This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of in…
Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a …
ABSTRACT The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations. Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. No…
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explaine…
ABSTRACT An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, …
In diesem Open-Access-Buch werden professionelle Kompetenzen von angehenden Mathematiklehrkräften untersucht, die sie zur Förderung des Mathematiklernens und zur Motivationsförderung von Schüler*innen mit Lernschwierigkeiten benötigen. Dazu werden zunächst Grundsätze der Förderung dieser Schüler*innengruppe formuliert und, unter Berücksichtigung der Forschung zu professionellen Kompet…
This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and en…
This book collects selected contributions presented at the INdAM Workshop "Geometric Challenges in Isogeometric Analysis", held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed geometries. A variety of research topics in this co…
Dieser Open-Access-Sammelband stellt Perspektiven auf digitalen MINT-Unterricht und die Lehrkräftebildung der Zukunft dar. Auf Grundlage aktueller Forschungsergebnisse beantwortet er aktuelle Fragestellungen, etwa: Welche Kompetenzen und welche Lerninhalte werden für die Herausforderungen von morgen benötigt und welchen Beitrag können die MINT-Fächer dazu leisten? Inwiefern kann die Digita…
This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer S…