APMA308-01 2009 BCM and Syllabus 08-31-2009

APMA308-01 2009 BCM and Syllabus 08-31-2009 - LINEAR...

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LINEAR ALGEBRA: APMA 308-01, FALL 2009 INSTRUCTOR: Prof. Marek-Jerzy Pindera, email: mp3g@virginia.edu , office phone: 924- 1040, office: Thornton Hall D214 TA: Simon E. Mushi, email: sem5t@virginia.edu , Office hours: M @ 4:00-6:00 pm in Thornton Hall C248 LECTURES : MWF @ 12:00-12:45 pm in Olsson Hall 005 OFFICE HOURS : MW @ 10:30 am-11:45 pm in Thornton Hall D-214 TEXT : Gareth Williams, Linear Algebra with Applications, 6 th Edit. We will be covering Chapters 1-7. AN OVERVIEW : The course is an introduction to the basic topic of matrix theory and linear algebra. It will be targeted to the needs of SEAS students. The student will learn how to manipulate matrices, how to solve systems of linear equations; how to compute determinants, eigenvalues/eigenvectors; etc. These topics will be put on the unifying setting of vector spaces, in particular inner product spaces, and linear transformations. These abstract concepts are essential ingredients towards developing an understanding of the different situations encountered in the solution of linear systems of equations, and thus will form a major part of the course. In light of this, it is essential that the student attends each lecture and comes to class prepared – the pace of the course will be quick and the student is expected to be familiar with the basic concepts of high-school level matrix algebra. Illustrations to Engineering and Science will be highlighted as required. COURSE OBJECTIVES : The specific course objectives are listed below. To understand the theory of systems of linear equations, and to know how to set up and solve a system of linear equations in matrix form Understand the nature of a best-possible solution (in the least-squares sense) to an unsolvable system b Ax = when b is not in the range of A , and how to obtain it Know the basic algebraic operations on vectors and matrices and their properties, and how to compute them efficiently Understand the theory of abstract vector spaces, and know the archetypal examples, Euclidean spaces, spaces of matrices, and the spaces of functions (including polynomial functions, continuous functions, and integrable functions) Understand the concept of abstract linear transformations, and what properties to expect of
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APMA308-01 2009 BCM and Syllabus 08-31-2009 - LINEAR...

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