# Mathematics II - Syllabus

Embark on a profound academic exploration as you delve into the Mathematics II course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2074 Syllabus, this course (MTH163) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 80+20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.

#### Units

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix

equations Ax = b, Applications of linear system, Linear independence

Transformation

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

business, science, and engineering

Matrix Algebra

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

Introduction, Properties, Cramerâ€™s rule, Volume and linear transformations

Vector Spaces

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

independent sets: Bases, Coordinate systems

Vector Space Continued

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

Applications to Markov Chains

Eigenvalues and Eigen Vectors

Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and

linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to

differential equations

Orthogonality and Least Squares

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

Groups and Subgroups

Binary Operations, Groups, Subgroups, Cyclic Groups

Rings and Fields

Rings and Fields, Integral domains

#### Lab works