|
|
|
B+ |
89-92 |
C+ |
75-80 |
D+ |
57-62 |
||
|
A |
97-100 |
B |
85-88 |
C |
69-74 |
D |
50-56 |
|
A- |
93-96 |
B- |
81-84 |
C- |
63-68 |
F |
0-49 |
but a minimum final examination score must also be obtained. There is no "grading on a curve" for this course.
Minimum examination grades
The final examination serves as a verification of the student's mastery of basic concepts and procedures. A student must obtain at least 10 points on the final examination; otherwise a grade of F is entered in the student's record. The examination shall contain 12 questions worth 2 points each from which the student may select 10 to answer. Of those selected, 50% must be answered correctly in order to obtain a passing grade. The examination is structured so that 50% of the questions shall represent basic concepts while the balance shall treat more advanced techniques.
Course Text
The course text is:
Matrix Analysis and Applied Linear Algebra, by Carl D. Meyer, SIAM, 2000 ISBN 0-8987 I-454-0
Homework
Homework is to be turned in at the end of the class held on the homework due date. Late homework is not allowed, examined or graded. Please be aware that a summer course has a rapid pace to it. Not applying the required effort for even a few days will lead to difficulties in obtaining a good grade. It is essential for a student to start the homework assignment on the day it is issued.
|
HW # |
Given |
Due |
Assignment |
Solution |
|
1 |
5/17 |
5/20 |
Meyer: 1.2.1 - 1.2.10 |
|
|
2 |
5/20 |
5/25 |
Meyer: 1.3.1-1.3.3, 1.4.1, 1.4.3, 1.5.1:(a) - (e) |
|
|
3 |
5/25 |
5/31 |
Meyer: 1.5.4:(a)-(d), 1.6.1: (a)-(f) |
|
|
4 |
5/31 |
6/2 |
Meyer: 2.1.1:(a)-(b), 2.2.1:(a)-(b), 2.3.1:-(a)-(b), 2.4.1:(a)-(b), 2.5.1:(a)-(b) |
|
|
5 |
6/2 |
6/7 |
Meyer: 3.2.3:(a)-(c), 3.2.6:(a)-(b), 3.3.1:(a), (c), (e), 3.4.2, 3.4.3 |
|
|
6 |
6/7 |
6/10 |
Write a Matlab code to solve linear systems through LU factorization. (1 point for the LU factorization, 1 point for forward substitution, 1 point for back substitution, 1 point for testing the code on systems with Hilbert matrices of sizes 5,10,...,50). Meyer: 3.5.4 (1 point for (a)-(c), 3.5.8. (a) & (b) (1 point), 3.5.8. (c), 3.6.3, 3.7.10 (a)-(b) |
|
|
7 |
6/10 |
6/15 |
Meyer: 4.1.7, 4.1.8, 4.1.12, 4.2.6, 4.2.9, 4.2.12, 4.2.13, 4.3.5, 4.3.6, 4.3.12 |
|
|
8 |
6/15 |
6/17 |
Meyer: 4.4.8, 5.1.5, 5.3.4, 5.4.1: (b), (d), 5.4.8, 5.4.10: (a), (b), 5.5.1: (a), (b) |
Extra credit projects
Project 1: Read Example 3.2.1 from Meyer. Simple ensembles of L springs and M point masses are often used as models in chemistry, engineering, physics. Write a Matlab code that computes the stiffness matrix and its inverse (Gauss-Jordan algorithm) after reading the known equilibrium positions and stiffnesses for L three-dimensional springs (2 points). Assume reasonable connectivity between the springs, e.g. consider them representative of molecular bonds. Consider that the ensemble is changed by adding one more spring element within the network. Use the Sherman-Morrison formula to get an update of the inverse of the stiffness matrix (4 points). Now consider a sequence of such updates. Write the Matlab code that reads in a new spring position and incrementally updates the stiffness matrix for L' additional springs.
Project 2: Read about rotations in 3D space (Meyer, p. 328). Consider now a reduced Rubik cube formed of 8 subcubes, i.e. instead of the variety you pick up at a toy store which has 27 = 3 x 3 x 3 subcubes, the one considered here is 2 x 2 x 2. Given some initial arbitrary orientation of the colored faces of the subcubes, write a Matlab code that uses reflection operations to solve the Rubik puzzle, i.e. have all faces of the large cube of the same color.
Extra credit projects are due on June 20.
Computer work
Practical computing work is an essential part of applied linear algebra. We shall use Matlab to carry out programming exercises needed to study linear algebra algorithms. An introduction to Matlab capabilities will be given on 5/18, 5/24 & 5/25 largely following the Matlab primer.
Final examination
The Final Examination will be given in Phillips 367 on Monday, June 20 from 11:30 AM to 2:30 PM.
Typical final examination questions
Basic concepts
Meyer: 1.2.10, 1.2.16, 2.1.1, 2.3.3, 2.4.1, 2.4.2, 2.5.4, 3.5.4, 3.6.8, 3.7.5, 3.7.8, 3.9.6, 3.10.2, 4.1.2, 4.1.7, 4.1.10, 4.2.5, 4.3.6, 4.4.4, 4.7.1, 4.7.14, 4.8.7, 4.8.8, 5.2.6, 5.4.3, 5.4.6, 5.5.2, 5.5.3, 5.5.5, 5.6.2, 5.6.4, 5.6.5, 7.1.1, 7.1.2, 7.2.1
Advanced techniques
Meyer: 3.7.11, 3.9.9, 3.10.3, 4.1.12, 4.2.7, 4.2.12, 4.3.8, 4.3.12, 4.3.13, 4.4.10, 4.4.16, 4.5.9, 4.5.12, 4.7.17, 4.8.10, 5.2.7, 5.4.9, 5.4.15, 5.5.11, 5.6.11, 7.1.8, 7.2.2