Syllabus

BSc CSIT · Semester II

Mathematics II syllabus

Official TU syllabus for Mathematics II (MTH168): 10 units, 50 topics, 3 credit hours. Every unit links to its notes and solved questions.

1

Linear Equations in Linear Algebra

5h · 16 Q
  • System of linear equations
  • Row reduction and Echelon forms
  • Vector equations
  • The matrix equations Ax = b
  • Applications of linear system
  • Linear independence
Unit notes →Solved questions →
2

Transformation

4h · 9 Q
  • Introduction to linear transformations
  • the matrix of a linear Transformation
  • Linear models in business, science, and engineering
Unit notes →Solved questions →
3

Matrix Algebra

5h · 10 Q
  • 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 notes →Solved questions →
4

Determinants

4h · 5 Q
  • Introduction
  • Properties
  • Cramer’s rule
  • Volume and linear transformations
Unit notes →Solved questions →
5

Vector Spaces

5h · 10 Q
  • Vector spaces and subspaces
  • Null spaces, Column spaces, and Linear transformations
  • Linearly independent sets: Bases
  • Coordinate systems
Unit notes →Solved questions →
6

Vector Space Continued

4h · 4 Q
  • Dimension of vector space and Rank
  • Change of basis
  • Applications to difference equations
  • Applications to Markov Chains
Unit notes →Solved questions →
7

Eigenvalues and Eigen Vectors

5h · 7 Q
  • Eigenvectors and Eigenvalues
  • The characteristic equations
  • Diagonalization
  • Eigenvectors and linear transformations
  • Complex eigenvalues
  • Discrete dynamical systems
  • Applications to differential equations
Unit notes →Solved questions →
8

Orthogonality and Least Squares

5h · 14 Q
  • 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
Unit notes →Solved questions →
9

Groups and Subgroups

5h · 6 Q
  • Binary Operations
  • Groups
  • Subgroups
  • Cyclic Groups
Unit notes →Solved questions →
10

Rings and Fields

4h · 6 Q
  • Rings and Fields
  • Integral domains
Unit notes →Solved questions →

Textbooks and references

  • Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley.
  • Linear Algebra and Its Applications, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning.

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