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Variational Principles

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Author(s): P. K. Townsend, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied

Introduction
Multivariate calculus
Stationary points
Convex functions
Convexity
First-order convexity condition
Second-order convexity condition
Legendre transform
Lagrange multipliers
Euler-Lagrange equation
Functional derivatives
First integrals
Constrained variation of functionals
Hamilton's principle
The Lagrangian
The Hamiltonian
Symmetries and Noether's theorem
Multivariate calculus of variations
The second variation
The second variation
Jacobi condition for local minima of F[x]