Bøger af Namdeo Khobragade

This book contains mathematical concepts and theories on topic of operations research. The concept of optimization techniques which forms the central theme of this book, finds its roots and application in branches of Mathematics, Physics and Engineering. The mathematical approach for optimization techniques may be of immense help for those students, researchers and teachers pursuing work on operations research and will be helpful to increase the maximization of profit This book consist of Alternative Approach to the Simplex Method, Solution of Integer Programming Problem by Alternative Approach, Alternative Approach to Fractional Programming Problem, Goal Programming Problem by Alternative Approach, Alternative Approach to the Wolfe¿s Modified Simplex Method for Quadratic Programming Problem and Alternative Approach to Game Theory Problems.

This book contains mathematical concepts and theories on topic of thermo elasticity. The concept of thermo elasticity which forms the central theme of this book, finds its roots and application in branches of Mathematics, Physics and Engineering. Thermoplastic behavior of different geometric structures and different boundary conditions are discussed in depth for better understanding of the topics. The mathematical approach for thermoplastic problems may be of immense help for those students, researchers and teachers pursuing work on thermo elasticity and will be helpful to increase the thermal efficiency of materials. This book includes An Analysis for the Thermoelastic Vibrations in the Circular Ring Sector Plate, Temperature and Stress Distribution in a Non-Simple Elastic Elliptical Plate due to Point Impulsive Heat Sources, Analytical Solution of Time-Fractional Heat Transfer Analysis in Composite Plates, Cylinders or Spheres, Thermoelastic Vibration of Simply Support Circular Plate Subjected to a Movable Laser Pulse, Thermally Induced Instability Analysis of a Thin Disk With an Internal Heat Source, etc.

This book contains mathematical concepts and theories on topic of thermo elasticity. The concept of thermo elasticity which forms the central theme of this book, finds its roots and application in branches of Mathematics, Physics and Engineering. Thermoplastic behavior of different geometric structures and different boundary conditions are discussed in depth for better understanding of the topics. The mathematical approach for thermoplastic problems may be of immense help for those students, researchers and teachers pursuing work on thermo elasticity and will be helpful to increase the thermal efficiency of materials. The book contains Thermoelastic Damped Vibration Analysis in A Thick Plate Subjected to Time-Dependent Rectangular Frame Sectional Heat Supply , Thermoelastic Vibrations Analysis of A Thin Isotropic Solid Elliptic Cross Section, An Integral Transform for A Gaussian Hypergeometric Differential Equation Amidst Conditions of Radiation Type Contour, Thermoelastic Analysis of A Functionally Graded Hollow Cylinder Under Electro-Thermo-Mechanical Loads, etc.

The book entitled ¿Classical Mechanics and Differential Geometry¿ contains eight chapters. This book contains Variational Principle and Lagrange¿s equations; Hamilton¿s Principle, some techniques of calculus of variations, Derivation of Lagrange equations from Hamilton¿s principle. Extension of principle to non holonomic systems. Conservation theorems and symmetry properties.Legendre transformations and the Hamilton equations of motion. Cyclic coordinates and conservation theorems. Routh¿s procedure and oscillations about steady motion, The Hamiltonian formulation of relativistic mechanics, The Principle of least action. the equations of canonical transformation. Examples of canonical transformation. The simplistic approach to canonical transformations. Poisson brackets and other canonical invariants. Equations of motion. Infinitesimal canonical transformations and conservation theorems in the Poisson bracket formulation, the angular momentum, Poisson bracket relations, symmetry groups of mechanical systems. Liouville¿s theorem. Definition of surface. Curves on a surface. Surfaces of revolution. Helicoids. Metric. Direction coefficients. Families of curves. Hilbert¿s theorem.

The book entitled ¿Dynamical System ¿ A Short Course¿ contains eight chapters. This book contains matrices and operators, subspaces, bases and dimension. determinants, trace and rank. direct sum decomposition. real eigen values. differential equations with real distinct eigen values. complex eigen values. complex vector spaces. real operators with complex eigen values. application of complex linear algebra to differential equations. review of topology in Rn. new norms for old. exponential of operators. homogeneous linear systems. a non homogeneous equation. higher order systems. the primary decomposition. the S+N decomposition. nilpotent canonical forms. Jordan and real canonical forms. canonical forms and differential equations. higher order linear equations on function spaces. sinks and sources. hyperbolic flows. generic properties of operators. significance of Genericity. dynamical systems and vector fields. the fundamental theorem. existence and uniqueness. continuity of solutions in initial conditions. on extending solutions. global solutions. global solutions. the flow of a differential equation. nonlinear sinks. stability. Liapunov function. gradient systems.

The book entitled Complex Analysis ¿ A Short Course contains five chapters. This book contains Power series representation of analytic function, zeros of an analytic function, the index of a closed curve, Cauchy¿s theorem and integral formula, counting zeros, the open mapping Theorem. Classification of singularities, residues, the argument principle, the maximum principle, Schwarz Lemma, convex functions and Hadamard¿s three circles theorem, Phragmen lindelof theorem. Spaces of analytical functions, Riemann¿s mapping theorem, Weierstrass factorization theorem, factorization of sine function, Gamma functions, Riemann zeta functions. Runge¿s theorem, Mittag-Leffler¿s theorem, Schwarz reflection principle, analytic continuation along a path, Monodromy theorem, Basic properties of harmonic functions, harmonic functions on a disk, Green¿s functions. Entire functions, Jensen¿s formula, Genus and order of an Entire functions, Hadamard Factorization theorem, Range of an analytic function, Bloch¿s theorem, the little Picard theorem, Schottky¿s theorem, the great Picard theorem.

The book entitled Real Analysis & contains eight chapters. This book is written for UG and PG students. It includes Uniform convergence. Uniform convergence and continuity. Uniform convergence and integration. Uniform convergence and ifferentiation. Equicontinuous families of functions. The Stone- Weierstrass theorem. Differentiation. The Contraction Principle. The Inverse Function Theorem. The Implicit Function Theorem. Partitions of unity. The space of tangent vectors at a point of Rn. Vector fields on open subsets of Rn. Topological manifolds. Differentiable manifolds. Real Projective space. Differentiable functions and mappings. Rank of a mapping. Immersion. Sub manifolds. Outer measure. Measurable sets and Lebesgue measure. A non-measurable set, Measurable functions, Littlewood¿s three principles. The Riemann integral. Lebesgue integral of a bounded function over a set of finite measure. Integral of a non-negative function. General Lebesgue integral. Convergence in measure. Differentiation of monotone functions. Functions of bounded variation. Differentiation of an integral. Absolute continuity. Convex functions. Lp-spaces. Holder and Minkowski inequality.

The book entitled Integral equation and Transforms consists of eight chapters.This book contains preliminary concepts of integral equations, some problems which give rise to integral equations, conversion of ordinary differential equations into integral equations, classification of linear integral equations, integro-differential equations. Fredholm equations, degenerate kernels, Hermitian and symmetric kernels, the Hilbert-Schmidt theorem, Hermitization and symmetrization of kernels, solution of integral equations with green¿s function type kernels,types of Voltera equations, Resolvent kernel of Voltera equations, convolution type kernels,non- linear Voltera equations. Fourier integral equations, Laplace integral equations Hilbert transform, Fourier integral theorem, Fourier transform Fourier cosine and sine transform,the convolution integral, multiple Fourier transform, solution of partial differential equation by means of Fourier transform, the Laplace transform of some elementary functions, Laplace transform of derivatives, the convolution of two functions, inverse formula for Laplace transform and solutions of ordinary differential equations by Laplace transform.