Functional Analysis I: Spectral Theorem

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Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

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Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

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Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

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Explores the spectral theorem for operators in a Hilbert space.