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Structure and Interpretation of Classical Mechanics, second edition

2015-02-06 Science
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Release : 2015-02-06
Genre : Science
Kind : eBook
Book Rating : 964/5 ( reviews)

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Book Synopsis Structure and Interpretation of Classical Mechanics, second edition by : Gerald Jay Sussman

Download or read book Structure and Interpretation of Classical Mechanics, second edition written by Gerald Jay Sussman. This book was released on 2015-02-06. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.

Functional Differential Geometry

2013-07-05 Mathematics
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Release : 2013-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 345/5 ( reviews)

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Book Synopsis Functional Differential Geometry by : Gerald Jay Sussman

Download or read book Functional Differential Geometry written by Gerald Jay Sussman. This book was released on 2013-07-05. Available in PDF, EPUB and Kindle. Book excerpt: An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

Software Design for Flexibility

2021-03-09 Computers
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Release : 2021-03-09
Genre : Computers
Kind : eBook
Book Rating : 473/5 ( reviews)

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Book Synopsis Software Design for Flexibility by : Chris Hanson

Download or read book Software Design for Flexibility written by Chris Hanson. This book was released on 2021-03-09. Available in PDF, EPUB and Kindle. Book excerpt: Strategies for building large systems that can be easily adapted for new situations with only minor programming modifications. Time pressures encourage programmers to write code that works well for a narrow purpose, with no room to grow. But the best systems are evolvable; they can be adapted for new situations by adding code, rather than changing the existing code. The authors describe techniques they have found effective--over their combined 100-plus years of programming experience--that will help programmers avoid programming themselves into corners. The authors explore ways to enhance flexibility by: Organizing systems using combinators to compose mix-and-match parts, ranging from small functions to whole arithmetics, with standardized interfaces Augmenting data with independent annotation layers, such as units of measurement or provenance Combining independent pieces of partial information using unification or propagation Separating control structure from problem domain with domain models, rule systems and pattern matching, propagation, and dependency-directed backtracking Extending the programming language, using dynamically extensible evaluators

Classical Dynamics of Particles and Systems

2013-10-22 Science
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Release : 2013-10-22
Genre : Science
Kind : eBook
Book Rating : 818/5 ( reviews)

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Book Synopsis Classical Dynamics of Particles and Systems by : Jerry B. Marion

Download or read book Classical Dynamics of Particles and Systems written by Jerry B. Marion. This book was released on 2013-10-22. Available in PDF, EPUB and Kindle. Book excerpt: Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.

Classical Mechanics

2004 Science
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Release : 2004
Genre : Science
Kind : eBook
Book Rating : 352/5 ( reviews)

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Book Synopsis Classical Mechanics by : T. W. B. Kibble

Download or read book Classical Mechanics written by T. W. B. Kibble. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth edition of a well-established textbook. It is intended to provide a thorough coverage of the fundamental principles and techniques of classical mechanics, an old subject that is at the base of all of physics, but in which there has also in recent years been rapid development. The book is aimed at undergraduate students of physics and applied mathematics. It emphasizes the basic principles, and aims to progress rapidly to the point of being able to handle physically and mathematically interesting problems, without getting bogged down in excessive formalism. Lagrangian methods are introduced at a relatively early stage, to get students to appreciate their use in simple contexts. Later chapters use Lagrangian and Hamiltonian methods extensively, but in a way that aims to be accessible to undergraduates, while including modern developments at the appropriate level of detail. The subject has been developed considerably recently while retaining a truly central role for all students of physics and applied mathematics.This edition retains all the main features of the fourth edition, including the two chapters on geometry of dynamical systems and on order and chaos, and the new appendices on conics and on dynamical systems near a critical point. The material has been somewhat expanded, in particular to contrast continuous and discrete behaviours. A further appendix has been added on routes to chaos (period-doubling) and related discrete maps. The new edition has also been revised to give more emphasis to specific examples worked out in detail.Classical Mechanics is written for undergraduate students of physics or applied mathematics. It assumes some basic prior knowledge of the fundamental concepts and reasonable familiarity with elementary differential and integral calculus.

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