Lectures related to Canonical Transformations: Existence and Equations

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.

Homogeneous Differential Equations

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Circular Motion and Harmonic Oscillator

Explores circular motion, harmonic oscillators, and double springs, elucidating the physics principles behind them.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, their orders, examples, and applications in various fields.

Canonical Transformations: Hamilton-Jacobi Equation

Covers canonical transformations and the Hamilton-Jacobi equation, emphasizing explicit motion solutions and system evolution.

First Order Differential Equation

Covers first-order differential equations, including linear equations and applications in physics.

Projectile Motion: Friction Effects

Explores projectile motion with friction effects and dynamics of polar expeditions.

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Vertical Metronome: Equilibrium and Stability

Explores equilibrium and stability of a vertical metronome system with springs.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

Addition of Springs: General Physical Exercises I

Covers the addition of springs in series and parallel, exploring equivalent movements.