Lectures related to Power series

P-adic Expansion: Unique Representations and Power Series

Explores p-adic expansion, unique representations, and power series for computing p-adic expansions.

Frobenius Method: General Case of Regular Singular Point

Explores the Frobenius method for regular singular points in ODEs, emphasizing the nature of roots and deriving solutions.

Frobenius Method: Illustration around an Ordinary Point

Covers the Frobenius method for solving ODEs around an ordinary point.

Limit of the Quotient and Periodicity

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

Convergence of Series: Solutions and Tests

Covers the convergence of series and various tests to determine convergence based on odd and even terms.

Analyzing Character Lifts in Cp

Covers constructing characters and lifting them to analytic functions on Cp, emphasizing the importance of correction terms for convergence.

Completeness of LP

Explores the completeness of LP, discussing implications of mathematical conditions and the convergence of series.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Frobenius Method: Regular Singular Points

Explores the Frobenius method for solving ODEs at regular singular points.

Network Inference from Textual Evidence

Delves into network inference from textual evidence, exploring information propagation, translation, and multi-input attention.

Taylor Series: Operations and Convergence

Explores Taylor series operations, convergence criteria, and radius of convergence in depth.

Convergence of Series

Explores the convergence of series, including geometric and harmonic series, absolute convergence, and comparison criteria.

Power series and Taylor series

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

Taylor Series: Convergence and Applications

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

Laurent Series and Convergence: Complex Analysis Fundamentals

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

Power Series Computations

Covers power series, generating functions, and operations like addition, multiplication, differentiation, and integration, with examples and the generalized binomial theorem.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Analysis I Exam Solutions

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

Convergence of Series

Explores point of accumulation, Bolzano-Weierstrass theorem, and series convergence, including harmonic series examples.

Comparison Series and Integrals

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