Matrix Definition RESET THEOREM Set Theory Norm-Preserving Extension of Linear Functionals Functional Analysis Regularity of Lebesgue Measure Analysis Reflexivity of Closed Subspaces Analysis Residue Computation Formulas for Poles Complex Analysis Solving Poisson's Equation via the Newtonian Potential Partial Differential Equations Monotone Convergence Theorem for Sequences Sequences Hilbert Space Structure of the Inhomogeneous Sobolev Space on the Torus Analysis Analysis Area