Analysis: Recap and Normed Space R^n

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Equivalent norms: properties and proofs

Explores equivalent norms in a vector space and their continuity properties, including proofs of norm equivalence.

Scalar Products: Definition, Examples

Covers the definition of a scalar product on a real vector space and provides examples.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Global Properties of Continuous Functions

Explores the global properties of continuous functions, including behavior, limits, and interval characteristics.

Metric Spaces: Norms and Distances

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Multiple Integration: Part 2

Explores double integrals over unbounded domains and convergence of sequences.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Distributions & Interpolation Spaces

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Continuous Functions: Criteria and Equivalences

Explores criteria for continuity, convergence of sequences, and equivalence conditions for continuous functions.