Abstract: In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the ...

Abstract: To establish an alternative analytical framework for the elastic‐wave imaging of underground cavities, the focus of this study is an extension of the concept of topological derivative, ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...

Quadratic functions are essential in the world of mathematics and have a wide range of applications in various fields, such as physics, engineering, and finance. An inverse function can be thought of ...

The sample inverse autocorrelation function (SIACF) plays much the same role in ARIMA modeling as the sample partial autocorrelation function (SPACF) but generally indicates subset and seasonal ...

1. Relations and Functions Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 2. Inverse Trigonometric Functions Definition, range, domain, ...