Michael Oberguggenberger's Books

Analysis for Computer Scientists

Foundations, Methods, and Algorithms

By: Michael Oberguggenberger,Alexander Ostermann

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Analysis for Computer Scientists

Foundations, Methods, and Algorithms

By: Michael Oberguggenberger,Alexander Ostermann

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises. Topics and features: describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); contains experiments, exercises, definitions, and propositions throughout the text; supplies programming examples in Python, in addition to MATLAB (NEW); provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material. Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.

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Page Count

372

Publisher

Springer

Published Date

ISBN 10

3319911554

ISBN 13

9783319911557

Geometric Theory of Generalized Functions with Applications to General Relativity

By: M. Grosser,M. Kunzinger,Michael Oberguggenberger,R. Steinbauer

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Geometric Theory of Generalized Functions with Applications to General Relativity

By: M. Grosser,M. Kunzinger,Michael Oberguggenberger,R. Steinbauer

Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.

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517

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401598452

ISBN 13

9789401598453

On the Foundations of Nonlinear Generalized Functions I and II

By: Michael Grosser

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On the Foundations of Nonlinear Generalized Functions I and II

By: Michael Grosser

In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827294

ISBN 13

9780821827291

Distribution Solutions of Nonlinear Systems of Conservation Laws

By: Michael Sever

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Distribution Solutions of Nonlinear Systems of Conservation Laws

By: Michael Sever

The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist. At any given time, the singularities thus arising admit representation as weak limits of suitable approximate solutions in the space of measures with respect to the space variable. Two distinct classes of singularities have emerged in this context, known as delta-shocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of delta-shocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for delta-shocks, the density approximations majorize the flux approximations, whereas for singular shocks, the flux approximations blow up faster. As against that admissible singular shocks have viscous structure.

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082183990X

ISBN 13

9780821839904

Lectures on Bifurcations, Dynamics and Symmetry

By: Michael J. Field

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Lectures on Bifurcations, Dynamics and Symmetry

By: Michael J. Field

This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.

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Page Count

172

Publisher

CRC Press

Published Date

ISBN 10

1000673472

ISBN 13

9781000673470

Adam Smith

Essays on Adam Smith’S Original Contributions to Economic Thought and the Parallels with the Economic Thought of John Maynard Keynes

By: MICHAEL EMMETT BRADY

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Adam Smith

Essays on Adam Smith’S Original Contributions to Economic Thought and the Parallels with the Economic Thought of John Maynard Keynes

By: MICHAEL EMMETT BRADY

Adam Smiths original, path breaking work on decision making, uncertainty and public policies to minimize the impact of uncertainty in the economy has been overlooked for well over two hundred years. One need only peruse the badly analyzed work of Smith in this area as presented by Henry D MacLeod in his The Elements of Political Economy on pp.212-220 or Henry Sidgwicks The Principles of Political Economy on pp.359-361, as well as the misevaluations of Smiths contributions made by Jacob Viner in 1927, Joseph Schumpeter in 1954, Murray Rothbard in 1995, or Salim Rashid in 1998 to realize that Smiths important contributions were never recognized. The claim that Smith made no original contributions to economic theory or economics is simply false.

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Page Count

190

Publisher

Xlibris Corporation

Published Date

ISBN 10

1503587320

ISBN 13

9781503587328

Computational Hydraulics

By: Michael B. Abbott,Anthony W. Minns

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Computational Hydraulics

By: Michael B. Abbott,Anthony W. Minns

This is the updated new edition from the founder and inventor of the subject. It provides an account of the principles and a survey of modelling in hydraulic, coastal and offshore engineering.

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Page Count

576

Publisher

Routledge

Published Date

ISBN 10

1351949853

ISBN 13

9781351949859

Fuzzy Randomness

Uncertainty in Civil Engineering and Computational Mechanics

By: Bernd Möller,Michael Beer

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Fuzzy Randomness

Uncertainty in Civil Engineering and Computational Mechanics

By: Bernd Möller,Michael Beer

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of stochastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit stochastic and nonstochastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

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Page Count

351

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662073587

ISBN 13

9783662073582

The Mathematica GuideBook for Programming

By: Michael Trott

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The Mathematica GuideBook for Programming

By: Michael Trott

This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists. An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.

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Page Count

1080

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387942823

ISBN 13

9780387942827

Analysis for Computer Scientists

Foundations, Methods, and Algorithms

By: Michael Oberguggenberger,Alexander Ostermann

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Analysis for Computer Scientists

Foundations, Methods, and Algorithms

By: Michael Oberguggenberger,Alexander Ostermann

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Solve jigsaw puzzle

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Page Count

372

Publisher

Springer

Published Date

ISBN 10

3319911554

ISBN 13

9783319911557

Geometric Theory of Generalized Functions with Applications to General Relativity

By: M. Grosser,M. Kunzinger,Michael Oberguggenberger,R. Steinbauer

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Geometric Theory of Generalized Functions with Applications to General Relativity

By: M. Grosser,M. Kunzinger,Michael Oberguggenberger,R. Steinbauer

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Page Count

517

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401598452

ISBN 13

9789401598453

Solution of Continuous Nonlinear PDEs Through Order Completion

By: Michael B. Oberguggenberger,Elemer E. Rosinger

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Solution of Continuous Nonlinear PDEs Through Order Completion

By: Michael B. Oberguggenberger,Elemer E. Rosinger

This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

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Page Count

432

Publisher

North Holland

Published Date

ISBN 10

0444820353

ISBN 13

9780444820358

Book's by Michael Oberguggenberger

Analysis for Computer Scientists

Analysis for Computer Scientists

Geometric Theory of Generalized Functions with Applications to General Relativity

Geometric Theory of Generalized Functions with Applications to General Relativity

On the Foundations of Nonlinear Generalized Functions I and II

On the Foundations of Nonlinear Generalized Functions I and II

Distribution Solutions of Nonlinear Systems of Conservation Laws

Distribution Solutions of Nonlinear Systems of Conservation Laws

Lectures on Bifurcations, Dynamics and Symmetry

Lectures on Bifurcations, Dynamics and Symmetry

Adam Smith

Adam Smith

Computational Hydraulics

Computational Hydraulics

Fuzzy Randomness

Fuzzy Randomness

The Mathematica GuideBook for Programming

The Mathematica GuideBook for Programming

Analysis for Computer Scientists

Analysis for Computer Scientists

Geometric Theory of Generalized Functions with Applications to General Relativity

Geometric Theory of Generalized Functions with Applications to General Relativity

Solution of Continuous Nonlinear PDEs Through Order Completion

Solution of Continuous Nonlinear PDEs Through Order Completion

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