Week #

Homework problems

Due date



Final Exam: Tuesday, May 8th, 2018, 7:309:30am, the same room as class. No calculators.
One page (two sides) of notes is allowed with definitions and algorithms only.
NO solutions of problems there! You will need to submit this page with your work.
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, 4.1.79;
Sauer, p. 224: 4.3.1, 4.3.2 (Using both GrammSchmidt process AND Givens' rotations (see lectures linalg45));
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: 3.2.13 (also work through problems in the Midterm);
Sauer, p. 164: 3.3.1, 3.3.5, 3.3.78;
Sauer, p. 176: 3.4.7, 3.4.12;
Sauer, p. 263: 5.2.13 (also you shall need understanding of error dependence on a grid step);
Sauer, p. 278: 5.5.13 (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.

910

Homework 0910 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.
NO solutions of problems there! You will need to submit this page with your work.
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: 13;
HW 5: 1, 2;
HW 6: 1;
HW 7: 3;
HW 8: 1, 4;
to be continued...

March 6th, 2018, class time.

78

Homework 078 HW07 Solution HW08 Solution.

March 1st 6th, 2018, class time.

56

Homework 056 HW05 Solution HW06 Solution.

February 20th 22nd, 2018, class time.

34

Homework 034 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: Sweepmethod for SturmLiouville problem.

Review for the Final.

14

TS 6.56.6.

Extra: sweepmethod.

13

TS 5.1, 6.16.2

TS 6.36.4

12

Lecture 24 (quad3)
, TS 5.25.4

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 4.24.3

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 4.14.2

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 3.23.3

6

TS 2.45,
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 1.35

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 1.23
(root3), TS 1.4

Lecture 06 (root3), TS 1.45

2

Lecture 03, Textbook TS 0.20.4

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 (matlab12)
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 (matlab12) Textbook TS 0.12
exsemilogy.m Analogous to explot.m, but provides larger semilogy format.
nest.m Evaluates a polynomial with shifts by Horner's method.

