Lectures related to Puiseux series

P-adic Expansion: Unique Representations and Power Series

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

Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Linear Differential Equations: Solution Methods

Covers solution methods for linear differential equations of second order with constant coefficients.

P-adic Expansion and Hensel's Lemma

Covers the p-adic expansion theorem and Hensel's Lemma in Qp.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Convergence of Parametrized Series

Explores the convergence of a series parameterized by alpha and its conditions for convergence.

Quantum Chemistry: Schrödinger Equation Solutions

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

Diffusion Equations in Spherical Coordinates

Explores solving diffusion equations in steady state conditions for concentric spheres with fixed concentration and flux, emphasizing the importance of linearity and homogeneity.

Power Series Computations

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

Method of Plates with Coefficients

Covers the method of plates with coefficients to find solutions of differential equations.

Method of Indeterminate Coefficients

Covers the method of solving differential equations using the method of indeterminate coefficients.

Particular Solutions in Differential Equations

Explores finding particular solutions in differential equations using indeterminate coefficients and solving associated homogeneous equations.

Approximation and Compound Interest

Explores evaluation methods, raising numbers to a power, chess game origins, and compound interest calculations.

Complex Analysis: Laurent Series and Residue Theorem

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.