Mathematics in the 21st Century
6th World Conference, Lahore, March 2013
Book and Conference Proceedings
Book
Chapter
Any real number is made accessible through its rational approximations, for example, cutting off the decimals starting with \((n+1)\) ...
Chapter
A suggestive definition (though not entirely accurate) for the notion of series, is that of a sum with infinitely many terms.
Chapter
The previous chapters outlined the important role played by the convergent sequences in their relationship with the topological theory of metric spaces.
Chapter
The Riemann integral applies only to bounded functions defined on compact intervals. This severe restriction can be relaxed by considering larger concepts of integrability.
Chapter
Differential calculus is devoted to the study of differentiable functions. Historically, there were two sources of differential calculus: the problem of finding the slope of the tangent line to the graph of a ...
Chapter
Fourier series decompose periodic functions or periodic signals into the sum of a countable family of simple oscillating functions, namely sines and cosines (or complex exponentials).
Chapter
Real analysis of one variable is based on a description of the main structures (algebraic, ordered, and metric) of \(\mathbb {R}\) ...
Chapter
Though in this book we are primarily interested in the properties of functions of a real variable, it is useful to know some concepts and facts in a greater generality. This not only gives a better perspective...
Chapter
Many problems in mathematical analysis lead to certain questions relative to the nature of suitable sets. For example, this is the case of the subject of continuity, that will be detailed in the next chapter.
Chapter
The purpose of this chapter is to give a self-contained presentation of the so-called elementary functions, such as the exponential, the logarithm, the power function, the sine and the cosine functions, and so on...
Chapter
In 1901, H. Lebesgue published the paper announcing the discovery of the integral that now bears his name.
Chapter
Since antiquity, people were interested in computing the length of curves, the area of surfaces, and the volumes of solids.
Article
Let X be a weakly 1-complete surface and (Y, π) be a, possibly ramified, Riemann domain over X. If \(H^1(Y,{\mathcal{O}}^*) = 0\) ...
Article
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family \(\{U(t, s)\}_{t \geq s \geq 0}\) ...
Article
Some codimension 2 projective complete intersections are related to local hypersurface singularities. Necessary and sufficient conditions are given such that the singularities obtained are isolated. Incidental...