Electrostatics and Green's Functions: Mathematical Methods

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Laurent Series and Convergence: Complex Analysis Fundamentals

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

Complex Analysis: Simply Connected Domains

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

Electric Field Between Infinite Planes: Laplace Equation

Focuses on finding the electric field between infinite planes in electrostatics.

Fourier Transform: Residue Method

Covers the calculation of Fourier transforms using the residue method and applications in various scenarios.

Complex Analysis: Holomorphic Functions and Cauchy-Riemann Equations

Introduces complex analysis, focusing on holomorphic functions and the Cauchy-Riemann equations.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Essential Singularity and Residue Calculation

Explores essential singularities and residue calculation in complex analysis, emphasizing the significance of specific coefficients and the validity of integrals.

Complex Analysis: Holomorphic Functions

Explores holomorphic functions in complex analysis and the Cauchy-Riemann equations.