Lectures related to Formal 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: Illustration around an Ordinary Point

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

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

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: Regular Singular Points

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

Unclosed Curves Integrals

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

Quantum Chemistry: Schrödinger Equation Solutions

Explores the solutions to the Schrödinger Equation in Quantum Chemistry, emphasizing wavefunction properties and energy quantization.

Power Series Computations

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

Euler's Formula Demonstration

Covers the demonstration of Euler's formula and its applications.

Generating Functions: Advanced Counting

Covers the definition of generating functions and their application in solving recurrence relations.

Integration Techniques: Series and Functions

Covers integration techniques for series and functions, including power series and piecewise functions.

Mechanical Joints: Snap Fits and Adhesive Bonding

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

Complex Numbers: Convergence, Equations, and Exponential Functions

Covers convergence of power series, complex equations, exponential functions, and function properties.

Developing Taylor's Theorem

Covers Taylor's theorem, power series, and representing functions by their Taylor series.

Power series and Taylor series

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

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.

Complex Analysis: Simply Connected Domains

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

Nth Derivative

Explores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.

Notation: Coproduct vs. Product

Explores the distinction between coproduct and product notation in categorical constructions within Abelian groups.

Direct Sums of Abelian Groups

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.