Lectures related to Numerical Analysis: Convergence and Divergence

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

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

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

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

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

Covers the application of numerical series, comparing An, Bu, and Cn.

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

Covers Fourier series, periodic functions, and Fourier transforms.

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

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

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Introduces fundamental concepts of Analysis I, focusing on functions of a variable and numerical sequences.

Explores the continuity of functions in R² and R³, emphasizing accumulation points and limits.

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

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

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

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

Explores Taylor series development, order of terms, and function convergence.

Covers the basic properties of limits and provides illustrative examples.

Explains limits at right and left endpoints, convergence conditions, and function behavior near specific values.