Multivariable Calculus and Mathematica

Author: Kevin R. Coombes
Publisher: Springer Science & Business Media
ISBN: 9781461216988
Release Date: 2012-12-06
Genre: Mathematics

Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica.

Multivariable Calculus with MATLAB

Author: Ronald L. Lipsman
Publisher: Springer
ISBN: 9783319650708
Release Date: 2017-12-06
Genre: Mathematics

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.

Analysis II

Author: Vladimir A. Zorich
Publisher: Springer
ISBN: 3540462317
Release Date: 2007-03-02
Genre: Mathematics

Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.

Panoptimum

Author: Stefan Hildebrandt
Publisher: Spektrum Akademischer Verlag
ISBN: 3922508820
Release Date: 1987
Genre: Minimal surfaces


Distributionen Und Hilbertraumoperatoren

Author: Philippe Blanchard
Publisher: Springer
ISBN: 321182507X
Release Date: 1993-09-21
Genre: Science

Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.

Mathematische Physik Klassische Mechanik

Author: Andreas Knauf
Publisher: Springer-Verlag
ISBN: 9783662557761
Release Date: 2017-11-07
Genre: Science

Als Grenztheorie der Quantenmechanik besitzt die klassische Dynamik einen großen Formenreichtum – vom gut berechenbaren bis zum chaotischen Verhalten. Ausgehend von interessanten Beispielen wird in dem Band nicht nur eine gelungene Auswahl grundlegender Themen vermittelt, sondern auch der Einstieg in viele aktuelle Forschungsgebiete im Bereich der klassischen Mechanik. Didaktisch geschickt aufgebaut und mit hilfreichen Anhängen versehen, werden lediglich Kenntnisse der Grundvorlesungen in Mathematik vorausgesetzt. Mit über 100 Aufgaben und Lösungen.

Differentialgeometrie von Kurven und Fl chen

Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 9783322850720
Release Date: 2013-04-17
Genre: Technology & Engineering

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Physik per Computer

Author: Wolfgang Kinzel
Publisher: Springer
ISBN: 3827400201
Release Date: 1996
Genre: Mathematical physics

Das Gebiet Computational Physics gewinnt zunehmend an Bedeutung - auch im Physikstudium. Anhand von vierzig Beispielen aus verschiedenen Bereichen der Physik zeigen die Autoren, wie physikalische Modelle numerisch untersucht werden kAnnen. Schritt fA1/4r Schritt werden Algorithmen formuliert und Programme entwickelt, um mit ihrer Hilfe das jeweilige physikalische Problem zu "verstehen" und zu lAsen. Die Autoren behandeln Modelle aus der klassischen Physik und aus der aktuellen physikalischen Forschung; als Programmiersprachen verwenden sie Mathematica A(R) und C. Die beiliegende Diskette enthAlt alle Programme - fA1/4r den PC unter DOS auch als ausfA1/4hrbaren Code.

Anschauliche Funktionentheorie

Author: Tristan Needham
Publisher: Oldenbourg Wissenschaftsverlag
ISBN: 348670902X
Release Date: 2011-09-21
Genre: Mathematics

Needhams neuartiger Zugang zur Funktionentheorie wurde von der Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der sonst oft als trocken empfundenen Funktionentheorie. 'Anschauliche Funktionentheorie ist eine wahre Freude und ein Buch so recht nach meinem Herzen. Indem er ausschließlich seine neuartige geometrische Perspektive verwendet, enthüllt Tristan Needham viele überraschende und bisher weitgehend unbeachtete Facetten der Schönheit der Funktionentheorie.' (Sir Roger Penrose)

Grassmann Algebra Volume 1 Foundations

Author: John Browne
Publisher: John M Browne
ISBN: 9781479197637
Release Date: 2012-10-25
Genre: Mathematics

Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grass­mann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.

Technische Mechanik 3

Author: Friedrich U. Mathiak
Publisher: Walter de Gruyter
ISBN: 3110438046
Release Date: 2015-09-01
Genre: Technology & Engineering

This third volume of the Engineering Mechanics series cover the kinematics and kinetics of rigid bodies including their oscillations and has as its aim to impart engineering students with a deeper knowledge of mathematical methods. The use of computer algebra and simulation systems enables extended interpretation with parameter studies.