Lectures related to Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Convexity and Optimization

Explores convexity, optimization, and critical points in mathematical functions using the second derivative.

Untitled

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

Derivability and Chain Rule

Covers the demonstration of the chain rule and the theorem of Rolle.

Ramanujan Graphs: Constructions and Similarities

Explores Ramanujan graphs' constructions, matching polynomials, perfect matchings, and universal covers, along with quantitation and qualitative aspects.

Derivative of a Function: Tangent Equation

Explores finding tangent equations and slopes through derivatives.

Derivability and Continuity

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.