Normed SpacesCovers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Euler-Lagrange EquationCovers the Euler-Lagrange equation in Sobolev spaces and discusses minimization, convexity, and weak forms.
Conditional ExpectationCovers conditional expectation, Fubini's theorem, and their applications in probability theory.
Quantum States and OperatorsCovers the description of states in quantum mechanics and their relation to probability, expectation values, and the Schrödinger equation.
