F11_MTS203_Linear_Algebra

=MTS 203: Linear Algebra=

Program:
BS(CS)

Semester:
Fall 2011

Instructor:
Dr. N. Touheed.

**Course Lead:**
Dr. N. Touheed.

**Credit Hours:**
3 credit hours.

Prerequisite(s):
MTS101 (Calculus 1).

Course Description:
Linear algebra is a very important subject of mathematics, that comes in handy in pure mathematics, applied mathematics, computer sciences, and business studies. Most applied problems have a linear algebraic aspect that must be exploited for a successful solution strategy. This course is the first exposure of BS-CS students to this subject, and builds up the core concepts from ground-up. The only exception is the knowledge of calculus which is used as a pr-requisite for teaching function spaces. The course knowledge is imparted through usual classroom lectures with multimedia teaching aids. Hands on practice of simple problems of computational linear algebra are also provided through Matlab-based exercises.

Course Objectives:
On culmination of this course, successful students are expected to be able to:
 * Describe basic linear algebraic structures, such as vector spaces, normed spaces, linear transformations. etc.
 * Apply the knowledge acquired in this course to problems from various areas of application that may have a computational side to them.
 * Use Matlab for solving simple computational linear algebra problem.
 * Understand orthogonality, and orthogonalization algorithms.
 * Perform an eigenvalue analysis of a matrix system.

Books:
Linear Algebra and Its Applications by David C. Lay, University of Maryland - College Park  3rd Edition ISBN 0-201-70970-8 • © 2003

Web Resources:
http://www.laylinalgebra.com/free_site/index.html

Grading Policy:
The grading policy that is followed for this course is summarized below:


 * **__Assessment__** ||= **__Points__** ||
 * Eight assignements each of one point ||= 08 ||
 * Four best quizzes (out of five) each of three points || 12 ||
 * First Term Exam (closed book exam) || 20 ||
 * Second Term Exam (closed book exam) || 20 ||
 * Terminal Exam (closed book exam) || 40 ||

Course Topics (Salient Outlines):
The entire course is disseminated into 28 lectures, which is described underneath.

__**Chapter 1 Linear Equations in Linear Algebra**__ Lecture 01 Systems of Linear Equations Lecture 02 Row Reduction and Echelon Forms Lecture 03 Vector Equations Lecture 04 The Matrix Equation Ax = b Lecture 05 Solution Sets of Linear Systems; Applications of Linear Systems Lecture 06 Linear Independence Lecture 07 Introduction to Linear Transformations Lecture 08 The Matrix of a Linear Transformation Lecture 09, Linear Models in Business, Science, and Engineering __**Chapter 2 Matrix Algebra**__ Lecture 10 Matrix Operations Lecture 11 The Inverse of a Matrix Lecture 12 Characterizations of Invertible Matrices __**Chapter 3 Determinants**__ Lecture 13 Introduction to Determinants Lecture 14 Properties of Determinants __**Chapter 4 Vector Spaces**__ Lecture 15 Vector Spaces and Subspaces Lecture 16 Null Spaces, Column Spaces, and Linear Transformations Lecture 17 Linearly Independent Sets; Bases Lecture 18 Coordinate Systems Lecture 19 The Dimension of a Vector Space, Rank Lecture 20 Applications to Difference Equations, Applications to Markov Chains __**Chapter 5 Eigenvalues and Eigenvectors**__ Lecture 21 Eigenvectors and Eigenvalues, Lecture 22 The Characteristic Equation Lecture 23 Diagonalization Lecture 24 Inner Product, Length, and Orthogonality Lecture 25 Orthogonal Sets Lecture 26 Orthogonal Projections Lecture 27 The Gram-Schmidt Process Lecture 28 Least-Squares Problem
 * __Chapter 6 Orthogonality and Least Squares__**

Lecture Notes