Lectures related to Derivatives of Entire Functions

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Provides solutions to an Analysis I exam, covering various topics.

Covers the properties of improper integrals, power series, and Taylor series.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

Taylor Series: Basics and Applications

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.

Approximating Functions with Taylor Series

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Limit of the Quotient and Periodicity

Explores the limit of the quotient for sequences and the periodicity of functions.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Convergence Criteria: Series & Functions

Explores convergence criteria for series and functions, including the squeeze theorem and D'Alembert's criterion.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Power series and Taylor series

Covers power series, Taylor series, and their applications in functions like logarithmic functions.

Distribution Interpolation Spaces

Explores distribution interpolation spaces, convergence of sequences, derivatives, weak derivatives, and their applications in minimization problems.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Power Series Functions: Logarithm and Exponential

Explores power series functions, particularly the logarithm and exponential functions, discussing convergence, extension, and roots of entire functions.