This page contains Syllabus of Mathematics II of CSIT.

Title Mathematics II
Short Name
Course code MTH163
Nature of course Theory and Practice
Semester second-semester
Full marks 80+20
Pass marks 32+8
Credit Hrs 3
Elective/Compulsary Compulsary

Course Description

 

Units and Unit Content

1. 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


2. Transformation
teaching hours: 4 hrs

Introduction to linear transformations, the matrix of a linear Transformation, Linear models in

business, science, and engineering


3. 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


4. Determinants
teaching hours: 4 hrs

Introduction, Properties, Cramer’s rule, Volume and linear transformations


5. Vector Spaces
teaching hours: 5 hrs

Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly

independent sets: Bases, Coordinate systems


6. Vector Space Continued
teaching hours: 4 hrs

Dimension of vector space and Rank, Change of basis, Applications to difference equations,

Applications to Markov Chains


7. 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


8. Orthogonality and Least Squares
teaching hours: 5 hrs

Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The Gram-

Schmidt process, Least squares problems, Application to linear models, Inner product spaces,

Applications of inner product spaces


9. Groups and Subgroups
teaching hours: 5 hrs

Binary Operations, Groups, Subgroups, Cyclic Groups


10. Rings and Fields
teaching hours: 4 hrs

Rings and Fields, Integral domains


Lab and Practical works