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Subject

Mathematics II

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.

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Tribhuvan University

Institute of Science and Technology

Bachelor of Science in Computer Science and Information Technology

Course Title: Mathematics II

Course no: MTH168

Semester: II

Nature of course: Theory and Practice

Full Marks: 80

Pass Marks: 32

Credit Hours: 3

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:
  • Linear Algebra and Its' Applications, David C. Lay, 4thEditon, Pearson Addison Wesley.
  • Linear Algebra and Its' Application, Gilbert Strang, 4thEdition, Addison, CENGAGE Learning.
  • A First Course in Abstract Algebra, John B. Farleigh, 7th Edition, Pearson
Reference Books:
  • Mathematics II, B. Sc. Second Semester, New Edition, Binod Prasad Dhakal and etal, KEC Publication and Distribution Pvt. Ltd.
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