Lectures related to Derivability implies Continuity

Taylor Expansion and Convex Functions

Explores Taylor expansion, convex functions, and Lipschitz continuity with illustrative examples.

Demonstration of Theorem 8.2

Explores the conditions for a function to be continuous and differentiable.

Differentiability Analysis

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Taylor's approximation: Analysis & Applications

Covers Taylor's approximation theorem, differentiability, error control, and function expansions.

Differentiability of Functions in Two Variables

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivability of Reciprocal Function

Covers the derivative of the reciprocal function and its properties.

Derivative Chain Rule

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

Darboux Theorem: Advanced Analysis I

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Existence of Limit Implies Continuity

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Differentiability and Derivatives

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

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Derivatives Rules: Notation, Extrema

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