Lectures related to Differential Equations: Solutions and Derivatives

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

Explores linear differential of functions, continuity, differentiability, and matrix representation.

Explores solutions of differential equations and their monotonicity properties.

Introduces limited developments and differential equations with practical applications.

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

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

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