An Elementary Course on Variational Problems in Calculus

by Naveen Kumar

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.

Table of Contents

• Variational Problems with Fixed 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 Moving boundaries in explicit form
• Moving boundaries in implicit form
• One side variation
• Exercises
• Sufficient conditions of Higher order variations
• Sufficient condition for extremum
• Jacobi equation and Jacobi conditions
• Exercises
• Direct 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 Ordinary differential equations
• Appendix Finite difference methods
• Appendix Eigen value and eigen value problem
• Appendix Gaussian elimination method

140 pages, Hardcover

Published January 30, 2005