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• 11:44 PM, Monday, 20 Sep 2021

 Course Postgraduate Semester Sem. I Subject Code MA619 Subject Title Mathematics For Electrical Engineering

##### Syllabus

Linear Algebra:

(a) Vector Spaces: Definition of Vector space, Sub spaces, linearly independence and dependence,linear Span, Basis, Dimension

(b) System of linear equations: Range space and Null space of a matrix, Rank of a matrix, Existence and uniqueness of solution of the system of linear equations, Dimension of the Solution Space associated with the system of linear equations

(C) Eigen values and Eigen vectors: Definition of Eigen values and Eigen vectors of a square matrix and their properties including similarity matrices

(C) Diagonalization and SVD: Diagonalization of a square matrix, Singular-Value-Decomposition (SVD) and Pseudo-inverse of a matrix

Fourier Series and Transform:

(a) Fourier Series: Fourier Series of 2pi periodic functions, Cosine Series, Sine Series, Fourier series of a function defined on an interval [a,b] of length T=b-a, Point-wise Dirichlet convergence Theorem for Fourier Series.

(b)Fourier Transform: Representation of a function defined over R in Fourier Integral and representation of Fourier Integral as a pair of transformations: Fourier Transform and Fourier Inverse Transform, Properties of Fourier Transform

(c)Laplace transform: Definition and necessity of Laplace transform, Inverse Laplace transform, Properties of Laplace Transform

Introductory Complex Analysis

(a) Complex Differentiation: Definition of Continuity and Differentiability-Cauchy-Riemann Equation -Analytic function

(b) Complex Integration: Defintion of Contour-Contour Integration (Complex Line Integration)

Introductory Probability Theory:

Random variables, probability distribution functions, discrete and continuous distributions. If time permits, multivariate distribution to be added.

##### References

1.Bracewell R., Fourier Transform and its applications(3rd edition), McGraw Hill, 2000

2.Strang G., Linear Algebra and its applications, (4th edition), Thomson 2006.

3.Leon-Garcia A., Probability, statistics and Random Processes for Electrical Engineers, Pearson Prentice Hall, 2008.

4.K. Hoffman and R. Kunze; Introduction to Linear Algebra , Prentice-Hall, 1996, 2/e.

5.R. Horn and C. Johnson, Matrix Analysis; Cambridge, C.U.P.,1991

6.H. A. Priestley, Introduction to Complex Analysis, 2nd edition (Indian), Oxford, 2006.

7.J. H. Mathews and R.W. Howell, Complex Analysis for Mathematics and Engineering, 3rdedition, Narosa, 1998.

8.J Heading,Mathematical Methods in Science and Engineering, 2nd ed.9.Trevor P. Humphreys,A Reference Guide to Vector Algebra.