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  • BTU Cottbus  (8)
  • SB Guben
  • Bildungsgesch. Forschung
  • Kreisbibliothek des Landkreises Spree-Neiße
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  • Einführung  (8)
  • 1
    Buch
    Buch
    New York [u.a.] :Oxford Univ. Press,
    UID:
    almahu_BV010893404
    Umfang: XIII, 306 S. : graph. Darst.
    ISBN: 0-19-510095-6
    Inhalt: "Why is the future so different from the past? Why does the past affect the future and not the other way around? What does quantum mechanics really tell us about the world? In this important and accessible book, Huw Price throws fascinating new light on some of the great mysteries of modern physics, and connects them in a wholly original way." "Price begins with the mystery of the arrow of time. Why, for example, does disorder always increase, as required by the second law of thermodynamics? Price shows that, for over a century, most physicists have thought about these problems the wrong way. Misled by the human perspective from within time, which distorts and exaggerates the differences between past and future, they have fallen victim to what Price calls the "double standard fallacy": proposed explanations of the difference between the past and the future turn out to rely on a difference which has been slipped in at the beginning, when the physicists themselves treat the past and future in different ways. To avoid this fallacy, Price argues, we need to overcome our natural tendency to think about the past and the future differently. We need to imagine a point outside time - an Archimedean "view from nowhen" - from which to observe time in an unbiased way."
    Inhalt: "Price then turns to the greatest mystery of modern physics, the meaning of quantum theory. He argues that in missing the Archimedean viewpoint, modern physics has missed a radical and attractive solution to many of the apparent paradoxes of quantum physics. Many consequences of quantum theory appear counter-intuitive, such as Schrodinger's Cat, whose condition seems undetermined until observed, and Bell's Theorem, which suggests a spooky "nonlocality," where events happening simultaneously in different places seem to affect each other directly. Price shows that these paradoxes can be avoided by allowing that at the quantum level the future does, indeed, affect the past. This demystifies nonlocality, and supports Einstein's unpopular intuition that quantum theory describes an objective world, existing independently of human observers: the Cat is alive or dead, even when nobody looks. So interpreted, Price argues, quantum mechanics is simply the kind of theory we ought to have expected in microphysics - from the symmetric standpoint."--BOOK JACKET
    Sprache: Englisch
    Fachgebiete: Physik , Philosophie
    RVK:
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    Schlagwort(e): Zeit ; Physik ; Zeitrichtung ; Physik ; Philosophie ; Zeit ; Physik ; Philosophie ; Zeitrichtung ; Einführung ; Einführung ; Einführung
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  • 2
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York :
    UID:
    almahu_9947362963902882
    Umfang: XII, 260 p. , online resource.
    ISBN: 9781461300779
    Serie: Undergraduate Texts in Mathematics,
    Inhalt: This is a reprint of "A First Course in Calculus," which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students'background was not as substantial as it might be. We are now back to those times, so it's time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950.
