MA9320 MATHEMATICAL MODELING AND SIMULATION SYLLABUS | ANNA UNIVERSITY MTECH NANO SCIENCE AND TECHNOLOGY 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER M.TECH NANOSCIENCE AND TECHNOLOGY DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI, TIRUNELVELI,COIMBATORE), 2009 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009
MA9320 MATHEMATICAL MODELING AND SIMULATION L T P C
3 0 0 3
UNIT I FUNDAMENTAL PRINCIPLES OF NUMERICAL METHODS 9
Scientific Modeling - Numerical data and Numerical operations -Numerical Algorithms -
Numerical Programs -Numerical Software - Approximations in Mathematical Model
building- Numerical integration -Differentiation -Variational finite element methods-
Rayleigh’s method-Ritz method.
UNIT II MATHEMATICAL MODELING 9
Mathematical modeling - physical simulation - advantages and limitations - process
control - Transport phenomena- concept of physical domain and computational domain -
assumptions and limitations in numerical solutions – Finite element method and Finite
difference method.
UNIT III DIFFERENTIAL EQUATIONS & APPLICATIONS 9
Euler method, Runge-Kutta method, Multi step-differential equations-boundary values-
Elliptic equations-one dimensional parabolic equation-hyperbolic equation- partial
differential equations -separation of variables-wave equation-Laplace equation-nonlinear
partial differential equations - approximation methods of nonlinear differential equations.
UNIT IV SIMULATION 9
Basic concepts of simulation- data manipulation, data exchange of the structure,
properties and processing of materials-Three dimensional model for capillary
nanobridges and capillary forces. Molecular dynamics simulation.
UNIT V MONTE CARLO METHODS 9
Basics of the Monte Carlo method-Algorithms for Monte Carlo simulation-Applications to
systems of classical particles-modified Monte Carlo techniques-percolation systemvariation
Monte Carlo method-diffusion Monte Carlo method - Quantum Monte Carlo
method.
TOTAL : 45 PERIODS
REFERENCES
1. S.C. Chapra and R.P.Canale, “Numerical methods for Engineers”, Tata McGraw Hill,
New Delhi, 2002.
2. Erwin Kreyzig, “Advanced Engineering Mathematics”, John Wiley & Sons, 2004.
3. R.J. Schilling and S.L. Harris, “Applied Numerical Methods for Engineers using
MATLAB and C”, Thomson publishers, New Delhi, 2004.
4. D. Frenkel and B. Smith, “Understanding molecular simulation from algorithm to
applications”, Kluwar Academic Press, 1999.
5. K. Ohno, K. Esfarjani and Y. Kawazoe, “Introduction to Computational Materials
Science from ab initio to Monte Carlo Methods”, Springer-Verlag, 1999.
MA9320 MATHEMATICAL MODELING AND SIMULATION L T P C
3 0 0 3
UNIT I FUNDAMENTAL PRINCIPLES OF NUMERICAL METHODS 9
Scientific Modeling - Numerical data and Numerical operations -Numerical Algorithms -
Numerical Programs -Numerical Software - Approximations in Mathematical Model
building- Numerical integration -Differentiation -Variational finite element methods-
Rayleigh’s method-Ritz method.
UNIT II MATHEMATICAL MODELING 9
Mathematical modeling - physical simulation - advantages and limitations - process
control - Transport phenomena- concept of physical domain and computational domain -
assumptions and limitations in numerical solutions – Finite element method and Finite
difference method.
UNIT III DIFFERENTIAL EQUATIONS & APPLICATIONS 9
Euler method, Runge-Kutta method, Multi step-differential equations-boundary values-
Elliptic equations-one dimensional parabolic equation-hyperbolic equation- partial
differential equations -separation of variables-wave equation-Laplace equation-nonlinear
partial differential equations - approximation methods of nonlinear differential equations.
UNIT IV SIMULATION 9
Basic concepts of simulation- data manipulation, data exchange of the structure,
properties and processing of materials-Three dimensional model for capillary
nanobridges and capillary forces. Molecular dynamics simulation.
UNIT V MONTE CARLO METHODS 9
Basics of the Monte Carlo method-Algorithms for Monte Carlo simulation-Applications to
systems of classical particles-modified Monte Carlo techniques-percolation systemvariation
Monte Carlo method-diffusion Monte Carlo method - Quantum Monte Carlo
method.
TOTAL : 45 PERIODS
REFERENCES
1. S.C. Chapra and R.P.Canale, “Numerical methods for Engineers”, Tata McGraw Hill,
New Delhi, 2002.
2. Erwin Kreyzig, “Advanced Engineering Mathematics”, John Wiley & Sons, 2004.
3. R.J. Schilling and S.L. Harris, “Applied Numerical Methods for Engineers using
MATLAB and C”, Thomson publishers, New Delhi, 2004.
4. D. Frenkel and B. Smith, “Understanding molecular simulation from algorithm to
applications”, Kluwar Academic Press, 1999.
5. K. Ohno, K. Esfarjani and Y. Kawazoe, “Introduction to Computational Materials
Science from ab initio to Monte Carlo Methods”, Springer-Verlag, 1999.
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