Page 12 - REC :: M.E. Avionics Curriculum and Syllabus - R2019

Department of Aeronautical Engineering, REC

Subject Code Subject Name Category L T P C
MH19101 ADVANCED APPLIED MATHEMATICS FC 3 1 0 4

Objectives:
⚫ To encourage students to develop a working knowledge of the central ideas of linear Algebra
⚫ To study and understand the concepts of probability and random variables.
To 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

UNIT-I LINEAR ALGEBRA 12
Vector spaces – norms – Inner Products – Eigen values 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 ONE DIMENSIONAL RANDOM VARIABLES 12
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.
UNIT-III RANDOM PROCESSES 12
Classification – Auto correlation - Cross correlation - Stationary random process – Markov process –- Markov chain -
Poisson process – Gaussian process.
UNIT-IV LINEAR PROGRAMMING 12
Formulation - Graphical solution – Simplex method - Two phase method - Transportation and Assignment Models
UNIT-V FOURIER TRANSFORM FOR PARTIAL DIFFERENTIAL EQUATIONS 12
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 Contact Hours : 60
Course Outcomes:
On completion of the course students will be able to
⚫ Understand the concepts and develop the working knowledge in linear algebra
⚫ Understand the concepts of probability and random variables.
⚫ Understand the Markov chain and the usage of conditional probability in discrete –time markov chain.
⚫ Construct the mathematical models for a linear programming
⚫ Get introduce with the fourier transforms and able to solve the partial differential equations.

Text Books:
1 Bronson R.,”Matrix Operation, Schaum’s outline series”, Mc-Graw Hill, New York , 1989.
Oliver C. Ibe, “Fundamentals of Applied Probability and Random Processes”, Academic Press, (An imprint of
2
Elsevier), 2010.
3 Taha H.A., “Operations Research: An introduction”, Pearson Education, Asia, New Delhi, Ninth Edition, 2012.
Sankara Rao K., “Introduction to partial differential equations” Prentice Hall of India
4
Pvt, Ltd, New Delhi, 1997
Reference Books / Web links:
Andrews L.C., and Philips R.L., “Mathematical Techniques for engineering and Scientists”, Prentice Hall of
1
India, 2006
O’Neil P.V.,“Advanced Engineering Mathematics”, (Thomson Asia Pvt Ltd, ingapore), Cengage learning India
2 private limited, 2007

Curriculum and Syllabus | M.E. Avionics | R2019 Page 12