Mathematics And Mechanics The Interplay

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Mathematics and Mechanics - The Interplay

Author : Luigi Morino
Publisher : Springer Nature
ISBN 13 : 3662632071
Total Pages : 1019 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Mathematics and Mechanics - The Interplay by : Luigi Morino

Download or read book Mathematics and Mechanics - The Interplay written by Luigi Morino and published by Springer Nature. This book was released on 2021-06-19 with total page 1019 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays an important role in mechanics and other human endeavours. Validating examples in this first volume include, for instance: the connection between the golden ratio (the “divine proportion" used by Phidias and many other artists and enshrined in Leonardo's Vitruvian Man, shown on the front cover), and the Fibonacci spiral (observable in botany, e.g., in the placement of sunflower seeds); is the coast of Tuscany infinitely long?; the equal-time free fall of a feather and a lead ball in a vacuum; a simple diagnostic for changing your car's shocks; the Kepler laws of the planets; the dynamics of the Sun-Earth-Moon system; the tides' mechanism; the laws of friction and a wheel rolling down a partially icy slope; and many more. The style is colloquial. The emphasis is on intuition - lengthy but intuitive proofs are preferred to simple non-intuitive ones. The mathematical/mechanical sophistication gradually increases, making the volume widely accessible. Intuition is not at the expense of rigor. Except for grammar-school material, every statement that is later used is rigorously proven. Guidelines that facilitate the reading of the book are presented. The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind. Sometimes mathematics was introduced independently of its mechanics applications, such as the absolute calculus for Einstein's general theory of relativity. Bio-sketches of all the scientists encountered are included and show that many of them dealt with both mathematics and mechanics.

Trends in Applications of Mathematics to Mechanics

Author : Johannes F. Besseling
Publisher : Springer Science & Business Media
ISBN 13 : 3642739334
Total Pages : 367 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Trends in Applications of Mathematics to Mechanics by : Johannes F. Besseling

Download or read book Trends in Applications of Mathematics to Mechanics written by Johannes F. Besseling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of mechanics the interplay between mathematics and physics is crucial for understanding not only underlying principles but also practical applications. This is particularly the case in hydrodynamics and elasticity. Over thirty articles in this volume discuss various aspects including perturbation methods and applications, instability, bifurcations and transition to chaos, multibody dynamics and control, mechanics and mathematics of non-classical materials, and new interactions of mathematics and mechanics. The book addresses scientists and engineers working in these areas including those interested in applied mathematical analysis.

A Mathematical Gift, III

Author : Koji Shiga
Publisher : American Mathematical Society
ISBN 13 : 9780821832844
Total Pages : 148 pages
Book Rating : 4.8/5 (328 download)

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Book Synopsis A Mathematical Gift, III by : Koji Shiga

Download or read book A Mathematical Gift, III written by Koji Shiga and published by American Mathematical Society. This book was released on 2005-07-18 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form).The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the Bolyai-Gerwien theorem about scissors-congruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, ""Mathematical World"".

Second Year Calculus

Author : David M. Bressoud
Publisher : Springer Science & Business Media
ISBN 13 : 1461209595
Total Pages : 399 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Second Year Calculus by : David M. Bressoud

Download or read book Second Year Calculus written by David M. Bressoud and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Circles Disturbed

Author : Apostolos Doxiadis
Publisher : Princeton University Press
ISBN 13 : 1400842689
Total Pages : 593 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Circles Disturbed by : Apostolos Doxiadis

Download or read book Circles Disturbed written by Apostolos Doxiadis and published by Princeton University Press. This book was released on 2012-03-18 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

The Mechanics and Thermodynamics of Continuous Media

Author : Miroslav Silhavy
Publisher : Springer Science & Business Media
ISBN 13 : 3662033895
Total Pages : 511 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis The Mechanics and Thermodynamics of Continuous Media by : Miroslav Silhavy

Download or read book The Mechanics and Thermodynamics of Continuous Media written by Miroslav Silhavy and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [...] It will be very useful for both mathematicians and physicists." EMS Newsletter

Algebraic Methods in Statistical Mechanics and Quantum Field Theory

Author : Dr. Gérard G. Emch
Publisher : Courier Corporation
ISBN 13 : 0486151719
Total Pages : 336 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Algebraic Methods in Statistical Mechanics and Quantum Field Theory by : Dr. Gérard G. Emch

Download or read book Algebraic Methods in Statistical Mechanics and Quantum Field Theory written by Dr. Gérard G. Emch and published by Courier Corporation. This book was released on 2014-08-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.

