Lectures related to Differential Equations: Part 2

Explores solutions to partial differential equations and their applications in various scenarios.

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Explores the Cauchy-Lipschitz theorem for local existence and uniqueness of solutions to differential equations.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

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

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.