Small Scale Stability: Gradient Systems

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Explores stability in ODEs, including error checks, equilibrium points, and global attractors, with a focus on numerical schemes like Euler's method.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Small Scale Stability: Equilibrium Point

Covers small scale stability at equilibrium points in dynamical systems for engineers.

Equilibrium Stability Analysis

Explores equilibrium stability analysis, emphasizing the importance of stability calculations for balanced systems.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Lyapunov II: Stability and Invariance

Explores Lyapunov stability and invariance of dynamical systems through examples and corollaries.

Mechanical Energy: Equilibrium and Oscillations

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

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

General Physics: Mechanics for SIE and GC

Covers constraints, equilibrium points, and stability in mechanics using examples like pendulums.

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.