), TS 1.4-5 Lecture 08, TS 1.3
3 Lecture 05 (root1), TS 1.1
bisection.m Bisection algorithm very similar to the one given by Sauer.
Lecture 06 (root2), TS 1.2
2 Lecture 03, Textbook TS 0.1-2 Lecture 04, Textbook TS 0.2-0.4
nest.m Evaluates a polynomial with shifts by Horner's method.
1 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)
exsemilogy.m Analogous to explot.m, but provides larger semilogy format.