Lectures related to Natural logarithm

Natural Logarithm: Definition and Properties

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

Natural Logarithm: Properties and Inequalities

Covers properties and inequalities of the natural logarithm function, including solving related inequalities.

Generalized Powers: Derivatives and Exponentials

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

Power Functions: Properties and Derivatives

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Natural Logarithm: Graph

Explores the properties and graph of the natural logarithm function, emphasizing its bijectivity and the Euler's number 'e'.

Exponential Function: Properties and Definitions

Explores the properties and definitions of the exponential function and its relation to the natural logarithm.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Quantum Field Theory: Fermions and Grassmann Numbers

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Logarithmic Functions: Properties and Applications

Explores the properties and applications of natural logarithmic functions, including area invariance and harmonic series divergence.

Dynamics on homogeneous spaces and interactions with number theory

Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.

Limit Study: Sinus and Logarithm

Focuses on studying a limit involving sinus and logarithm functions as x approaches positive infinity.

Limit of a Sequence

Simplifies limit calculations by applying properties of logarithms and exponentials.

Exponential Functions: Properties and Logarithms

Explores exponential functions, their properties, and the relationship with logarithmic functions.

Exponential Functions and Logarithms

Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.

Complexity of Algorithms: Advanced Big-O Facts

Covers big-O estimates for factorial function and combinations of functions.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Domain Verification in Equations

Emphasizes the importance of verifying the possible domain of a function before solving an equation.

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.

Properties of Entropy

Explores the properties of entropy, including positivity and nullity conditions.