Lectures related to Taylor Series: Convergence and Applications

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

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

Functions: Differentials, Taylor Expansions, Integrals

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

Comparison Series and Integrals

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

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Convergence Criteria: Series & Functions

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

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Integration of Functions: Series and Limits

Covers the integration of functions through series and limits, focusing on the development of limit expansions and the integration of entire series.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Numerical Analysis: Convergence and Divergence

Covers convergence and divergence in numerical analysis, focusing on series and functions.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Laurent Series and Convergence: Complex Analysis Fundamentals

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

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Derivatives and Continuity

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

Approximating Functions with Taylor Series

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

Integration: Limited Development

Covers the limited development of integration and methods for calculating the limit development of functions and antiderivatives.

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.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.