Separation Theorem: Convex Sets

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Functional Analysis I: Norms and Bounded Operators

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

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Minkowski-Weyl: Convexity and Separation Theorem

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Weak Derivatives: Definition and Properties

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

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.