3C5 David Rittenhouse Lab

(215)898-6285

robim at math (dot) upenn {dot} edu

Office hours: Tuesdays 2-3pm, Wednesdays 11am-12pm, or by appointment

Supplemental office hours: Thursday, 30 April: 10am-12pm and Monday, 4 May: 10am-12pm

My research website http://www.drmichaelrobinson.net/

Feel free to contact me with any questions (course-related or not)

Homework assignments

Course schedule

Concerning programming in this course

Information about exams

Some useful links

Course policies

Some specific topics: the solution of systems of linear equations by
Gaussian elimination, dimension of a linear space, inner product,
cross product, change of basis, affine and rigid motions, eigenvalues
and eigenvectors, diagonalization of both symmetric and non-symmetric
matrices, quadratic polynomials, and least squares optimazation.

Applications will include the use of matrix computations to computer
graphics, use of the discrete Fourier transform and related techniques
in digital signal processing, the analysis of systems of linear
differential equations, and singular value deompositions with
application to a principal component analysis.

The ideas and tools provided by this course will be useful to students
who intend to tackle higher level courses in digital signal
processing, computer vision, robotics, and computer graphics.

The course textbook is

Gilbert Strang, *Introduction to linear algebra*, Third edition, Wellesley-Cambridge, 2003.

Homework 1, Due Friday, 23 January 2009 at 1pm.

- Set 1.1: 5, 14, 21
- Set 1.2: 6, 21, 29
- Set 2.1: 6, 11, 25
- And a MATLAB problem as well...

- Set 2.2: 5, 12, 28
- Set 2.3: 7, 8, 16, 26
- Set 2.4: 6, 24, 35
- MATH 513 Addendum: read about partial pivoting (pp450-452) and do problems 9.1: 1, 10 (don't find the LU factorization, but do the elimination "by hand" before using MATLAB to check/do your arithmetic)

- Set 2.5: 7, 32, 39
- Set 2.6: 5, 15, 34
- Set 2.7: 2, 5, 18
- And a fun MATLAB problem too...

- Set 3.1: 2, 7, 11, 17
- Set 3.2: 2, 7, 18, 30
- MATH 513 Addendum

- Set 3.3: 5, 10, 15, 19
- Set 3.4: 1, 4, 19, 29
- And a MATLAB problem

- Set 3.5: 5, 10, 23, 31
- Set 3.6: 3, 10, 23, 28
- MATH 513 Addendum: read about norms and condition numbers (section 9.2) and do problems 9.2: 13, 14 (use Matlab to do the computations if you like)

- Set 4.1: 3, 15, 29
- Set 4.2: 3, 9, 17
- Set 4.3: 4, 14, 15
- And a MATLAB problem

- Set 4.4: 6, 22, 30, 35
- Set 5.1: 4, 8, 15, 32
- MATH 513 Addendum

- Set 5.2: 3, 6, 25, 34
- Set 6.1: 4, 13, 15, 25
- And a MATLAB problem

- Set 6.2: 9 (use MATLAB), 17, 24, 25, 29
- Set 6.3: 5, 8, 13
- MATH 513 Addendum

- Set 6.4: 5, 11, 14, 21, 28
- Set 6.5: 5, 12, 20, 24
- And a MATLAB problem

- Set 6.6: 3, 9, 12, 17
- Set 6.7: 2, 9, 11, 13
- one final MATLAB problem...
- And a parting MATH 513 Addendum!

Below is a listing of topics (and links to course notes if they exist) that we will cover...

15 January: Sections 1.1-1.2. Introduction to vectors

20 January: Sections 2.1-2.2. Vectors, linear equations, and elimination

22 January: Section 2.3. Matrix elimination

27 January: Section 2.4. Elementary matrix operations

29 January: Section 2.5. Matrix inversion

3 February: Section 2.6. Factorization and elimination

5 February: Section 2.7. Transposes

10 February: Section 3.1. Vector spaces

12 February: Section 3.2. The nullspace

17 February: Section 3.3. Rank and row reduction

19 February: Section 3.4. Solving Ax=b

24 February: Section 3.5. Independence, spanning, and dimension

26 February: Section 3.6. The dimension theorem

3 March: Review for the midterm exam

5 March: Midterm exam in class

10,12 March: spring break, no class

17 March: Sections 4.1-4.2. Orthogonality and projections

19 March: Section 4.3. Least squares

24 March: Section 4.4. Gram-Schmidt

26 March: Section 5.1. What is a determinant?

31 March: Section 5.2. Ways to compute determinants

2 April: Section 6.1. Introduction to Eigenvalues

7 April: Section 6.2. Diagonalization

9 April: Section 6.3. Applications to differential equations

14 April: Section 6.4. Symmetric matrices

16 April: Section 6.5. Positive definiteness

21 April: Section 6.6. Similarity

23 April: Section 6.7. Singular value decomposition

28 April: Review for the final exam

5 May: Final exam

If you don't have a strong preference, I will suggest that you learn
some Matlab or Octave. Matlab is available on the SAS computers in the on campus computer labs. I've heard that students can obtain Matlab relatively cheaply, though Octave is free to use. If you do have a
strong programming language preference for another language,
you may be permitted to use it, but you **must** contact me first about
it early in the course.

Midterm exam was in class Thursday, 5 March 2009.

Final exam is 5 May 2009, 12-2pm, in DRL 3C2.

Matlab

Cleve Moler (the original author of Matlab) has written two books (

Academic calendar

Schedule of classes being held in the DRL computer labs

Campus map

40% Homeworks

25% Midterm exam

35% Final exam

Homework drop policy: The lowest two homework scores will automatically be dropped in the computation of the homework grade. Late homeworks will not be accepted, unless there is an official (University-approved) reason for doing so.