Advanced Mathematics

IE 5101 Advanced Mathematics

Numerical Methods to ordinary differential equations: Numerical solutions to ordinary differential equations of first & second order with initial & boundary conditions, Picard窶冱 method, Taylor series methods, Euler窶冱 method & modified Euler窶冱 method, Plilne窶冱 method & Runge Kutta methods. Numerical Solutions to partial differential equations: Finite difference equivalence to partial derivatives, elliptic, parabolic & hyperbolic equations, applications to one dimensional & two dimensional equations, Schmidt窶冱 & Cronk Nicholson窶冱 method.

Linear Programming Problems: Introduction & formations of the problems, graphical method, simplex method, duality concept in LPP & solution of the dual. Statistical Quality Control: Introduction, control charts of all types, ISO 9000 series & their importance, OC curves, advantages & limitations of SQL in industries.

Random Variables & theoretical distributions: Discrete & continuous frequency distributions, Stochastic process, Marovian chain, simulation techniques. Reliability Theory: Theory of reliability, maintainability, availability, failure distribution, MTTF, MTBF, Hazard rate, Bath tub curve, state dependent systems, series & parallel connection, redundancy of systems.

Reference Books

1. Numerical methods by S. S. Sastry, (Pearson Education)

2. Statistical methods by S. P. Gupta.

3. Reliability & Maintainability Engg. By Charles E. Ebeling, (Pearson Education Mc- Graw Hill)

4. Operations Research by S. D. Sharma, Kedar Nath Ram Nath Company,Meerut.