Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

Adjoint algorithmic differentiation is an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Often the differentiation does not cover the full pricing ...

Abstract: This paper concerns a derivation of second-order necessary conditions for a fixed-endpoint control problem of Lagrange involving mixed equality and/or inequality constraints, posed over ...

Abstract: For a class of input-delayed disturbed linear systems, this paper considers the problem of finite-time implicit-Lyapunov-function (ILF)-based control. With ILF as the evaluation of system ...

In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...

Implicit differentiation handles curves described by equations that do not solve neatly for $y$ as a function of $x$. Instead of rewriting the equation first, we ...

Recall that an indefinite integral (or antiderivative) is so called as it provides a family of solutions with a constant term. It is called indefinite as the constant \(c\) can take any real value, ...