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M.Tech., , Avionics, , Regulations 2019, , SEMESTER – I, , MAD 6185, , ADVANCED APPLIED MATHEMATICS, , L, , T, , P, , C, , 3, , 1, , 0, , 4, , OBJECTIVES:, The aim of this course is, , , To develop a working knowledge of the central ideas of linear algebra., , , , To study and understand the concepts of probability and random variable of the, various functions., , , , Understand the notion of a Markov chain, and how simple ideas of conditional, probability and matrices can be used to give a thorough and effective account, of discrete-time Markov chains., , , , To formulate and construct a mathematical model for a linear programming, problem in real life situation., , , , Introduce the Fourier Transform as an extension of Fourier techniques on, periodic functions and to solve partial differential equations., , MODULE I, , LINEAR ALGEBRA, , 9+3, , 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., MODULE II, , ONE DIMENSIONAL RANDOM VARIABLES, , 9+3, , Random variables - Probability function – moments – moment generating functions, and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma, and Normal distributions – Function of a Random Variable., MODULE III, , RANDOM PROCESSES, , 9+3, , Classification – Auto correlation - Cross correlation - Stationary random process –, Markov process –- Markov chain - Poisson process – Gaussian process., MODULE IV, , LINEAR PROGRAMMING PROBLEM, , 9+3, , Formulation – Graphical solution – Simplex method – Two phase method Transportation and Assignment Models, Sequencing problems., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 28

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M.Tech., , Avionics, , MODULE V, , Regulations 2019, , FOURIER TRANSFORM FOR PARTIAL DIFFERENTIAL, , 9+3, , EQUATIONS, Fourier transforms: Definitions, properties-Transform of elementary functions, Dirac, Delta functions – Convolution theorem – Parseval‘s identity – Solutions to partial, differential equations: Heat equations, Wave equations, Laplace and Poison‘s, equations., TOTAL: 45+15:60 PERIODS, TEXT BOOKS:, 1. Bronson, R.Matrix Operation, Schaum‘s outline series, McGrawHill, Newyork, (1989)., 2. Oliver C. Ibe, ―Fundamentals of Applied Probability and Random Processes,, Academic Press, (An imprint of Elsevier), 2010., 3. Taha H.A. ―Operations Research : An introduction‖ Ninth Edition, Pearson, Education, Asia, New Delhi 2012., 4. Sankara Rao, K. ―Introduction to partial differential equations‖ Prentice Hall of, India, pvt, Ltd, New Delhi, 1997., REFERENCES:, 1. Andrews, L.C. and Philips.R.L. ―Mathematical Techniques for engineering and, scientists‖, Printice Hall of India,2006., 2. O‘Neil P.V. ―Advanced Engineering Mathematics‖, (Thomson Asia pvt ltd,, Singapore) 2007, Cengage learning India private limited., OUTCOMES:, At the end of the course students will be able to, , , understand and solve linear algebra problems, , , , solve one dimensional random variable problem., , , , solve problems in random processes, , , , deal with linear programming problems., , , , apply Fourier transform and PDE techniques to solve general problems in, Avionics., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 29