Concept

Lower limit topology

Related lectures (31)

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Discusses the recognition of a quotient in topology and the properties of the quotient topology.

Functions of Class Cn: Theorem 2

Focuses on Theorem 2 for functions of class Cn and their Taylor expansion around a.

Continuous Functions on Open Intervals

Explores continuous functions on open intervals and elementary functions constructed from algebraic functions.

Developpements limités

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Taylor's Theorem: Advanced Analysis I

Explores Taylor's theorem for functions on open intervals, focusing on nth derivatives.

Derivatives Rules: Notation, Extrema

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Extreme Points and Compact Intervals

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Integrals of Type 1

Covers the definition of integrals of type 1 and the importance of continuity.

Continuous Derivable Functions

Covers continuously derivable functions on open intervals with continuous derivatives and examples of different derivative orders.

Quotients in Abelian Groups

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Differentiability and Derivatives

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Limits and Continuity

Explores limits, continuity, and elementary functions' properties, emphasizing the importance of understanding continuous functions.

Differentiating under the integral sign

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Inequalities on Real Numbers

Explores inequalities on real numbers, including real intervals and comparison properties.

Advanced Analysis I: Taylor with Integral Remainder

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