The laplace transform

In essence, the Laplace transform changes the operation of differentiation into the operation of multiplication, so that a differential equation is converted to an algebraic equation. By using the inverse Laplace transform, the algebraic solution can be transformed into the solution of the original differential equation. Technology makes it easy to handle the algebraic and analytic complexities that arise in using Laplace transform techniques, especially expressions involving algebraic fractions or piecewise continuous functions.

• Publication year

  1991

• Venue

  Heat Transfer 1

• Publication date

  1991-06-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1002/9780470823552.CH11
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• No references are available for this paper.

• Relational de Sitter state counting with an SU(3) clock

  2026influential citation
• Fractional integro-differential equations in square average exponential growth functions spaces

  2026influential citation
• Moments of sums of exponentials, beyond CHS

  2026cites this paper
• From Laplace to Mellin: A Unified Biorthogonal Transform Framework

  2026cites this paper
• A New Approach for Solving Fractional Differential Equations Incorporating Ramadan Group Transform and Machine Learning

  2025cites this paper
• Moments of Generalized Fractional Polynomial Processes

  2025cites this paper
• Long time asymptotic behavior of a self-similar fragmentation equation

  2025cites this paper
• Ergodic Hankel operators

  2025influential citation
• Fractional Approach to Two-Group Neutron Diffusion in Slab Reactors

  2025cites this paper
• Delta-Shaped Kernels Generated by Laplace Transform Inversion Methods

  2025cites this paper
• Fault Localisation in Infinite-Dimensional Linear Electrical Networks

  2025cites this paper
• Absolutely monotonic functions involving the zero-balanced Gaussian hypergeometric functions with applications

  2025influential citation
• Monotonicity and positivity of several functions involving ratios and products of polygamma functions

  2025cites this paper
• A class of positive Fox H-functions

  2025cites this paper
• Deviation matrix in denumerable Markov processes: Characterisation, rank-one perturbation and restart

  2025cites this paper
• Stochastic comparisons of aggregate claim amounts under Archimedean copula

  2025cites this paper
• Complete monotonicity of log-functions

  2025cites this paper
• Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications

  2025cites this paper
• On local large deviations for decoupled random walks

  2025cites this paper
• Detecting Homoclinic Points in Nonlinear Discrete Dynamical Systems via Resurgent Analysis

  2025cites this paper
• Analytical Investigation for Some Problems Under Different Fractional Differential and Integral Operators

  2025cites this paper
• Post-widder type operators through the lens of truncated exponential polynomials

  2025cites this paper
• Complete Monotonicity of the function involving derivatives of Barnes G-function

  2025influential citation
• Multidimensional Widder–Arendt Theorem in Locally Convex Spaces

  2025cites this paper
• Normalized Remainders: Definition, Origins, Backgrounds, Recent Results, and Basic Properties

  2025cites this paper
• Analytical Transfer Function for the Blocked-Diffusion Warburg Impedance with Frequency Dispersion. Simulation of the Impedance Spectrum and Voltage Response of a Lithium-ion Battery

  2025cites this paper
• On the Effectiveness of the z-Transform Method in Quadratic Optimization

  2025cites this paper
• Regularization of Some Methods of Inversion of the Integral Laplace Transform

  2025cites this paper
• Drug concentration after intravenous administration: A mathematical approach

  2025cites this paper
• Unbounded Integral Hankel Operators

  2025influential citation
• Legendre Polynomials and Their Use for Karhunen-Loève Expansion

  2025influential citation
• Law of large numbers for non-linear traces of the Choquet type on finite factors

  2025cites this paper
• An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function

  2025cites this paper
• Some Analytical Properties of the Remainder of Binet-Like Expression for the Barnes G-Function

  2025cites this paper
• Unbiased Estimation in One-Parameter Exponential Families of the Natural Parameter with Extensions

  2025cites this paper
• On completely monotonic functions

  2025influential citation
• Deconvolution of Arbitrary Distribution Functions and Densities

  2025cites this paper
• Broadly discrete stable distributions

  2025influential citation
• Uniqueness sequences for multidimensional vector-valued Laplace transform

  2025cites this paper
• Multidimensional vector-valued Laplace transform and applications

  2025cites this paper
• Extension of a complete monotonicity theorem with applications

  2025cites this paper
• A Poisson representation of the positive sojourn time of L\'evy processes

  2025influential citation
• The polarization problem for the honeycomb structure

  2025cites this paper
• An asymptotic expansion for the Mellin transform of a beta function and applications

  2025cites this paper
• Fisher information from quantum many-particle arrival time measurements

  2025cites this paper
• Asymptotic Behaviours of Laplace Transforms of Generalized Functions

  2025cites this paper
• Approximating Feynman Integrals Using Complete Monotonicity and Stieltjes Properties

  2025cites this paper
• Deconvolution of distribution functions without integral transforms

