Presenting basic results of topology calculus of several variables and approximation theory
which are rarely treated in a single volume this textbook includes several beautiful but
almost forgotten classical theorems of Descartes Erdös Fejér Stieltjes and Turán. The
exposition style of Topology Calculus and Approximation follows the Hungarian mathematical
tradition of Paul Erdös and others. In the first part the classical results of Alexandroff
Cantor Hausdorff Helly Peano Radon Tietze and Urysohn illustrate the theories of metric
topological and normed spaces. Following this the general framework of normed spaces and
Carathéodory's definition of the derivative are shown to simplify the statement and proof of
various theorems in calculus and ordinary differential equations. The third and final part is
devoted to interpolation orthogonal polynomials numerical integration asymptotic expansions
and the numerical solution of algebraic and differential equations. Students of both pure and
applied mathematics as well as physics and engineering should find this textbook useful. Only
basic results of one-variable calculus and linear algebra are used and simple yet pertinent
examples and exercises illustrate the usefulness of most theorems. Many of these examples are
new or difficult to locate in the literature and so the original sources of most notions and
results are given to help readers understand the development of the field.
