Lectures related to Logarithmic differentiation

Natural Logarithm: Definition and Properties

Delves into the definition, geometric interpretation, and properties of the natural logarithm, including its continuity and behavior as x approaches infinity or zero.

Derivatives and Reciprocal Functions

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

Logarithmic Derivative of Zeta

Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.

Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Derivatives and Tangents

Introduces derivatives, tangent lines, rules of differentiation, and practical examples.

Logarithmic Derivative of Zeta

Explores the behavior of the zeta function and its explicit formula.

Differential Calculus: Definition and Derivability

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

Generalized Powers: Derivatives and Exponentials

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Existence of Limit Implies Continuity

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

Functions: Limits, Continuity, Differentiability

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

Properties of Integrals

Covers properties of integrals and differentiation, focusing on exercise solutions and function behavior.

Natural Logarithm: Definition and Properties

Explores the definition, properties, and limits of the natural logarithm function.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Directional Derivatives: Definition and Applications

Explains the concept of directional derivatives and their applications in differentiating functions.

Derivability and Differentiability

Covers derivability, differentiability, rules of differentiation, and the relationship between differentiability and continuity.

Partial Differentiation

Explores simple examples of partial differentiation, demonstrating how to calculate partial derivatives and gradients in various scenarios.

Data Compression and Entropy Properties Demonstration

Covers the properties of entropy and demonstrates their application in data compression.

Derivative: Linear Approximation

Explains differentiation and linear approximation for function approximation near a point.

Functions: Multivariable Functions and Exact Differentials

Explores functions as a function of time and space, differentiation of multivariable functions, exact differentials, and gradients.

Text-Based Representations of Market Structure

Delves into text-based representations to model market structure and firm innovation.