Math241

Course Description form

Faculties and departments requiring this course (if any): Faculty of

      Engineering. Faculty of Science. Department of Computer Sciences.

      Department of Statistics.

Objectives:  Prefer In points

1- Making the student acquainted with fundamental techniques in Linear Algebra such as: Solving linear systems, Matrix calculus, Determinants.

2- Allowing the student to get autonomy for finding the right method to be applied

3- Helping the student in how to use adequately a text book to get the appropriate information

Contents: Prefer In points

1-    Systems of Linear Equations. Solving a Linear System. Row operations on the Augmented Matrix. Existence and Uniqueness questions. Row Echelon Form and Reduced Row Echelon Form. The Row Reduction Algorithm. Calculus in the setting of the Euclidean spaces. Vectors. Linear Combinations. Vector Equations. Linear Independence. The Matrix Equation Ax = b. Homogeneous and non Homogeneous systems

2- Matrix Algebra. Matrix Operations.

    The Transpose of a  Matrix. The Inverse of a Matrix. Algorithm for finding .the Inverse.  Linear Transformations and Matrices in the setting of. the Euclidean spaces.  

 3- Determinants. Properties. The Cramer’s Rule.

4 - Vector spaces. Subspaces. Spanning Sets. Linear Independence. Bases. Dimension. Linear Transformations. The Kernel and The Range of A Linear Transformation. Eigen values and Eigenvectors.

Course Outcomes:

A-  Knowledge:

 (Specific facts and knowledge of concepts, theories, formula etc.)

 The goal is that student becomes fairly able to master basic techniques of

 Linear Algebra as:

·         Solving Linear Systems (Gauss Jordan Method).

·         Matrix Calculus. Determinants.

·         Vector Spaces . Linear Transformations.

·         Computing Eigen values and Eigenvectors.

B-Cognitive Skills:

(Thinking, problem solving )

(a) The students must grasp the techniques of solving Linear Systems and how these techniques lead to Matrix Algebra.

(b) Teaching strategies to be used to develop these cognitive skills: (1) From concrete ideas to abstract concepts; (2) Standard problems to get the manipulation of the techniques (3) Several applications.

C- Interpersonal skills and responsibilities:

(group participation, leadership, personal responsibility, ethic and

 moral behavior, capacity for  self directed learning)

 All teaching strategies should basically consist in developing communication

 and increasing the opportunities for the student to express oneself. This

 leads to favor working in group sessions guided by the teacher. 

D- Analysis and communication:

)communication, mathematical and IT skills)

 Ability to seek information about the subject considered, or some

 complement of it, from text books proposed by the teacher. The student

 must learn how to read and understand a topic in a book and definitely give

 up the memorizing reflex.

Assessment methods for the above elements

Class discussions on the problems given to the groups of students.

Methods of assessment of students include:

(a) Cross questionings and class discussions;

(b) Simple unseen problems proposed in Quizzes;

(c) Home assignments, midterm exams,  and final exam.

Text book: Only one

R. Larson and D.C. Falvo, Elementary Linear Algebra, Sixth Edition, Brooks/Cole cengage Learning, 2010.

Other Information Resources

          Web site: www.kau.mylabsplus.com