Lectures related to Laurent series

Laurent Series and Convergence: Complex Analysis Fundamentals

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

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Frobenius Method: Regular Singular Points

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

Complex Analysis: Simply Connected Domains

Explores simply connected domains in complex analysis, including holomorphic functions, Cauchy's integral formula, and Taylor series.

Analyzing Character Lifts in Cp

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

Laurent Series and Residue Theorem: Complex Analysis Concepts

Discusses Laurent series and the residue theorem in complex analysis, providing examples and applications for evaluating complex integrals.

Frobenius Method: Illustration around an Ordinary Point

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

Laurent Series: Definition and Properties

Covers the definition and properties of Laurent series, including convergence and function expansion.

Power Series and Taylor Series

Explores power series, Taylor series, convergence criteria, and applications in mathematics.

Mechanical Joints: Snap Fits and Adhesive Bonding

Covers mechanical joints, focusing on snap fits and adhesive bonding principles.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

Residues Theorem Applications

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Analysis and Synthesis of Deterministic Signals

Explores the representation of signals as vectors, projection theorem, orthogonal functions, and examples.

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: Introduction

Introduces the Frobenius method for solving second-order linear ODEs around ordinary points.

Analytical Real Functions

Explores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series, residue theorem, and their applications in complex analysis.

P-adic Expansion: Unique Representations and Power Series

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