Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Bachelors Level/First Year/Second Semester/Science csit/second semester/mathematics ii/syllabus

B.Sc Computer Science and Information Technology

Institute of Science and Technology, TU

Nature of the course: (Theory)

F.M: 60+40 P.M: 24+16

Credit Hrs: 3Hrs

Mathematics II [MTH168]
Course Objective
i.
The main objective of the course is to make familiarize with the concepts and techniques of linear algebra, solve system of linear equation with Gauss-Jordon 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, Ring, and Field.
Course Description

The course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigen values and eigenvectors, and singular value decomposition of a matrix

S1:Linear Equations in Linear Algebra[5]
1
System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence
S2:Transformation[4]
1
Introduction to linear transformations, the matrix of a linear Transformation, Linear models in business, science, and engineering
S3:Matrix Algebra[5]
1
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
S4:Determinants[4]
1
Introduction, Properties, Cramer’s rule, Volume and linear transformations
S5:Vector Spaces[5]
1
Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems
S6:Vector Space Continued[4]
1
Dimension of vector space and Rank, Change of basis, Applications to difference equations, Applications to Markov Chains
S7:Eigenvalues and Eigen Vectors[5]
1
Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to differential equations
S8:Orthogonality and Least Squares[5]
1
Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The GramSchmidt process, Least squares problems, Application to linear models, Inner product spaces, Applications of inner product spaces
S9:Groups and Subgroups[5]
S10:Rings and Fields[4]
1
Rings and Fields, Integral domains
References
1.
Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley
2.
Linear Algebra and Its Applications, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning
Labrotary Work