Introduction – linear programming – duality and sensitivity analysis – transportation and assignment problems – integer programming – network optimization models – dynamic programming – non-linear programming – unconstrained and constrained optimization – non-traditional optimization algorithms.

Foundations of Biological Neural Networks and Artificial Neural Networks (Learning, Generalization, Memory, Abstraction, Applications), McCulloch-Pitts Model, Historical Developments.ANN Architectures, Learning Strategy (Supervised, Unsupervised, Reinforcement), Applications: Function Approximation, Prediction, Optimization. Associative Memories: Matrix memories, Bidirectional Associative Memory, Hopfield Neural Network.

Optimization: Need for unconstrained methods in solving constrained problems, Necessary conditions of unconstrained optimization, Structure methods, Quadratic models, Methods of line search, Steepest descent method, Quasi-Newton methods: DFP, BFGS, Conjugate-direction methods:, Methods for sums of squares and nonlinear equations ,Linear Programming: Simplex Methods, Duality ii LPP, Transportation problem, Nonlinear programming: Lagrange Multiplier, KKT conditions, Convex programming.

Meaning and importance of simulation and modelling, classification of models, Variables and problem formulation, performance measures, Data collection and analysis, SIMSCRIPT language concept: general syntax, Discrete event modelling, process and resources, timing and pending list, accumulate and tally, process instance and object oriented aspects, sets and data structures, Probability distribution, Random number and random variant generation. Input modelling and output analysis.

Introduction to Geographic Information System (GIS) – Hardware, Software, Data types and models – Spatial data quality, Thematic maps, Symbolization, Scale and generalization – Co-ordinate systems, Map projections and visualization – Input / output techniques in GIS (spatial and non-spatial), Editing, Topology, Database structure – Analysis: spatial, network analysis, optimization of path, time and cost, Routing and events, Facility location, Interpolation methods, Digital elevation model, Surface analysis – Geovisualizatio –  Decision support systems, OpenGIS, WebGIS, Enterprise GIS –

Flows on the line: Introduction; Fixed points and stability; Population growth; Linear Stability Analysis; Existence and Uniqueness; Impossibility of oscillations; Potentials

Bifurcations: Saddle-node bifurcation; Transcritical bifurcation; Laser threshold; Pitchfork bifurcation; Overdamped bead on a rotating hoop; Imperfect bifurcations and catastrophes; Insect outbreak

Flows on a circle: Examples and Definitions; Uniform Oscillator; Nonuniform Oscillator; Overdamped Pendulum; Fireflies; Superconducting Josephson junctions

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X-ray diffraction
X-ray fluorescence
Dielectric loss variation with frequency and temperature
Curie temperature measurement
Magnetic susceptibility by quink's tube
Electrical conductivity by two probe and four probe
NMR
ESR
Hall effect
Band gap of LED using Newton's ring
P-N junction characterization

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