This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

Transactions of the American Mathematical Society, Vol. 176 (Feb., 1973), pp. 305-318 (14 pages) The theory of monotone matrix functions has been developed by K. Loewner; he first gives some necessary ...

Functions of two variables can be visualized in many ways: heat maps in 2D, contour curves in 2D, wireframes in 3D, surfaces in 3D. We begin by defining a function of two variables, building an array ...

Abstract: Functions of two variables appear frequently in engineering studies. Students have particular difficulties in understanding how the graphs of these functions are. This paper presents a ...

Many types of economic problems require that we consider two variables at the same time. A typical example is the relation between price of a commodity and the demand or supply of that commodity. The ...

Let $f$ be a [[functions of two variables]] whose domain $D$ includes points arbitrarily close to $(a, b)$. Then we say that the [[limit]]of $f(x, y)$ as $(x, y ...

THIS is emphatically a text-book, deductive in method and Euclidean in arrangement; as such, it has the defects of its qualities, but its merits are undeniable. In this volume the author deals with ...

ABSTRACT: The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and ...