Overview

Providing an elementary level experience of calculus, this book imparts knowledge on various areas, such as using Legendre and Jacobi conditions, the Euler equation and the notion of extremum conditions of a function in one variable to such conditions of a function in the form of a definite integral. All areas are explained in detail supported by figures and exercises and the book lists some direct (approximate) methods to solve boundary value problems containing ordinary/partial differential equations by variational and residue methods, some of them being of immense importance in the treatment of finite element numerical methods.

Full Product Details

Author:   N. Kumar
Publisher:   Alpha Science International Ltd
Imprint:   Alpha Science International Ltd
ISBN:  

9781842651957

ISBN 10:   1842651951
Pages:   140
Publication Date:   30 January 2005
Audience:   College/higher education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Variational Problems with Fixed Boundaries: Functional/Necessary condition of extremum Euler equation Euler-Poisson equation Euler-Ostrogradsky equation Euler equation in parametric form Invariance of Euler equation Other forms of boundary conditions Isoperimetric problems Principle of reciprocity Exercises Variational Problems with moving boundaries: Moving boundaries in explicit form Moving boundaries in implicit form One side variation Exercises Sufficient conditions of extremum: Higher order variations Sufficient condition for extremum Jacobi equation and Jacobi conditions Exercises Direct Methods: Ritz method Ritz method for computing eigen values Ritz method for boundary value problems Galerkin method Collocation method Least square method Kantorovich method Finite difference method Appendix -A: Ordinary differential equations Appendix -B: Finite difference methods Appendix -C: Eigen value and eigen value problem Appendix -D: Gaussian elimination method

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Author Information

Naveen Kumar.: Dept. of Mathematics, Faculty of Science Banaras Hindu University, Varanasi, India

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