Commonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and ...

The tfc Python module is designed to help you quickly and easily apply the Theory of Functional Connections (TFC) to optimization problems. For more information on the code itself and code-based ...

Have you ever wondered why we discard process knowledge and revert to Laplace transforms and linear models for control when first-principles models can work? So did I. Have you ever wondered why we ...

First principles models are ready for prime time in process control. Have you ever wondered why we discard process knowledge and revert to Laplace transforms and linear models for control when ...

Heat energy plays an essential role in numerous engineering applications, from thermal management in electronic devices to the design of efficient energy systems. Understanding and predicting the ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...

Department of Chemical and Biological Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, OntarioK1N 6N5, Canada ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...