A comprehensive analysis of continuous time in dynamic economic models, characterized by differential equations, contrasting with discrete time approaches using difference equations.
A comprehensive look at differential equations, their historical context, types, applications, and importance in mathematics and science.
Differential equations involve unknown functions and their derivatives and are fundamental in describing various physical phenomena.
Differential games are strategic scenarios played in continuous time where the state of the system evolves according to differential equations influenced by the players' strategies.
An in-depth exploration of eigenvalues and eigenvectors, their importance in various mathematical and applied contexts including PCA for dimensionality reduction and solving systems of differential equations.
Integral calculus is closely related to differential equations and forms a fundamental part of calculus, which is essential in mathematics and its applications.
An in-depth look at Ito Calculus, including its historical context, mathematical framework, key formulas, applications, and importance in financial mathematics and other fields.
Explore the Laplace Transform, a mathematical technique for transforming time-domain functions into the s-domain, simplifying the solution of linear differential equations.
A detailed exploration of the Logistic Curve, its historical context, mathematical formulation, applications, and significance in various fields.
Optimal Control is a method used to solve dynamic optimization problems formulated in continuous time, typically by using Pontryagin's maximum principle or solving the Hamilton--Jacobi--Bellman equation.
Comprehensive understanding of Stochastic Differential Equations (SDEs), their types, applications, and significance in modeling systems influenced by random noise.
A comprehensive guide to boundary conditions, including their definition, types, applications in various fields, and their importance in determining the price range of options.
