Numerical Methods and Advanced Computing Techniques Detailed Syllabus for Nano Technology M.Tech first year first sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.
The detailed syllabus for Numerical Methods and Advanced Computing Techniques M.Tech 2017-2018 (R17) first year first sem is as follows.
M.Tech. I Year I Sem.
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:
- Advanced engineering mathematics, by Erwin Kreyszig, wiley publications
- Probability and statistics, scham series, Arnold o. allen, academic press
- Probability and statistics, Arnold o. allen, academic press
- Probability and statistics for engineers, miller and john e. freund, prentice hall of india
- A primer for the monte carlo method, llya M. Sobol’ CRC Press
- Simulation and monte carlo method by reuven y. rubisten
- The monte carlo method, popular lectures in mathematics by sobol.i.m
For all other M.Tech 1st Year 1st Sem syllabus go to JNTUH M.Tech Nano Technology 1st Year 1st Sem Course Structure for (R17) Batch.
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