See the syllabus on my web page.

Homework Assignments:

- For Tuesday Feb. 14th, section 1.2: 3; section 1.3: 10, 27; section 1.4: 2, 4, 22, 39; section 1.5: 2, 29; bonus exercises (not mandatory but will give bonus points), section 1.6: 6, 27.
- For Tuesday Feb. 28th, section 1.7: 1, 7; section 2.1: 1, 2, 3, 7, 25; bonus exercises (not mandatory but will give bonus points), section 2.2: 2, 6, 26.
- For Tuesday March 13th, section 2.3: 2,3, 20, 26; section 2.4: 10, 14, 16; bonus exercises (not mandatory but will give bonus points), section 2.6: 3, 6.
- For Tuesday April 3rd, section 3.1: 4, 6, 45; section 3.2: 3, 7; section 3.3: 1, 4; bonus exercises (not mandatory but will give bonus points), section 3.4: 6, 13.
- For Tuesday April 17th, section 3.5: 1, 5; section 4.2: 1, 4; section 4.3: 1,3, 34; bonus exercises (not mandatory but will give bonus points), section 4.4: 13, 17.
- For
Thursday May 3rd, section 5.1: 5, 7, 9, 10; section 5.2: 12, 13, 18;
section 5.3: 9, 14; bonus exercises (not mandatory but will give bonus
points), section 5.4: 12, 15.

Tests and quizzes:

- Thursday Feb. 9th, Quizz, with subject and solution.
- Tuesday Feb. 21st, Quizz, with subject and solution.
- Tuesday Feb. 28th, 1st Midterm with subject and solution.

- Tuesday March 6th, Quizz with subject and solution.
- Thursday April 12th, Quizz with subject and solution.
- Tuesday April 17th, 2nd Midterm (covers all material till section 3.4 included) with subject and solution.
- Tuesday April 24th, Quizz with subject and solution.
- Thursday May 17th, Final exam with subject and solution.

Classes and Reading:

- Week 1 (01/25-01/27) : Introduction, first part of 1.7, 1.1

- Week 2 (01/30-02/03) : 1.2, 1.3, 1.4,

- Week 3 (02/06-02/10) : 1.5, 1.6
- Week 4 (02/13-02/17) : 1.6 (end), 1.7, 2.1
- Week 5 (02/20-02/24) : 2.1 (end), 2.2, 2.3
- Week 6 (02/27-03/02) : 2.3 (end), 2.4, 2.6 (beginning)
- Week 7 (03/05-03/09) : 2.6 (end), one example of application, 3.1 (beginning)
- Week 8 (03/12-03/16) : 3.1, 3.2

- Week 9 (03/26-03/30) : 3.3, 3.4
- Week 10 (04/02-04/06) : 3.4 (end), 3.5, examples of applications
- Week 11 (04/09-04/13) : 4.1, 4.2, 4.3
- Week 12 (04/16-04/20) : end of chapt. 4
- Week 13 (04/23-04/27) : 5.1, 5.2

Numerical projects assignments:

The projects consists in writing a code (in matlab) implementing the corresponding algorithm. Students can work in small teams (up to 3 people). The language by default is Matlab so please ask me before if you want to use something else.

There are two deadlines for each project assignment. The latest one is the date at which the project must be completed and submitted to me. The first one is the date before which students must decide on their project and the composition of their team.

Each team has to send me an e-mail before the first date (with all members of the team in copy) indicating their choice and the composition of the team.

The final project has to be submitted by e-mail to my address pjabin@umd.edu. Each submission should recall in the e-mail the names of the students having worked on it and the subject chosen. To each e-mail should be attached the source code (typically a .m file) and a short report (Latex, word, pdf...). The report should describe summarily how the algorithm was implemented and the main conclusion (typically a few pages are more than enough).

1st assignment

Choice before March 1st, completion before March 29th. The proposed projects are

- Write a program which given a square matrix A, a vector y as
entries returns the vector x solution to Ax=y and an error message if A
is not invertible. The program will use the gaussian elimination
method. The use of matlab routines performing the same role, such as
A/y, is of course prohibited.

- Write a program which to a given square matrix A as entry returns its determinant (computed for instance by using LU decomposition or others efficient methods). As before the use of matlab routines performing the same role is prohibited.
- Write
a program which to a given square matrix A as entry returns its LU
decomposition or an error when this is not possible. The use of matlab
routines performing the same role is prohibited as always.

- Find about the Gauss-Seidel method to solve linear systems. Write a program which given a square matrix A, a vector y, an initial vector z and a number n as entries returns the vector x approximete solution to Ax=y after n steps of the method starting from z.The use of matlab routines performing the same role is prohibited as always.

Choice before April 12th, completion before April 27th. The proposed projects are

- Write a program which given a rectangular matrix A returns a matrix E containing the equations that a right handside b should satisfy to be able to find a solution to Ax=b. For instance if the conditions are b_1+b_2=0 and b_2+b_3=0 then E would have 1 1 0 on the first lign, 0 1 1 on the second line and 0 0 0 on the third. As always the use of routines performing the same role is prohibited.
- Write a program which given a rectangular matrix A returns the
dimension of the kernel/null space with a basis for the kernel. For
example if the kernel has dimension 2 and is generated by (1,1,0) and
(0,0,1) then the program would return 2 and the matrix
1

0

1

0

0

1

- Write a program which given a rectangular matrix A of size n*m with n>m, and a vector b, returns a vector x which is the least square approximation for the system Ax=b. The program will return an error if n<=m or if the null space of A is not reduced to 0.As before the use of routines performing the same role is prohibited.
- Write a program which to a square matrix A returns its QR decomposition (or an error if the null space of A is not reduced to 0). As before the use of routines performing the same role is prohibited.
- Write a program which given a vector x will return its Fourier transform Fx or the inverse Fourier transform. Test your program with various filters. As before the use of routines performing the same role is prohibited, however you may use routines to represent and encode pictures if you wish.
- Write a program which given a matrix A returns one eigenvalue and one eigenvector by the power method. As before the use of routines performing the same role is prohibited.
- Write a program which given a matrix A returns all eigenvalues and eigenvectors by the power method. As before the use of routines performing the same role is prohibited.