Well-Posedness of Elliptic PDEs

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Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Linear Operators: Quantum Mechanics and Linear Algebra

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Semigroups of Linear Operators

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Finite Element Method: Weak Formulation and Galerkin Method

Explores the weak formulation and Galerkin method in Finite Element Method applications, including boundary conditions and linear systems of equations.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.