M.Tech (Engineering Physics)

1^ST SEMESTER

Code No: BAEP 601
Paper : MATHEMATICAL PHYSICS 

Unit – I     

Differential Equations: ODE, PDE, exact and approximation solution methods, green’s function.

Unit – II  

Special Functions: Hermite, Legendre, Chebeyshev, Gamma and Beta functions,  Bessel functions of 1^st and 2^nd kind, Hypergeometric function and error function, Differential equation and generating function, Reccurence relations, Concept of function space. 

Unit – III

Transforms: Fourier, Laplace, Zeta transform, Convolution theorem, Parseval’s relations,Transfer function (Theta function), Dirac-Delta function.

Unit – IV 

Non linear methods: Non linear equations, Sensitivity to initial condition, Introduction to chaos, Fractals, Bernoulli and Ricati equations.

 Code No: BAEP 603
Paper : OPTIMIZATION METHODS

Mathematical Modeling and the Operation Research Approach, Introduction to Formulation and Classification of Optimization Models, Search-Based Optimization, Algorithms, Formulation and Classification of Linear Programs.

Simplex Algorithms for Solving Linear Programs, Interior Point Algorithms for solving Linear Programs, Duality and Sensitivity in Linear Programming, Goal Programming, Shortest Path in CPM, Formulation and Structure Of Network Flow Models, Formulation and Classification of Discrete Optimization Models, Methods for Solving Discrete Optimization Models.

Nature and Diversity of Nonlinear Programs, Improving Search Paradigm for Nonlinear Optimization, Formulation of Unconstrained Nonlinear Programs One-Dimensional Search, Conditions for Local Optimality, Convex and Concave Functions,  Gradient Search and Newton’s Method, Quasi-Newton Methods for Unconstrained Optimization, Unconstrained Optimization without Derivatives, Formulation and Classification of Constrained Nonlinear Programs, Lagrange Multiplier Methods.

Code No: BAEP 605
Paper : COMPUTATIONAL  PHYSICS

Unit – I

Perturbation Theory: Time dependent and time independent, Variational method, WKB Approximation. 

Unit – II

Scattering Theory: Classical and Quantum theory of scattering, Born approximation, Elastic and Inelastic Scattering.

Unit – III

Computer Simulations of Linear Systems.  

Unit – IV

Computer Simulations of Non-Linear Systems: Introduction to chaos and Fractals.

Code No: BAEP 607
Paper : STATISTICAL PHYSICS

 Unit – I

Random Variables: Fundamentals of probability theory and Statistics, Entropy, Computation with Random Variables. 

Unit – II

Random Variables of Space States: Classical Statistical Mechanics, Introduction to Ensembles, Micro-canonical,macro-canonical and Grand canonical ensembles, Equipartition theorem, Approximate methods

Unit – III: 

Time dependent Random Variables: Classical Stochastic  process, Markov process, Master equation, Simulation of  Stochastic processes and fields.

Unit – IV

Quantum Random Systems: Ideal Fermi and Bose gases, Simple  applications.

Code No: ITEP 701
Paper : Object Oriented Programming Using C++

Objects, relating to other paradigms ( functional, data decomposition),basic terms and ideas (abstraction, encapsulation, inheritance, polymorphism ).

Overview of C, Encapsulation, information hiding, abstract data types, object & classes: attributes, methods. C++ class declaration, state identity and behavior of an object, constructors and destructors, instantiation of objects, default parameter value, object types, C++ garbage collection, dynamic memory allocation, metaclass.

Inheritance, Class hierarchy, derivation – public, private & protected, aggregation, omposition vs classification hierarchies, polymorphism, operator overloading, parametric polymorphism, generic function – template function, function name overloading, overriding inheritance methods, run time polymorphism.