Mathematics II
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Course Title: Mathematics II
Course No: MTH168
Nature of the Course: THEORY
Semester: 2
Full Marks: 60 + 40
Pass Marks: 24 + 16
Credit Hours: 3
Course Description
Course Objectives
Course Contents
1.1. Systems and Solutions
- System of linear equations
- Row reduction and Echelon forms
- Vector equations
- The matrix equations Ax = b
- Applications of linear system
- Linear independence
2. Transformation
4 hrs
2.1. Linear Transformations and Applications
- Introduction to linear transformations
- The matrix of a linear Transformation
- Linear models in business, science, and engineering
3. Matrix Algebra
5 hrs
3.1. Matrix Operations and Properties
- Matrix operations
- The inverse of a matrix
- Characterizations of invertible matrices
- Partitioned matrices
- Matrix factorization
- The Leontief input output model
- Subspace of Rn
- Dimension and rank
4. Determinants
4 hrs
4.1. Determinant Theory and Applications
- Introduction
- Properties
- Cramer's rule
- Volume and linear transformations
5. Vector Spaces
5 hrs
5.1. Vector Space Fundamentals
- Vector spaces and subspaces
- Null spaces, Column spaces, and Linear transformations
- Linearly independent sets: Bases
- Coordinate systems
6.1. Advanced Vector Space Topics
- Dimension of vector space and Rank
- Change of basis
- Applications to difference equations
- Applications to Markov Chains
7.1. Eigenvalue Theory and Applications
- Eigenvectors and Eigenvalues
- The characteristic equations
- Diagonalization
- Eigenvectors and linear transformations
- Complex eigenvalues
- Discrete dynamical systems
- Applications to differential equations
8.1. Orthogonal Systems and Applications
- Inner product, Length, and orthogonality
- Orthogonal sets
- Orthogonal projections
- The Gram-Schmidt process
- Least squares problems
- Application to linear models
- Inner product spaces
- Applications of inner product spaces
9.1. Group Theory Fundamentals
- Binary Operations
- Groups
- Subgroups
- Cyclic Groups
10. Rings and Fields
4 hrs
10.1. Ring and Field Theory
- Rings and Fields
- Integral domains
Text Books
- 1.Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley
- 2.Linear Algebra and Its Applications, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning