This page contains Syllabus of Mathematics II of CSIT.

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 |

### 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