    Anmerkung: I Numbers and Functions -- 1. Integers, rational numbers and real numbers -- 2. Inequalities -- 3. Functions -- 4. Powers -- II Graphs and Curves -- l. Coordinates -- 2. Graphs -- 3. The straight line -- 4. Distance between two points -- 5. Curves and equations -- 6. The circle -- 7. The parabola. Changes of coordinates -- 8. The hyperbola -- III The Derivative -- l. The slope of a curve -- 2. The derivative -- 3. Limits -- 4. Powers -- 5. Sums, products, and quotients -- 6. The chain rule -- 7. Rate of change -- IV Sine and Cosine -- l. The sine and cosine functions -- 2. The graphs -- 3. Addition formula -- 4. The derivatives -- 5. Two basic limits -- V The Mean Value Theorem -- 1. The maximum and minimum theorem -- 2. Existence of maxima and minima -- 3. The mean value theorem -- 4. Increasing and decreasing functions -- VI Sketching Curves -- 1. Behavior as x becomes very large -- 2. Curve sketching -- 3. Pol ar coordinates -- 4. Parametric curves -- VII Inverse Functions -- 1. Definition of inverse functions -- 2. Derivative of inverse functions -- 3. The arcsine -- 4. The arctangent -- VIII Exponents and Logarithms -- 1. The logarithm -- 2. The exponential function -- 3. The general exponential function -- 4. Order of magnitude -- 5. Some applications -- IX Integration -- 1. The indefinite integral -- 2. Continuous functions -- 3. Area -- 4. Upper and lower sums -- 5. The fundamental theorem -- 6. The basic properties -- X Properties of the Integral -- 1. Further connection with the derivative -- 2. Sums -- 3. Inequalities -- 4. Improper integrals -- XI Techniques of Integration -- 1. Substitution -- 2. Integration by parts -- 3. Trigonometric integrals -- 4. Partial fractions -- XII Some Substantial Exercises -- 1. An estimate for (n!)1/n -- 2. Stirling’s formula -- 3. Wallis’ product -- XIII Applications of Integration -- 1. Length of curves -- 2. Area in polar coordinates -- 3. Volumes of revolution -- 4. Work -- 5. Moments -- XIV Taylor’s Formula -- 1. Taylor’s formula -- 2. Estimate for the remainder -- 3. Trigonometric functions -- 4. Exponential function -- 5. Logarithm -- 6. The arctangent -- 7. The binomial expansion -- XV Series -- 1. Convergent series -- 2. Series with positive terms -- 3. The integral test -- 4. Absolute convergence -- 5. Power series -- 6. Differentiation and integration of power series -- Appendix 1. ? and ? -- 1. Least upper bound -- 2. Limits -- 3. Points of accumulation -- 4. Continuous functions -- Appendix 2. Physics and Mathematics -- Answers -- Supplementary Exercises.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9780387953274
    Sprache: Englisch
    Schlagwort(e): Einführung
    URL: Volltext  (lizenzpflichtig)
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  • 3
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York :
    UID:
    almahu_9947362881602882
    Umfang: XII, 440 p. , online resource.
    ISBN: 9780387216843
    Serie: Undergraduate Texts in Mathematics,
    Inhalt: Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past presentations of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians such as Dieudonne, Littlewood and Osserman. This book is based on the honors version of a course which the author has taught many times over the last 35 years at Berkeley. The book contains an excellent selection of more than 500 exercises.
    Anmerkung: 1 Real Numbers -- 2 A Taste of Topology -- 3 Functions of a Real Variable -- 4 Function Spaces -- 5 Multivariable Calculus -- 6 Lebesgue Theory.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781441929419
    Sprache: Englisch
    Schlagwort(e): Einführung
    URL: Volltext  (lizenzpflichtig)
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  • 4
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York :
    UID:
    almahu_9947362976302882
    Umfang: XII, 180 p. 1 illus. , online resource.
    ISBN: 9781461299233
    Serie: Graduate Texts in Mathematics, 51
    Inhalt: This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin­ ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.
    Anmerkung: 0 Calculus in Euclidean Space -- 1 Curves -- 2 Plane Curves: Global Theory -- 3 Surfaces: Local Theory -- 4 Intrinsic Geometry of Surfaces: Local Theory -- 5 Two-dimensional Riemannian Geometry -- 6 The Global Geometry of Surfaces -- References -- Index of Symbols.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781461299257
    Sprache: Englisch
    Schlagwort(e): Einführung
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  • 5
    Online-Ressource
    Online-Ressource
    New York, NY :Springer New York,
    UID:
    almahu_9947362835302882
    Umfang: XII, 205 p. , online resource.
    ISBN: 9781461227267
    Serie: Springer Texts in Statistics,
    Inhalt: These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron­ Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com­ putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.
