Linear Algebra I  (MA371-01)  -  S. Allen Broughton, Spring 2001

Course Guide and Syllabus

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Course Information

• Instructor:
• Professor S. Allen Broughton,
• Office: G205-A,
• Phone x8179
• Email: allen.broughton@rose-hulman.edu
• Schedule
• Time & Place: 7'th hour, 1:35 to 2:25, MTRF in G310,
• Office hours: 4'th hour MTRF or by appointment
• Class Webpage: http://www.rose-hulman.edu/class/ma/broughton/courses/ma371/
• Text: Linear Algebra With Applications, Steven J. Leon  Text Web Site

Course Goals

1. Develop a deeper understanding of linear algebra concepts and processes and the corresponding matrix concepts such as:
• Gaussian elimination --  LU factorization
• eigenvalues eigenvectors -- diagonalization
• inner product, orthogonality, -- orthogonal diagonalization, symmetric matrices, positive definite matrices
• least squares, Gram Schmidt -- projections, QR and SVD decompositions
2. Develop a deeper understanding of vector space concepts and their geometrical interpretation such as
• relations among the ranges and nullspaces of a matrix and its transpose
• the matrix as a (geometrical) linear transformation
• linear dependence and independence,
• bases
• eigenvalues and eigenvectors
3. Introduce applications of linear algebra and matrices, especially to science and engineering.
4. Improve mathematical modeling and analytical problem solving skills, using linear algebraic models and matrix computations.
5. Improve skill using the computer as a tool for mathematical analysis and problem solving, using linear algebraic models and matrix computations
6. Develop ability to communicate mathematically.

Major Topics Studied

• Review of Gaussian elimination
• more emphasis on pivots and free variables
• LU decomposition
• Properties of  N(A), R(A), N(A^t ), and R(A^t )
• projections
• least squares approximations
• Gram Schmidt process
• Eigenvalues and eigenvectors
• determinants - not much
• diagonalization
• diagonalization of symmetric matrices
• applications of diagonalization
• Singular value decomposition

• definitions and properties of special matrices
• diagonal and triangular
• symmetric and Hermitian
• positive definite
• orthogonal and unitary
• projection
• Vector spaces (most will be informal, but some proofs should be required)
• definitions and examples other than Rⁿ
• subspaces
• linear dependence and independence
• basis and dimension
• inner products in Rⁿ  and Cⁿ

Course Policies

Exams: The tentative dates for the in-class tests are (you will have a one-week warning):

• Test 1: Monday, Mar 25
• Test 2: Thursday, Apr 18
• Test 3: Thursday, May 9

Projects: Some challenge problems and projects, to develop your ability in application, modeling and problem solving with the material in the course, will be given. These problems will be done as group work. Project rules will be given out with the first project. There are  1-2 projects of about one week's duration.

Final Grades: Various components of the course will contribute to the course point total as follows:
 

Group Work: Some class work and all of the projects will be done in teams.

• Be aware of the Rose-Hulman Honor Code and that honesty and integrity in one's work is of the utmost importance. Inappropriate sharing of work and information, including electronic sharing, will not be tolerated

• Note, however that you are encouraged to collaborate with others on homework, and in class you may be directed to work in groups. If you are in doubt about what is or is not appropriate just ask me. If you consult others in your submitted work you must acknowledge their contributions in writing on the assignments. You will not be penalized for honest collaboration, but don't just copy.

Computer Policy: Make sure you have Maple V on your computer and know how to use it. We will also be using Matlab. The instructions for installing and using Matlab will be given out a few days after the beginning of class.  We will use the computer in class from time to time, you will be told in advance when to  bring it. You will be expected to use the computer for various homework and project activities. The course work will consist of a mixture of paper and pencil work and computer work. The web pages are given above.

Exam Policy:  The short quizzes will be paper and pencil only, no other aids. The final exam policy is:

"The final exam will consist of two parts. The first part will "by-hand". No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam.  The laptop, starting with a blank Maple work sheet and/or Matlab command window, and a calculator, may be used during the second part of the exam. No "cheat sheets", prepared Maple worksheets, m-files or prepared programs on the calculator may be used. The second part of the exam will cover all skills: concepts, calculation, modeling, problem solving, interpretation.