MA4102 Applied Mathematics for Signal Processing Engineers Syllabus:

MA4102 Applied Mathematics for Signal Processing Engineers Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES :

This course will help the students to
 study the vector space theory, inner product, eigenvalues, generalized eigenvectors and apply these in linear algebra to solve system of linear equations.
 study the solution of Bessel’s equations, Recurrence relations, Bessel’s functions and its properties.
 study the linear programming models and transportation models and various techniques to solve them.
 acquire the knowledge of solving an algebraic or transcendental equations and system of liners equations using an appropriate numerical methods.
 study the numerical solution of differential equations by single and multistep methods.

UNIT I LINEAR ALGEBRA

Vector spaces – Norms – Inner products – Eigenvalues using QR transformations – QR factorization – Generalized eigenvectors – Canonical forms – Singular value decomposition and applications – Pseudo inverse – Least square approximations –Toeplitz matrices and some applications.

UNIT II BESSEL FUNCTIONS

Bessel’s equation – Bessel function – Recurrence relations – Generating function and orthogonal property for Bessel functions of first kind – Fourier – Bessel expansion.

UNIT III LINEAR PROGRAMMING

Formulation – Graphical solution – Simplex method – Big M method – Two phase method – Transportation problems – Assignment models.

UNIT IV NUMERICAL SOLUTION OF ALGEBRAIC EQUATIONS

Systems of linear equations : Gauss elimination method – Pivoting techniques – Thomas algorithm for tridiagonal system – Gauss – Jacobi, Gauss – Seidel, SOR iteration methods – Conditions for convergence – Systems of nonlinear equations : Fixed point iterations, Newton’s method, Eigenvalue problems : Power method and Given’s method.

UNIT V NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

Runge – Kutta method of fourth order for system of IVPs – Numerical stability of Runge – Kutta method – Adams – Bashforth multistep method – Shooting method – BVP : Finite difference method – Collocation method – Orthogonal collocation method.

TOTAL: 60 PERIODS

COURSE OUTCOMES :

At the end of the course, students will be able to
 concepts on vector spaces, linear transformation, inner product spaces, eigenvalues and generalized eigenvectors, to solve system of linear equations.
 solution of Bessel’s differential equations, Bessel functions and its properties.
 could develop a fundamental understanding of linear programming models, able to develop a linear programming model from problem description, apply the simplex method for solving linear programming problems.
 solve an algebraic or transcendental equation and linear system of equations using an appropriate numerical method.
 numerical solution of differential equations by single and multistep methods.

REFERENCES :

1. Andrews, L.C., “Special Functions of Mathematics for Engineers”, 2nd Edition, Oxford University Press, 1998.
2. Bronson, R. and Costa, G. B., “Linear Algebra”, 2nd Edition, Academic Press, 2007.
3. Jain, M. K., Iyengar, S.R.K, and Jain, R.K., “Computational Methods for Partial Differential Equations”, New Age International, 2007.
4. Jain, M. K., Iyengar, S. R. K and Jain, R. K., “Numerical Methods for Scientific and Engineering Computation”, 6th Edition, New Age International, 2014.
5. Sastry, S. S., “Introductory Methods of Numerical Analysis “, 5th Edition, PHI Learning, 2015.
6. Taha, H.A., “Operations Research”, 10th Edition, Pearson Education, 2018.