  2025cites this paper
• Inequalities involving a Ramanujan Integral

  2025cites this paper
• A general Hardy-Hilbert-type integral inequality theorem

  2025cites this paper
• Linear time-and-space-invariant relaxation systems

  2025cites this paper
• Fisher-KPP waves and the minimal speed on hexagonal lattice

  2025cites this paper
• From Frequency Dependent Specific Heat to Fictive Temperature of a Glassy Liquid

  2025cites this paper
• A Study on Advanced Techniques for Fractional Differential Equations: Integrating the Frobenius Method, ZZ Transform, and Diverse Machine Learning Approaches

  2024cites this paper
• Exploring Remote Cardiac Signals for Biometric Verification: A Study Using Eulerian Video Magnification

  2024cites this paper
• Completely monotone functions in general and some applications

  2024cites this paper
• On variants of Chebyshev’s conjecture

  2024cites this paper
• Revisiting the Laplace transform in quantum mechanics: correcting a flawed approach for the stationary Schrödinger equation

  2024cites this paper
• Series expansion, higher-order monotonicity properties and inequalities for the modulus of the Grötzsch ring

  2024influential citation
• Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities

  2024cites this paper
• Integral representation and functional inequalities involving generalized polylogarithm

  2024cites this paper
• Traveling wave fronts for a nonlocal system with delays in both diffusion and reaction terms

  2024influential citation
• Laplace-Stieltjes Transform and its Asymptotic Expansion

  2024cites this paper
• An incomplete Riemann Zeta function as a fractional integral

  2024cites this paper
• On some inequalities for the two-parameter Mittag-Leffler function in the complex plane

  2024influential citation
• Interaction Between Initial Behavior of Temperature and the Mean Curvature of the Interface in Two-Phase Heat Conductors

  2024cites this paper
• A Higher-Order Otto Calculus Approach to the Gaussian Completely Monotone Conjecture

  2024cites this paper
• Formalization of Differential Privacy in Isabelle/HOL

  2024cites this paper
• Positivity properties of scattering amplitudes

  2024influential citation
• A characterization of completely alternating functions

  2024cites this paper
• On regularity of mild solutions for autonomous linear retarded functional differential equations

  2024influential citation
• ON ABSOLUTELY MONOTONIC FUNCTIONS AND SOME INEQUALITIES FOR SPECIAL FUNCTIONS

  2024cites this paper
• One-point correlators of conserved and nonconserved charges in QCD

  2024cites this paper
• Bounds for certain function related to the incomplete Fox-Wright function

  2024cites this paper
• On the Laplace transform

  2024cites this paper
• Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function

  2024cites this paper
• Applying Laplace Transformation on Epidemiological Models as Caputo Derivatives

  2024cites this paper
• Rounding Error Analysis of an Orbital Collision Probability Evaluation Algorithm

  2024cites this paper
• Characteristics of Convergence and Stability of Some Methods for Inverting the Laplace Transform

  2024cites this paper
• Effect of non-local thermoelasticity on diffusion under hydrostatic pressure

  2024cites this paper
• \({K}\)-Positivity Preservers and Their Generators

  2024cites this paper
• Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity

  2024influential citation
• Laplace Transform in Mathematics and Electrical Engineering: A Praxeological Analysis of Two Textbooks on the Differential Equations and Signal Processing

  2024influential citation
• The effect of reducible Markov modulation on tail probabilities in models of random growth

  2024cites this paper
• The Leray transform: distinguished measures, symmetries and polygamma inequalities

  2024cites this paper
• Complete monotonicity of the remainder in an asymptotic series related to the psi function

  2024influential citation
• Cesàro operators associated with Borel measures acting on weighted spaces of holomorphic functions with sup-norms

  2024cites this paper
• Some Grönwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes

  2024cites this paper
• A Hybrid Laplace Transform-Optimal Homotopy Asymptotic Method (LT-OHAM) for Solving Integro-Differential Equations of the Second Kind

  2024influential citation
• Traveling waves for a nonlocal dispersal SIRS epidemic model with age structure

  2024cites this paper
• Pseudo rough Vol-of-Vol through Markovian Approximation

  2024cites this paper
• Inequalities for 1/(1-cos(x)) and its derivatives

  2024cites this paper
• The Slepian model based independent interval approximation of persistency and zero-level excursion distributions

  2024cites this paper
• Precise large deviations through a uniform Tauberian theorem

  2024cites this paper
• On the relaxation property of nonlinear circuit elements

  2024cites this paper
• Mixed Poisson families with real-valued mixing distributions

  2024cites this paper
• On discrete-time arrival processes and related random motions

  2024cites this paper
• Integral representations with logarithmic and certain special functions

  2024influential citation
• Hankel operators with band spectra and elliptic functions

  2023cites this paper
• Bounds on the size of the convex hull of planar Brownian motion and related inverse processes

  2023cites this paper