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Canonical Transforms: Hamilton-Jacobi Equation
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Canonical Transformations: Hamilton-Jacobi Equation
Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.
Canonical Transformations: Existence and Equations
Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.
Quantum Mechanics: Jacobi Identity and Gauge Invariance
Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.
Hamiltonian Formalism: Harmonic Oscillator
Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.
Partial Derivatives and Differential Equations
Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.
Canonical Transformations in Analytical Mechanics
Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.
Ordinary Differential Equations: Definitions and Examples
Covers ordinary differential equations, their orders, examples, and applications in various fields.
Material Point Model: Basics
Covers the material point model, initial conditions, and Newton's laws in physics.
Differential Equations: Existence and Uniqueness Theorems
Covers the existence and uniqueness of solutions for differential equations.
Numerical Analysis: Stability in ODEs
Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.