Applied Mathematicsematics

Calculus with Curvilinear Coordinates Problems and Solutions

This book presents problems and solutions in calculus with curvilinear coordinates. Vector analysis can be performed in different coordinate systems, an optimal system considers the symmetry of the problem in order to reduce calculatory difficulty. The book presents the material in arbitrary orthogonal coordinates, and includes ...

Sciences des donnees et apprentissage en grande dimension

Les sciences des données ont pour but de répondre à des questions à partir de données ayant un très grand nombre de variables, qu’il s’agisse d’images, de sons, de textes, de données génomiques, de liens dans des réseaux sociaux ou de mesures physiques. Cette multitude de variables ouvre un champ gigantesque des possibles, ce qu...

Scientific Computing: An Introductory Survey (Revised 2nd Edition)

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including...

Quantitative Methods of Data Analysis for the Physical Sciences and Engineering (1st Edition)

This book provides thorough and comprehensive coverage of most of the new and important quantitative methods of data analysis for graduate students and practitioners. In recent years, data analysis methods have exploded alongside advanced computing power, and it is critical to understand such methods to get the most out of data,...

Tensor Numerical Methods in Quantum Chemistry

The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality," that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multiva...

Elementary Introduction to the Lebesgue Integral

It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a devi...

Applied Mathematics: A Very Short Introduction

Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics...

Tensor Analysis: Spectral Theory and Special Tensors

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory - some of which are nontrivial - have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimiz...