Linear Algebra and Complex Variable
Course Code: MAT 125
Credit Hour: 3
Course Group: Mathematics
Linear Algebra: Introduction to systems of linear equations. Gaussian elimination. Definition of matrices. Algebra of matrices. Transpose of a matrix and inverse of matrix. Factorization. Determinants. Quadratic forms. Matrix polynomials. Euclidean n-space. Linear transformation from IRn to IRm. Properties of linear transformation from IRn to IRm . Real vector spaces and subspaces. Basis and dimension. Rank and nullity. Inner product spaces. Gram-Schmidt process and QR-decomposition. Eigenvalues and eigenvectors. Diagonalization. Linear transformations. Kernel and Range. Application of linear algebra to electric networks.
Complex Variable: Concept of complex numbers, General functions of a complex variable, Complex differentiation and derivatives, Open and closed sets of complex numbers; Cauchy-Rieman equations, Mapping by elementary functions, Line integral of a complex function, Cauchy’s integral theorem, Tailor’s & Laurrent’s theorems, Singular points, Residue, Cauchy’s residue theorem, Evaluation of residue, Contour integration..
Reference Books:
- Abdur Rahman : Linear Algebra
- Schaum’s Outline Series: Linear Algebra
- Brown Churchil: Complex Variable and Applications
- Schaum’s Outline Series: Complex Variable