Fractional calculus extends the classical notions of differentiation and integration to non-integer orders, offering an adaptable framework that is particularly well suited to modelling anomalous ...

Real and complex functions form the backbone of modern mathematical analysis, uniting the study of continuity, differentiability, and integrability on the real line with the rich structure of analytic ...

Explore the profound connection between Euler's Identity and the Taylor series, two foundational concepts in mathematics. This overview explains how the expansion of exponential functions using the ...

Complex analysis, or the calculus of complex-valued functions, is one of the most beautiful self-contained areas of mathematics. In many ways simpler than real one-variable calculus, it is possible to ...

Complex analysis, or the calculus of complex-valued functions, is one of the most beautiful self-contained areas of mathematics. In many ways simpler than real one-variable calculus, it is possible to ...

We present a definition of holomorphic function and an approach to the Cauchy theory that presents complex function theory as a natural outgrowth of multivariable calculus. Journal Information ...

Applications of Fréchet derivative emerge in the sensitivity analysis of matrix functions. Our work extends the generalized complex step approximation using the complex computation f(A + eiθhE) as a ...

The Applied Mathematics Program is open to those students who have earned a B.S. degree in engineering, science, or mathematics, provided that the student has completed a program in undergraduate ...