دانلود کتاب The Dialectic Relation Between Physics and Mathematics in the XIXth Century

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The aim of this book is to analyse historical problems related to the use of mathematics in physics as well as to the use of physics in mathematics and to investigate Mathematical Physics as precisely the new discipline which is concerned with this dialectical link itself. So the main question is: When and why did the tension between mathematics and physics, explicitly practised at least since Galileo, evolve into such a new scientific theory? The authors explain the various ways in which this science allowed an advanced mathematical modelling in physics on the one hand, and the invention of new mathematical ideas on the other hand. Of course this problem is related to the links between institutions, universities, schools for engineers, and industries, and so it has social implications as well. The link by which physical ideas had influenced the world of mathematics was not new in the 19th century, but it came to a kind of maturity at that time. Recently, much historical research has been done into mathematics and physics and their relation in this period. The purpose of the Symposium and this book is to gather and re-evaluate the current thinking on this subject. It brings together contributions from leading experts in the field, and gives much-needed insight in the subject of mathematical physics from a historical point of view. Table of Contents The Dialectic Relation Between Physics and Mathematics in the XIXth Century ISBN 9789400753792 ISBN 9789400753808 Foreword Contents The Construction of Group Theory in Crystallography 1 Preamble: Contexts 2 The Origins of the Model of Triperiodic Assemblage 2.1 The First Approaches 2.2 The Sensualists 3 Ha�y's Great Geometrical Studies 3.1 The Reduction of Real Properties 3.2 Hauy's� Theory of Structure of 1792: A Step Towards Generalization 3.3 The Trait� de Mineralogy of 1801 3.4 The Final Studies: A New Classi cation, the Law of Symmetry 4 Crystals and the Naturphilosophie Movement 5 Lattices and Space Groups of Symmetry 5.1 Lattices 5.2 Space Groups 6 Conclusion Historical Reflection on the Physics Mathematics Relationship in Electromagnetic Theory 1 Physics Mathematics from a Physical Standpoint 1.1 Maxwell's Debate with Faraday 1.2 On Modelling and Processes of Reasoning 1.3 On Physical Ideas and Mathematical Quantities 1.4 On Electric Induction 2 Physics Mathematics from a Mathematical Standpoint 2.1 On Physics Mathematics in Electromagnetic Theory 2.2 On the Field Concept and Mathematical Operators 2.3 On Magnetic Vector Potential and Electric Displacement 2.4 A Road to Physics Mathematics? 3 Conclusion Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity 1 Introduction 2 The Milanese School 2.1 Gabrio Piola 3 The Pisan School 3.1 Enrico Betti 3.2 Betti's Students 4 The Pavia School 4.1 Eugenio Beltrami 4.2 Beltrami's Students 5 Conclusion The Interaction of Physics, Mechanics and Mathematics in Joseph Liouville's Research 1 Introduction 2 Laplacian Physics and Differentiation of Arbitrary Order 3 Electrostatics and Inversions in Spheres 4 Theory of Heat and Sturm-Liouville Theory 5 Celestial Mechanics 6 Rational Mechanics and Geometry 7 Conclusion Mathematical Physics in the Style of Gabriel Lam� and the Treatise of Emile Mathieu 1 The "Matematical Physics" of Laplace, Fourier, and Poisson 2 The "Matematical Physics" of Gabriel Lam� 3 The Unity of Physics: The Aether and Its Equation 4 Emile Mathieu and His Treatise Project 6 Conclusion The Emergence of Mathematical Physics at the University of Leipzig 1 Introduction 2 Neumann's Appointment at the University of Leipzig 3 Neumann's View of Mathematical Physics 4 Neumann's Investigations in Mathematical Physics - Electrodynamics 5 Some Consequences of Neumann's Work - The Blossom of Mathematical Physics in Leipzig 6 Conclusion On Boundaries of the Language of Physics 1 Introduction 2 Linguistic Approach to the Development of Physics 3 Re-presentations in the History of Physics 3.1 Newtonian Physics 3.2 The Theory of Continua and Fluids 3.3 The Theory of Atoms and Energies 3.4 Field Theory 4 Conclusions The Relationship Between Physics and Mathematics in the XIXth Century: The Disregarded Birth of a Foundational Pluralism 1 Introduction 2 The Two Basic Options in the Foundations of Physics 3 The Births of Four Kinds of RPMs: Incommensurability Phenomena 4 The Manifest Conflits Generated by Mutually Incommensurable RPMs 5 Restoration of the Newtonian Paradigm and the Almost Ignored Inventions of Radical Novelties 6 The Mid-Century: The Re-births of the Alternative RPMs Through New Theories 7 The Debate Between the Two False Conscioussness of the Different RPMs 8 The Crisis in Science of the First Years of the XXth Century 9 Conclusions Index