Finite Elements: Convergence Analysis and Variational Formulation

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Explains the basics and precision of triangular and quadrangular finite elements.

Explores axial loading, stress, strain, and equilibrium states in deformable bodies, emphasizing stability and equilibrium types.

Explores mechanical energy, equilibrium, and small oscillations in rectilinear motion.

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores potential energy, mechanical energy, and resonance in mechanical systems, including conservative forces and energy transformation.

Explores stability criteria, equilibrium types, reaction loads computation, and potential energy variations in mechanical systems.

Explores work, energy, and momentum in physics, including potential energy diagrams and conservation principles applied to practical situations.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.