1. Tentative Course Plan Spring 2022
Department of Engineering
Course Objectives:
This course is designed as an introduction to linear algebra by emphasizing the
geometric significance of the subject. Student will specially see the vectors in 2 and 3
dimensions geometrically. The objective of the course is to provide a rigorous approach towards
the solutions of linear models which involves more than one variable. The techniques discussed
in this course can be implemented on a wide range of applications from physical world. The
matrix algebra will be helpful in performing and understanding of matrix computations on a
machine. The concept of basis for the solution space helps to describe the good basis for the
solution space. The eigenvalues, eigenvectors, inner product spaces, orthogonality are useful
concepts for the analysis of dynamical systems.
Course Outcomes
On successfully completion of this course, the students will be able to:
1. Solve linear equations using elementary operations.
2. Work with matrix algebra, including matrix inverses and determinants.
3. To use the concepts of subspace, basis and dimension.
4. To construct the “good” basis for the solution spaces and apply the concept on linear
models.
5. Compute and apply Eigenvalues and Eigenvectors.
6. To construct the orthogonal and orthonormal basis.
Books:
1. Curtis Ch. W., Linear Algebra, Springer, 2004.
2. Gareth Williams, Linear Algebra with Applications, 7th edition, Jones and Bartlett, 2011.
3. Anton H., C. Rorres , Elementary Linear Algebra: Applications Version, 10th Edition,
John Wiley
and sons, 2010.
+Couse Name Linear Algebra Pre-requisite None
Course Code MATH-2103 Cr. H 03
Instructor: Maryam Batool Class BS-SWEN-2A
BS-AGEN-2
BS-CPEN-2
2. 4. Friedberg S. and Insel A., Linear Algebra, 4th edition, Pearson Education Canada, 2003.
5. Grossman S. I., Elementary Linear Algebra, 5th edition, Cengage Learning, 2004.
6. David C. L., Steven R. L., Judi J. M., Linear Algebra and its Applications, 5th Edition,
AddisonWesley, 2016
Note: for better understanding, internet resources can also be use.
Course Evaluation:
Marks
Assignment 10
Quizzes+ presentation 15
Mid 25
Final 50
Total 100
Detailed outlines:
Week Lecture # Topics
1 1 Matrix Algebra
2 Matrix Operations
2 1 The Inverse of a Matrix
2 Characterization of Invertible Matrix
3 1 Matrix Factorizations and Applications
2 Determinants
4 1 Properties of Determinants
2 System of Linear Equation
5 1 Row Reduction and Echelon Forms
2 Vectors Equations
6 1 The Matrix Equation
2 Solution Sets of Linear System
7 1 Linear Independence, Introduction to Linear Transformations
2 The Matrix of Linear Transformations
8 1 Assignment, Presentation
2 Quiz and discussion before mid exam
9 1 Vector Spaces and Subspaces
2 Basis, Null Spaces and Column Spaces
10 1 Coordinate Systems
2 The Dimension of Vector Spaces and Rank
11 1 Eigenvalues and Eigenvectors
3. 2 The Characteristic Equation
12 1 Diagonalization
2 Diagonalization
13 1 Inner Product
2 Length and Orthogonality
14 1 Orthogonal Sets
2 Orthogonal Projections
15 1 The Gram-Schmidt Process
2 Cayley Hamilton Theorem and Application
16 1 Assignment, Presentation
2 Quiz and discussion before final exam
