Functions: Continuity and Derivability

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Related lectures (31)

Page 3 of 4

Rolle's Theorem

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.

Continuous Functions: Theory and Applications

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

Closed Intervals: Definitions and Remarks

Explains definitions and remarks about closed intervals in functions.

Advanced Analysis I: Continuous Functions on Compact Sets

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

Intermediate Value Theorem

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

Uniform Continuity: Proof and Theorem

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

Limits and Continuity

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

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Integrals of Type 1

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