Real Functions: Definitions and Theorems

Related lectures (30)

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Discusses limits of multivariable functions, focusing on definitions, examples, and techniques for calculating limits effectively.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

Covers the conditions for finding absolute extrema in multivariable functions.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

Explores definitions and examples of real functions of a real variable.

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.