CAAM 335 · Matrix Analysis

Spring 2017 · Rice University

INSTRUCTORS:

 Yin Zhang (email: yzhang_AT_rice.edu) Section 2: MWF 9:00-9:50am, DCH 1064 Office: Duncan Hall 3090, (713) 348-5744 Office hours: Mondays 4:00-6:00pm Sanja Pantic (email: sanja_AT_rice.edu) Section 1: MWF 2:00-2:50am, HRZ 212 Office: Duncan Hall 3085, (713) 348-6160 Office hours: Tuesdays 2:00-4:00pm

TEACHING ASSISTANT:

Mr. Xiao Liu (email: xiao.liu_AT_rice.edu), Duncan Hall 2033
Office hours: Thursdays 12:30-2:00pm in Duncan Hall 3110.
(Exceptions: Feb. 16, 12:00-1:00pm; March 30, 12:30-1:30pm in DCH 1044)

RECITATIONS:

Tuesdays 7:00-8:30pm, Sewall Hall 309. (Recitations start the second week of classes)

COURSE OBJECTIVES:

Students should learn how to characterize the solution of systems of linear equations and linear least squares problems, apply basic solution techniques to linear problems involving electrical circuits and planar trusses, compute the eigendecompsition of matrices and apply it to solve linear dynamical systems, and compute the eigenvalue problem and inverse Laplace transform via complex integration.

OUTCOMES:

Apply the Fundamental Theorem of Linear Algebra to characterize solutions of linear systems.
Solve linear systems and linear least squares problems, and apply these techniques to problems involving electrical circuits and planar trusses.
Compute eigenvalues and eigenvectors of matrices.
Apply the eigendecomposition to solve linear dynamical systems.
Compute the singular value decomposition and apply it to relevant problems.

PREREQUISITES:

MATH 212 and CAAM 210. Less formally: you should be familiar with multivariable calculus and elementary matrix manipulations (matrix addition and multiplication, Gaussian elimination), and be able to write MATLAB programs.

60% exams, 40% homeworks (class participation and improving performance on the exams will be considered when assigning borderline grades).

HOMEWORKS:

Homeworks will be assigned roughly once a week. Typically a homework assignment is due one week after it has been posted. Unless otherwise stated, you may collaborate with other students, but you must write up your solutions separately. Transcribed solutions are unacceptable. You may not consult solutions from previous sections of this class.
Homeworks will be assigned via the Canvas course site, please visit this course site regularly. The lowest homework grade will be dropped.

EXAMS:

There will be 3 exams: Exams 1 and 2, and the Final. The two midterms are take-home, timed and closed-book. The Final is scheduled and comprehensive. These exams, in the above order, account for 15%, 20%, and 25% of the final grade, respectively. Each exam must be your individual, unassisted effort; indicate compliance by writing out in full and signing the honor code pledge.

LATE POLICY:

Homeworks and exams must be turned in on time.

Linear Algebra in Situ (Fall 2016 Edition) by Steven Cox. Available as a course pack from the campus store.
Supplemental notes will be posted on the lectures page; make sure you visit it before and after each class.
Chapter 1 of Linear Algebra in Situ by Steven Cox is available online.

COVERAGE:

Chapters 1 through 13 in the course notes (by Steven Cox) with the exception of Chapter 7. The materials in Chapters 11 to 13 (eigenvalue problems and SVD) will be covered earlier between Chap. 6 and 8, which will follow the supplemental notes (by Matthias Heinkenscholoss).

SYLLABUS:

PDF file

Carl Meyer, Applied Matrix Analysis and Linear Algebra
Gilbert Strang, Linear Algebra and Its Applications
Gilbert Strang, Introduction to Applied Mathematics
Lars Ahlfors, Complex Analysis, 3rd ed.
R. V. Churchill and J. W. Brown, Complex Variables and Applicatons

MATLAB:

D. J. Higham and N. J. Higham, MATLAB Guide, 2nd ed.
Getting Started with MATLAB from MathWorks

Any student with a disability requiring accommodation in this course is encouraged
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.