Department of Mathematics & Statistics

MTH 221 Course Policy and Syllabus –FALL 2008

Course Description (catalog):

Covers systems of linear equation, algebra of matrices, linear transformations, determinants, vector spaces, eigenvalues and eigenvectors, diagonalization and orthogonality.

Prerequisite: MTH 104 Calculus II

Instructor Information

Textbook and References

1. Text Book: Linear Algebra and its Applications, 3 rd Edition, David C. Lay

Course Objectives: This course is designed to help the student:

• Use the techniques of linear algebra to analyze and solve real life problems.
• Use the concept of vector space to visualize the solution of science/engineering problems.
• Use matrices to model real life problems.

 Course Outcomes: After successfully completing this course, students should possess a working knowledge of the following:

• Solve systems of linear equations using Gaussian elimination and Gauss-Jordan elimination.
• Find the inverse of a given matrix (if it exists).
• Factor a given matrix into a product of elementary matrices and write it as a product of lower and upper triangular matrices.
• Evaluate the determinant of a given matrix using elementary row or column operations.
• Evaluate the determinant of a given matrix using expansion by cofactors.
• Solve a system of linear equations using Cramer's Rule.
• Recognize standard examples of vector spaces.
• Determine whether a given subset of a vector space is a subspace.
• Determine whether a given finite set of vectors in a vector space is linearly independent.
• Determine whether a given finite set of vectors forms a basis for a vector space.
• Determine the dimension of a vector space.
• Find the rank and basis for the row or column space of a matrix.
• Determine if a function from one vector space to another is a linear transformation.
• Determine the kernel and range of a given linear transformation
• Find the characteristic equation and the eigenvalues and corresponding eigenvectors of a given matrix.
• Diagonalize a diagonalizable matrix.
• Know the basic definitions in the subject and be able to write them in a correct logical manner.
• Write proofs, including appropriate justification/explanation, for elementary theorems.

Assessment

Topics to be covered :

Chapter 1:Linear equations in Linear Algebra 1.1 to 1.9 (1.6 is optional)

Chapter 2:Matrix Algebra 2.1 to 2.3. 2.8 and 2.9 (2.4 and 2.5 are optional)

Chapter 3: 3.1 to 3.3

Chapter 4:4.1 to 4.6 (4.7 optional)

Chapter 5: 5.1 to 5.4 (5.7 optional)

Chapter 6: 6.1, 6.2, 6.3, 6.4

 Getting Help

Students are encouraged to go and consult any of the instructors teaching the course during their office hours. However, before seeking help from any of the instructor make sure you read your lecture notes, and textbook. See the examples similar to the problem in question then try to do the problem yourself. Please do not seek help from instructors if they do not have office hours during that time.

Academic dishonesty

will not be tolerated. The American University of Sharjah affirms the importance of integrity and respecting the work of each individual. As an institution of higher education, the university views academic integrity as an educational as well as judicial issue. Academic violations include (but not limited to) the following: plagiarism, inappropriate collaboration, dishonesty in examinations, dishonesty in papers, work done for one course and submitted to another, deliberate fascination of data, etc.

 Incomplete Grades:

Failing to show up in time for the final exam will result in a zero in that exam. Only in exceptional cases of compelling medical or other emergencies certified by a medical or other professional and approved by the instructor, the Chair and the Dean; will the student be given an “Incomplete” grade. In this case, the instructor will schedule a make-up exam within the first two weeks of the next semester. It is the responsibility of the student to find out from his/her instructor the exact date, time and place of the make-up exam.

Suggested Problems

Although your instructor may not collect homework problems for grading, but it is highly recommended that you attempt these problems on your own. Your instructor will inform you of any addition to or deletion from this list of problems.