Lectures related to Elliptic integral

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Comparison Series and Integrals

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

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Functions xr, r>0, on 10,1

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Elliptic Problems: Model and Deformation

Covers elliptic problems related to a model and deformation, discussing concepts such as the model problem and deformation energy.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Elliptic Equations: Well-Posedness and Comparison Principle

Explores well-posedness and comparison principles for elliptic equations and their implications.

Calculus of Variation and Euler's Elastica

Covers variational methods, equilibrium shape of a bent beam, Euler's Elastica, and numerical and analytical methods.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Functional Equation of Zeta and Hadamard Products

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

Geometric Examples: Triangles and Functions

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.

Weak Formulations & Solutions: Elliptic Problems

Explores weak formulations and solutions for elliptic problems using Galerkin methods.

Principal Value of an Integral: Examples

Covers examples of principal value of an integral with sin functions and singularities.

Linear PDEs of Order 2

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Conduction Heat Transfer: Formulations and Theorems

Explores the strong and integral formulations of conduction heat transfer in 2D media, along with weak formulations and boundary conditions.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Angle Calculation on Regular Surfaces

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.