# Mathematics II Syllabus

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

### 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

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