Hamilton-Jacobi Equation: Analytical Mechanics

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Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Explores the classical harmonic oscillator and its algebraic approach to studying the system.

Covers the fundamental conservation laws and properties of space and time beyond mechanics.

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Explores Hamiltonian mechanics in diatomic molecules, emphasizing polar coordinates and conservation laws.

Explains cofactors, eigenvectors, eigenvalues, and studying linear applications.

Explores the dynamics of a block pulled by a spring under various conditions.

Explores canonical basis, linear mapping, and eigenvalues in linear algebra.