    Anmerkung: I. Univariate Random Variables -- Discrete Random Variables -- Properties of Expectation -- Properties of Characteristic Functions -- Basic Distributions -- Absolutely Continuous Random Variables -- Basic Distributions -- Distribution Functions -- Computer Generation of Random Variables -- Exercises -- II. Multivariate Random Variables -- Joint Random Variables -- Conditional Expectation -- Orthogonal Projections -- Joint Normal Distribution -- Multi-Dimensional Distribution Functions -- Exercises -- III. Limit Laws -- Law of Large Numbers -- Weak Convergence -- Bochner’s Theorem -- Extremes -- Extremal Distributions -- Large Deviations -- Exercises -- IV. Markov Chains—Passage Phenomena -- First Notions and Results -- Limiting Diffusions -- Branching Chains -- Queueing Chains -- Exercises -- V. Markov Chains—Stationary Distributions and Steady State -- Stationary Distributions -- Geometric Ergodicity -- Examples -- Exercises -- VI. Markov Jump Processes -- Pure Jump Processes -- Poisson Process -- Birth and Death Process -- Exercises -- VII. Ergodic Theory with an Application to Fractals -- Ergodic Theorems -- Subadditive Ergodic Theorem -- Products of Random Matrices -- Oseledec’s Theorem -- Fractals -- Bibliographical Comments -- Exercises -- References -- Solutions (Sections I–V).
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781461276432
    Sprache: Englisch
    Schlagwort(e): Einführung ; Electronic books.
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  • 6
    Buch
    Buch
    New York [u.a.] : Wiley
    UID:
    b3kat_BV011520694
    Umfang: XII, 195 S. , graph. Darst.
    ISBN: 0471154083
    Serie: Wiley-Interscience series in discrete mathematics and optimization
    Inhalt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections - Existence, Enumeration, and Construction - begins with a simply stated, first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text - in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
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    Schlagwort(e): Kombinatorik ; Einführung
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  • 7
    Online-Ressource
    Online-Ressource
    New York, NY : Springer New York
    UID:
    b3kat_BV045186405
    Umfang: 1 Online-Ressource (XVIII, 522 p)
    ISBN: 9781461261261
    Serie: Texts and Monographs in Physics
    Inhalt: This book was written as a text, although many may consider it a mono­ graph. As a text it has been used several times in both the one-year graduate quantum-mechanics course and (in its shortened version) in a senior quantum mechanics course that I taught at the University of Texas at Austin. It is self-contained and does not require any prior knowledge of quantum mechanics. It also introduces the mathematical language of quantum mechanics, starting with the definitions, and attempts to teach this language by using it. Therefore, it can, in principle, be read without prior knowledge of the theory of linear operators and linear spaces, though some familiarity with linear algebra would be helpful. Prerequisites are knowledge of calculus and of vector algebra and analysis. Also used in a few places are some elementary facts of Fourier analysis and differential equations. Most physical examples are taken from the fields of atomic and molecular physics, as it is these fields that are best known to students at the stage when they learn quantum mechanics. This book may be considered a monograph because the presentation here is different from the usual treatment in many standard textbooks on quantum mechanics. It is not that a "different kind" of quantum mechanics is pre­ sented here; this is conventional quantum mechanics (" Copenhagen inter­ pretation ")
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 9781461261285
    Sprache: Englisch
    Schlagwort(e): Quantenmechanik ; Quantentheorie ; Bohmsche Quantenmechanik ; Einführung ; Lehrbuch
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 8
    Online-Ressource
    Online-Ressource
    Berlin, Heidelberg : Springer Berlin Heidelberg
    UID:
    b3kat_BV042423148
    Umfang: 1 Online-Ressource (IX, 79p. 65 illus)
    ISBN: 9783642967993
    Originaltitel: Teorija katastrof
    Anmerkung: Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of bypassing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bibliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-controversial results from the mathematical theories of singularities and bifurcation. The author has tried to explain the essence of the fundamental results and applications to readers having minimal mathematical background but the reader is assumed to have an inquiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-540-12859-5
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    RVK:
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    Schlagwort(e): Singularität ; Kataklysmentheorie ; Katastrophentheorie ; Einführung
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