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

## Books:

Section 001. TR 09:30-10:45. Room: SMLC 356. Syllabus for Math/CS 375 (32515/39119) 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.

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, May 8th, 2018, 7:30-9:30am, the same room as class. No calculators.
One page (two sides) of notes 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 Credit Homework 12.
Help with analytical solution.
May 1st, 2018, class time.
11 Homework 11 HW11 Solution.
April 17th, 2018, class time.
9-10 Homework 09-10 HW09 Solution HW10 Solution.
March 29th April 5th, 2018, class time.
- Midterm: March 6th, 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 using Newton's method.
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...
March 6th, 2018, class time.
7-8 Homework 07-8 HW07 Solution HW08 Solution.
March 1st 6th, 2018, class time.
5-6 Homework 05-6 HW05 Solution HW06 Solution. February 20th 22nd, 2018, class time.
3-4 Homework 03-4 HW03 Solution HW04 Solution. February 8th, 2018, class time.
2 Homework 02 HW02 Solution. February 2nd, 2018, class time.
1 Homework 01 HW01 Solution. January 25th, 2018, class time.

Below you can find additional material.
Week # Lectures Notes and scripts (by courtesy of Prof. Lau)
15 Extra: Sweep-method for Sturm-Liouville problem. Review for the Final.
14 TS 6.5-6.6. Extra: sweep-method.
13 TS 5.1, 6.1-6.2 TS 6.3-6.4
12 Lecture 24 (quad3) , TS 5.2-5.4 TS 5.4, 5.5
11 Lecture 21 (root4) TS 2.7, Lecture 22 (quad1) , TS 5.2 Lecture 22 (quad1) , Lecture 23 (quad2)
10 Lecture 20 (linalg5) , TS 4.2-4.3 Lecture 20 (linalg5) , Lecture 21 (root4) TS 2.7
9 Lecture 17 (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.
Lecture 18 (splines1), TS 3.4
Lecture 19 (linalg4) , TS 4.1-4.2
8 Midterm. Review of the typical Midterm mistakes, TS 3.3, Lecture 16 (splines1), TS 3.4
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
Lecture 15 (interp4), TS 3.2-3.3
6 TS 2.4-5, Lecture 12 (interp1) , TS 3.1 Lecture 12 (interp1), TS 3.1
Lecture 13 (interp2), TS 3.2
5 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.
Lecture 11 (linalg3), TS 2.3, 2.4
Extra Lecture (linalg4),
Extra Lecture (linalg5),
GE.m LU factorization without pivoting (unstable!).
4 Lecture 07 (root3), TS 1.3-5 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.
3 Lecture 05, part 2 (root2), TS 1.2-3
(root3), TS 1.4
Lecture 06 (root3), TS 1.4-5
2 Lecture 03, Textbook TS 0.2-0.4 Lecture 04, (root1), TS 1.1
(root2), TS 1.2
bisection.m Bisection algorithm very similar to the one given by Sauer.
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) Textbook TS 0.1-2
exsemilogy.m Analogous to explot.m, but provides larger semilogy format.
nest.m Evaluates a polynomial with shifts by Horner's method.