Canonical Transformations: Existence and Equations

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Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in 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.

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Canonical Transforms: Hamilton-Jacobi Equation

Explores canonical transforms and the Hamilton-Jacobi equation, emphasizing explicit solutions and initial conditions.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Hamiltonian Formalism: Conservation Laws

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.