The Intermediate Value Theorem

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Fundamental Theorem of Integral Calculus

Explores the Fundamental Theorem of Analysis for continuous functions on closed intervals, illustrated with examples like integrating cos(x).

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.

Uniform Continuity: Proof and Theorem

Covers the concept of uniform continuity and a theorem on continuous functions.

Derivability on an Interval: Rolle's Theorem

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Closed Intervals: Definitions and Remarks

Explains definitions and remarks about closed intervals in functions.

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Limits and Continuity

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

Integrals of Type 1

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

Developpements limités

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