English | 2021 | ASIN: B09652DRSX | 253 pages | PDF | 1.67 MB

CONTENTS- CALCULUS OF VARIATIONS,
Chapter 1: Variational Problems with Fixed Boundaries
1.1 Calculus of Variation
1.2 Functionals
1.3 Extremal
1.4 Euler's Equation
1.5 Other Form of Euler's Equation
1.6 Solutions of Euler's Equation
1.7 Particular Cases of Euler's Equation
1.8 Geodesics
1.9 Functional Dependent on Higher Derivatives
1.10 Functional for Several Dependent Variable
1.11 Functionals Dependent on Several Independent Variables
1.12 Isoperimetric Problems
1.13 Invariance of Euler's Equation under Co-ordinate Transformation
Chapter 2: Variational Problems with Moving Boundaries
2.1 Introduction
2.2 Transversality Conditions
2.3 Orthogonality Conditions
2.4 Variational Problem with a Moving Boundary for a Functional Dependent on Two Functions
2.5 One Sided Variations
Chapter 3: Sufficient Conditions for an Extremum
3.1 Definitions
3.2 Jacobi Condition
3.3 Sufficient Condition for Extremum (Legendre Condition)
3.4 Weak and Strong Extremum
3.5 Application of the Calculus of Variation
3.6 Hamilton's Principle
3.7 Lagrangian of a System
3.8 Lagrange's Equation
3.9 Hamiltonian
3.10 Hamilton's Canonical Equation of Motion
3.11 Principal of Least Action
Chapter 4: Variational Method for Boundary Value Problems
4.1 Introduction
4.2 Rayleigh-Ritz Method (For Ordinary Differential Equation)
4.3 Galerkin's Method
4.4 Partial Differential Equation (By Rayleigh-Ritz Method)
4.5 Kantorovich Method
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