MA4152 Advanced Applied Mathematics Syllabus:
MA4152 Advanced Applied Mathematics Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To encourage students to develop a working knowledge of the central ideas of Linear Algebra.
To enable students to understand the concepts of Probability and Random Variables.
To make students 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 familiarize the students with the formulation and construction of a mathematical model for a linear programming problem in real life situation.
To introduce the Fourier Transform as an extension of Fourier techniques on parodic functions and to solve partial differential equations.
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 ONE DIMENSIONAL RANDOM VARIABLES
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
Classification – Auto correlation – Cross correlation – Stationary random process – Markov process – Markov chain – Poisson process – Gaussian process.
UNIT – IV LINEAR PROGRAMMING
Formulation – Graphical solution – Simplex method – Two phase method – Transportation and Assignment models.
UNIT – V FOURIER TRANSFORM FOR PARTIAL DIFFERENTIAL EQUATIONS
Fourier transforms: Definitions, properties – Transform of elementary functions, Dirac Delta functions – Convolution theorem, Parseval’s identity – Solutions to partial differential equation: Heat equations, Wave equations, Laplace and Poisson’s equations.
TOTAL: 60 PERIODS
COURSE OUTCOMES:
At the end of the course, students will be able to
apply the concepts of linear algebra to solve practical problems.
use the ideas of probability and random variables in solving engineering problems.
classify various random processes and solve problems involving stochastic processes.
formulate and construct mathematical models for linear programming problems and solve the transportation and assignment problems.
apply the Fourier transform methods of solving standard partial differential equations.
REFERENCES:
1. Andrews, L. C. and Philips. R.L., “Mathematical Techniques for engineering and scientists”, Prentice Hall of India, New Delhi,2006.
2. Bronson, R.,” Matrix Operation”, Schaum’s outline series, Tata McGrawHill, New York,2011.
3. O’Neil P.V.,, “Advanced Engineering Mathematics”, Cengage Learning”, 8th Edition, India, 2017.
4. Oliver C. Ibe, “Fundamentals of Applied Probability and Random Processes”, Academic Press, Boston, 2014.
5. Sankara Rao,K., “ Introduction to partial differential equations” Prentice Hall of India Pvt. Ltd., 3rd Edition, New Delhi,2010.
6. Taha H.A., “Operations Research: An Introduction”, Ninth Edition, Pearson Education, Asia, 10th Edition, New Delhi, 2017.