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Lecture
Bisection Method: Proposition and Demonstration
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Bisection Method
Covers the bisection method for finding function roots within intervals and its geometric interpretation.
Fundamental Theorem of Calculus Example
Demonstrates the practical importance of the fundamental theorem of calculus through a detailed example.
Extreme Values Theorem
Discusses the Extreme Values Theorem for continuous functions on closed intervals.
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Explains the definition and uniqueness of developments limites for continuous functions on open intervals.
Intermediate Values Theorem
Explores the Intermediate Values Theorem for continuous functions on closed intervals.
The Intermediate Value Theorem
Covers the Intermediate Value Theorem for continuous functions on closed intervals.
Properties of Continuous Functions
Explores the continuity of elementary functions and the properties of continuous functions on closed intervals.
Continuous Functions and Derivatives
Covers the definitions of continuous functions and derivatives, emphasizing the concept of functions being continuous at a point and the notion of derivatives.
Uniform Continuity: Proof and Theorem
Covers the concept of uniform continuity and a theorem on continuous functions.
Fundamental Theorem of Integral Calculus
Explores the Fundamental Theorem of Analysis for continuous functions on closed intervals, illustrated with examples like integrating cos(x).