Bøger af Volker Michel

Wozu braucht man eigentlich Mathematik? Haben Sie sich das auch schon gefragt oder sind Sie selbst Mathematiker/-in und hören dies oft?Mathematik ist weit mehr als die Suche nach der nächsten Primzahl oder dem x-ten Beweis des Satzes von Pythagoras. Mathematik ist eine zentrale Schlüsseltechnologie für viele Wissenschaftsbereiche. Die Frage, ob es einen Klimawandel gibt und wie man Veränderungen im Klima beobachtet, kann ohne Mathematik genauso wenig beantwortet werden wie die Frage, wie sich eine Pandemie ausbreitet. Viele weitere Beispiele werden in dem Buch angesprochen.In einem lockeren Erzählstil erläutert der Autor, wo überall Mathematik verborgen ist und wie man mit einfachen Mitteln schon verstehen kann, wie brisante Probleme gelöst werden. Vorausgesetzt werden (je nach Kapitel) teils gar keine Mathematik-Vorkenntnisse bis maximal zum Abitur-Wissen.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include:* the advantages and disadvantages of Fourier, spline, and wavelet methods* theory and numerics of orthogonal polynomials on intervals, spheres, and balls* cubic splines and splines based on reproducing kernels* multiresolution analysis using wavelets and scaling functionsThis textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

During the last few decades, the subject of potential theory has not been overly popular in the mathematics community. Neglected in favor of more abstract theories, it has been taught primarily where instructors have ac­ tively engaged in research in this field. This situation has resulted in a scarcity of English language books of standard shape, size, and quality covering potential theory. The current book attempts to fill that gap in the literature. Since the rapid development of high-speed computers, the remarkable progress in highly advanced electronic measurement concepts, and, most of all, the significant impact of satellite technology, the flame of interest in potential theory has burned much brighter. The realization that more and more details of potential functions are adequately visualized by "zooming­ in" procedures of modern approximation theory has added powerful fuel to the flame. It seems as if, all of a sudden, harmonic kernel functions such as splines and/or wavelets provide the impetus to offer appropriate means of assimilating and assessing the readily increasing flow of potential data, reducing it to comprehensible form, and providing an objective basis for scientific interpretation, classification, testing of concepts, and solutions of problems involving the Laplace operator.

Provides a basic foundation for students, practitioners, and researchers interested in some of the diverse areas of multiscale (geo)potential theory. This book develops mathematical methods enabling the gravitational potential of a planetary body to be modeled and analyzes using a continuous flow of observations from land or satellite devices.