A Mathematical Gift, I

Author : Kenji Ueno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821832820
Total Pages : 156 pages
Book Rating : 4.8/5 (328 download)

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Book Synopsis A Mathematical Gift, I by : Kenji Ueno

Download or read book A Mathematical Gift, I written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2003 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three volumes originating from a series of lectures in mathematics given by professors of Kyoto University in Japan for high school students.

The Theoretical Foundations of Quantum Mechanics

Author : Belal E. Baaquie
Publisher : Springer Science & Business Media
ISBN 13 : 146146224X
Total Pages : 274 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Theoretical Foundations of Quantum Mechanics by : Belal E. Baaquie

Download or read book The Theoretical Foundations of Quantum Mechanics written by Belal E. Baaquie and published by Springer Science & Business Media. This book was released on 2013-01-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

Production Factor Mathematics

Author : Martin Grötschel
Publisher : Springer Science & Business Media
ISBN 13 : 364211248X
Total Pages : 405 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Production Factor Mathematics by : Martin Grötschel

Download or read book Production Factor Mathematics written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.

Circles Disturbed

Author : Apostolos Doxiadis
Publisher : Princeton University Press
ISBN 13 : 0691149046
Total Pages : 592 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Circles Disturbed by : Apostolos Doxiadis

Download or read book Circles Disturbed written by Apostolos Doxiadis and published by Princeton University Press. This book was released on 2012-03-18 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

The Mathematical Mechanic

Author : Mark Levi
Publisher : Princeton University Press
ISBN 13 : 1400830478
Total Pages : 197 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Mathematical Mechanic by : Mark Levi

Download or read book The Mathematical Mechanic written by Mark Levi and published by Princeton University Press. This book was released on 2009-07-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

Flag Varieties

Author : V Lakshmibai
Publisher : Springer
ISBN 13 : 9811313938
Total Pages : 312 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Flag Varieties by : V Lakshmibai

Download or read book Flag Varieties written by V Lakshmibai and published by Springer. This book was released on 2018-06-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.

A Comprehensible Universe

Author : George V. Coyne
Publisher : Springer Science & Business Media
ISBN 13 : 3540776265
Total Pages : 163 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis A Comprehensible Universe by : George V. Coyne

Download or read book A Comprehensible Universe written by George V. Coyne and published by Springer Science & Business Media. This book was released on 2008-05-15 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why is our world comprehensible? This question seems so trivial that few people have dared to ask it. In this book we explore the deep roots of the mystery of rationality. The inquiry into the rationality of the world began over two-and-a-half-thousand years ago, when a few courageous people tried to understand the world with the help of reason alone, rejecting the comforting fabric of myth and legend. After many philosophical and theological adventures the Greek concept of rationality laid the foundations of a revolutionary way of thinking: the scientific method, which transformed the world. But looking at the newest fruits of the world's rationality - relativity theory, quantum mechanics, the unification of physics, quantum gravity - the question arises: what are the limits of the scientific method? The principal tenet of rationality is that you should never stop asking questions until everything has been answered ... "A Comprehensible Universe is a thoughtful book by two authors who have professional expertise in physics and astronomy and also in theology. They are exceptionally well informed about the history of the relation between science and theology, and they maintain throughout their discussion a respect for empirical evidence and a dedication to rationality. Even though I do not agree with all of their conclusions on matters of great complexity I am impressed by the fairness of their argumentation." Abner Shimony, Professor Emeritus of Philosophy and Physics, Boston University

Partial Differential Equations of Mathematical Physics

Author : S. L. Sobolev
Publisher : Courier Corporation
ISBN 13 : 9780486659640
Total Pages : 452 pages
Book Rating : 4.6/5 (596 download)

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Book Synopsis Partial Differential Equations of Mathematical Physics by : S. L. Sobolev

Download or read book Partial Differential Equations of Mathematical Physics written by S. L. Sobolev and published by Courier Corporation. This book was released on 1964-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Mathematics and Materials

Author : N.J.) Staff Institute for Advanced Study (Princeton
Publisher :
ISBN 13 : 9781470437497
Total Pages : 342 pages
Book Rating : 4.4/5 (374 download)

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Book Synopsis Mathematics and Materials by : N.J.) Staff Institute for Advanced Study (Princeton

Download or read book Mathematics and Materials written by N.J.) Staff Institute for Advanced Study (Princeton and published by . This book was released on 2017 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this volume are based on lectures presented at the Park City summer school on "Mathematics and Materials" in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics

Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians

Author : Franco Strocchi
Publisher : World Scientific Publishing Company
ISBN 13 : 981310659X
Total Pages : 157 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians by : Franco Strocchi

Download or read book Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians written by Franco Strocchi and published by World Scientific Publishing Company. This book was released on 2005-11-17 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich-Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.