BSc. CSIT Second Semester Mathematics II Course Overview
| Title | Mathematics II |
| Course code | MTH 163 |
| Nature of course | Theory |
| Semester | Second-Semester |
| Full marks | 80 + 20 |
| Pass marks | 32 + 8 |
| Credit Hrs | 3 |
| Elective/Compulsory | Compulsory |
Study Materials:
| Notes | Books | Old Questions |
Course Description:
The course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigen values and eigenvectors, and singular value decomposition of a matrix.
Course Objectives:
The main objective of the course is to make familiarize with the concepts and techniques of linear algebra, solve system of linear equation with Gauss-Jordon method, to impart knowledge of vector space and subspace, eigenvalues and eigenvectors of a matrix and get the idea of diagonalization of a matrix, linear programming, Group, Ring, and Field.
Course Contents:
- Linear Equations in Linear Algebra
Teaching Hours : 5 hrs
System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence
- Transformation
Teaching Hours : 4 hrs
Introduction to linear transformations, the matrix of a linear Transformation, Linear models in business, science, and engineering
- Matrix Algebra
Teaching Hours : 5 hrs
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.
- Determinants
Teaching Hours : 4 hrs
Introduction, Properties, Cramer’s rule, Volume and linear transformations.
- Vector Spaces
Teaching Hours : 5 hrs
Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems
- Vector Space Continued
Teaching Hours : 4 hrs
Dimension of vector space and Rank, Change of basis, Applications to difference equations, Applications to Markov Chains
- Eigenvalues and Eigen Vectors
Teaching Hours : 5 hrs
Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to differential equations - Orthogonality and Least Squares
Teaching Hours : 5 hrs
Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The GramSchmidt process, Least squares problems, Application to linear models, Inner product spaces, Applications of inner product spaces - Groups and Subgroups
Teaching Hours : 5 hrs
Binary Operations, Groups, Subgroups, Cyclic Groups. - Rings and Fields
Teaching Hours : 4 hrs
Rings and Fields, Integral domains
Text Books:
- Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley
- Linear Algebra and Its Applications, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning.
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