Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

Scientists employed a mathematical model to simulate the differentiation of epithelial cells based on signaling molecules from the liver's portal vein. This work may lead to new tools to better ...

Model natural and engineered hydraulic and hydrologic systems. Manage large datasets and develop models for hydrodynamics. Gain in-depth modeling experience using real-world case studies in a ...

In fields such as physics and engineering, partial differential equations (PDEs) are used to model complex physical processes to generate insight into how some of the most complicated physical and ...

SIAM Journal on Numerical Analysis, Vol. 46, No. 5 (2008), pp. 2411-2442 (32 pages) This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial ...

In this paper, a partial differential equation model for the pricing of pension plans based on average salary is posed by using the dynamic hedging methodology. The existence and uniqueness of ...

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for ...

We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into the ...