Mathematics II Syllabus (MTH 168) – TU BSc CSIT 2nd Semester

Tribhuvan University
Institute of Science and Technology
Bachelor of Science in Computer Science and Information Technology

Course Description: The course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigenvalues and eigenvectors and singular value decomposition of matrix.

Course Objective: The main objective of the course is to make students familiar with the concepts and techniques in linear algebra, solve system of linear equations with Gauss-Jordan 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, Rings and Fields.

Course Contents

Unit 1. Linear Equations in Linear Algebra (5 Hrs.)

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence

Unit 2. Transformations (4 Hrs.)

Introduction to linear transformations, the matrix of a linear Transformation, Linear models in business, science, and engineering

Unit 3. Matrix Algebra (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

Unit 4. Determinants (4 Hrs.)

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

Unit 5. Vector Spaces (5 Hrs.)

Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems

Unit 6. Vector Space Continued (4 Hrs.)

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

Unit 7. Eigenvalues and Eigen Vectors (5 Hrs.)

Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to differential equations

Unit 8. Orthogonality and Least Squares (5 Hrs.)

Inner product, Length, and orthogonality, Orthogonal sets, Orthogonal projections, The Gram Schmidt process, Least squares problems, Application to linear models, Inner product spaces, Applications of inner product spaces

Unit 9. Groups and Subgroups (5 Hrs.)

Binary Operations, Groups, Subgroups, Cyclic Groups

Unit 10. Rings and Fields (4 Hrs.)

Rings and Fields, Integral domains

Text Books

1. Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley.
2. Linear Algebra and Its Application, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning.
3. A First Course in Abstract Algebra, John B. Farleigh, 7th Edition, Pearson

Reference Books

1. Mathematics II, B. Sc. Second Semester, New Edition, Binod Prasad Dhakal and etal, KEC Publication and Distribution Pvt. Ltd.