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COURSE OUTLINE
COURSE TITLE: LINEAR ALGEBRA
COURSE CODE:L14053
CREDIT POINTS: 2.5
CONTACT HOURS: 40
LEVEL: Undergraduate, 2nd semester
DELIVERY: Lectures
Course Description:
This course encompasses the study of linear equations, matrices, determinants, vectors in the plane and space, vector spaces, linear transformations, inner products, Eigen values and eigenvectors. Students will learn to recognize and express the mathematical ideas graphically, numerically, and symbolically.
Course Outcomes:
Upon successful completion of this course, the student will be able to:
1. Gain an understanding of matrices and its implications.
2. Know what the vector space is and its applications.
Course Content:
Introduction and systems of linear equations, definition of matrix, and row echelon form; matrix algebra; elementary and partitioned matrices; determinant of a matrix, properties of determinants, and Cramer’s rule; vector spaces, subspaces, and linear independence (basis and dimension); change of basis; row space and column space linear transformations; matrix representations of linear transformations, similarity;
scalar product in Rn; orthogonal subspaces; least squares problems; inner product spaces; orthonormal sets; Gram-Schmidt orthogonalization process, Eigen values and eigenvectors; systems of linear differential equations; diagonalisation.
Textbooks and Reference Materials:
1. Linear Algebra (8th Edition), Steven J. Leon
COURSE TEACHING PLAN
Lectures and Tutorials
|
Serial No. |
Contact Hours |
Topic |
|
1 |
2 |
Introduction, Systems of linear equations, |
|
2 |
2 |
Definition of matrix. |
|
3 |
2 |
Row echelon form |
|
4 |
2 |
Matrix algebra |
|
5 |
2 |
Elementary matrices. |
|
6 |
2 |
The determinant of a matrix. |
|
7 |
2 |
Properties of determinants; Cramer’s rule. |
|
8 |
2 |
Summary |
|
9 |
2 |
Vector spaces; Subspaces 1. |
|
10 |
2 |
Subspaces 2, Linear independence. |
|
11 |
2 |
Basis and dimension Change of basis. |
|
12 |
2 |
Row space and column space. |
|
13 |
2 |
Linear Transformation |
|
14 |
2 |
Summary |
|
15 |
2 |
The scalar product in Rn |
|
16 |
2 |
Orthogonal subspaces. |
|
17 |
2 |
Inner product spaces; Orthonormal sets. |
|
18 |
2 |
The Gram-Schmidt orthogonalization process. |
|
19 |
2 |
Eigenvalues and eigenvectors; Diagonalization. |
|
20 |
2 |
General revision |
|
Total |
40 |
|
Type of Assessment
The contents of test/examination/assignment will be from lectures and recommended reference reading material.
|
|
Tests (2 times) |
Mid-term exam |
Final exam |
|
20% |
20% |
20% |
40% |
Developed by: LIN Lin, College of Science
Date: 03.June 2015
Approved by: Academic Committee of College of International Education
Date: 03.July 2015
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