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Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.
Explores closure finiteness in CW complexes, proving compact subspaces are contained in finite subcomplexes through induction and characteristic maps.
Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.
Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.
Explores the transition from atoms to solid metal structures, covering crystal lattices, compactness, cubic systems, and allotropic forms of iron.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
