The Laplace Transform
Explore the Laplace Transform in engineering mathematics, covering its applications and fundamental principles. Gain insights into this powerful tool for solving differential equations and analyzing systems.
The Functional Volume Product Under Heat Flow
Explores monotonicity of functional volume product along Fokker-Planck heat flow, leading to improved Borell's hypercontractivity and Laplace transform quasi-norm lower bound.
A Simple Proof of the Wiener-Ikehara Tauberian Theorem
Explore a concise demonstration of the Wiener-Ikehara Tauberian Theorem, a fundamental result in analytic number theory with wide-ranging applications.
Solving Ordinary Differential Equations with Constant Coefficients Using Laplace Transform
Solve linear ODEs with constant coefficients using Laplace transforms, a powerful technique for simplifying complex differential equations.
Laplace Transform of Periodic Function - Engineering Mathematics Problem
Learn to apply Laplace transforms to periodic functions, focusing on square waves. Gain practical skills for solving engineering math problems involving periodic signals.
Unit Step Function and Heaviside Function - Problems and Laplace Transform Applications
Learn to convert piecewise functions to unit step functions, understand Heaviside functions, and explore their applications in Laplace transforms through practical examples.
Laplace Transforms of Derivatives - Problems in Engineering Mathematics
Learn to solve problems involving Laplace transforms of derivatives, a key concept in engineering mathematics for analyzing differential equations and system behavior.
First Shifting Theorem in Laplace Transform - Problems and Applications
Learn to apply the First Shifting Theorem in Laplace transforms, with practical examples and problem-solving techniques for engineering mathematics.
New Perspectives on Borel Summation - Lecture 4
Explore Airy-Lucas functions through Borel summation, focusing on thimble integrals and hypergeometric Laplace transforms. Gain insights into Stokes phenomenon reflections in the Borel plane.
Methods for Differential Equations Physics Students Need to Know
Explore five powerful methods for solving differential equations in physics: ansatz, energy conservation, series expansion, Laplace transform, and Hamiltonian flow, with practical applications to harmonic oscillators.
What's New in Calculus and Algebra - Upcoming Wolfram Language Features
Explore upcoming calculus and algebra features in Wolfram Language, including performance improvements, new functions, and algorithmic advances for symbolic and numerical computations.