JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Basic engineering mathematics probability & statistics

Course Objective:

The course is intended to cover, basics concepts of mathematics like numerical algebra, probability , simulations specially Monte- Carlo simulations which will help in understanding theoretical concepts of Nanotechnology.

Course Outcome:

• To know the importance of simulations in nanotechnology.
• Students without mathematics back ground will be able to understand the concept of mathematics.
• To evaluate nanostructured simulations in nanotechnology.

UNIT - I

Numerics in general: Interpolation, Gauss elimination, Solution by iteration, least square method.

UNIT - II

Numeric Linear Algebra and differential equations: Matrix Eigen value problems: Introduction, Inclusion of Matrix Eigen values, Tridiognalization and RQ factorization. Methods for first order ODEs, Multi step methods, Higher order ODES

UNIT - III

Introduction to probability: Probability, Sample space and events- Probability- the axioms of probability, some elementary theorems-conditional probability Baye’s theorem Random Variables- Discrete and continuous – distribution- distribution function Distribution Binomial and poison distributions and normal distribution – related properties.

UNIT - IV

Systems, Models, Simulations and the Monte Carlo Methods: Systems,Models,Simulation and the Monte Carlo Methods, Random number generation, Introduction, Congruential Generators, Statistical Tests of Pseudorandom Numbers, Random variate generation, inverse Transform Method, Composition Method, Acceptance-Rejection Method,

UNIT - V

Monte Carlo integration and Variance reduction techniques: Introduction, Monte Carlo Integration, The Hit or Miss Monte Carlo Method, The Sample-Mean Monte Carlo Method, Efficiency of Monte Carlo Method, Integration in Presence of Noise,

TEXT BOOKS:

• 1. Advanced engineering mathematics, by Erwin Kreyszig, wiley publications
• 2. Probability and statistics, scham series, Arnold o. allen, academic press
• 3. Probability and statistics, Arnold o. allen, academic press
• 4. Probability and statistics for engineers, miller and john e. freund, prentice hall of india
• 5. A primer for the monte carlo method, llya M. Sobol' CRC Press
• 6. Simulation and monte carlo method by reuven y. rubisten
• 7. The monte carlo method, popular lectures in mathematics by sobol.i.m