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The Mathematical Mechanic
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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: In this delightful book, 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.
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 2023-01-24 with total page 201 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.
Book Synopsis Mathematical Methods of Classical Mechanics by : V.I. Arnol'd
Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Book Synopsis Classical Mechanics with Calculus of Variations and Optimal Control by : Mark Levi
Download or read book Classical Mechanics with Calculus of Variations and Optimal Control written by Mark Levi and published by American Mathematical Soc.. This book was released on 2014-03-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
Book Synopsis Mathematical Mechanics: From Particle To Muscle by : Ellis D Cooper
Download or read book Mathematical Mechanics: From Particle To Muscle written by Ellis D Cooper and published by World Scientific. This book was released on 2011-03-28 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unprecedented book offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of latest mathematical technologies — Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory — to explicate Particle Mechanics, The Theory of Substances (categorical thermodynamics), and computer simulation using a diagram-based parallel programming language (stochastic timing machinery). Proofs rely almost entirely on algebraic calculations without set theory. Metaphors and analogies, and distinctions between representational pictures, mental model drawings, and mathematical diagrams are offered.AP level high school calculus students, high school science teachers, undergraduates and graduate college students, and researchers in mathematics, physics, chemistry, and biology may use this integrated publication to broaden their perspective on science, and to experience the precision that mathematical mechanics brings to understanding the molecular mechanism vital for nearly all animal behavior.
Book Synopsis The Math Mechanic by : Kendric L. Bryant
Download or read book The Math Mechanic written by Kendric L. Bryant and published by . This book was released on 2003-04-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Math Mechanic Series by : The Math Mechanic
Download or read book The Math Mechanic Series written by The Math Mechanic and published by Virtualbookworm Publishing. This book was released on 2003-04 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Math Mechanic does the dirty work that textbooks and other supplementary books don't. It shows the step-by-step mechanics of solving mathematical problems. To survive in today's world it is imperative that you have the ability to solve mathematical problems. Whether it is working out problems for schoolwork or performing calculations related to money, strong mathematical skills are a necessity. Our books are easy to understand guides that are designed to eliminate the frustration that many Children and Adults have with mathematics. Each book is a combined Tutorial, Workbook, and Reference Manual. From Students to Parents to Professionals, The Math Mechanic Series provides the most potent and comprehensive set of tools for helping anyone to become proficient with mathematics.
Book Synopsis Foundations Of Mechanics by : Ralph Abraham
Download or read book Foundations Of Mechanics written by Ralph Abraham and published by CRC Press. This book was released on 2019-04-24 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Download or read book Power-Up written by Matthew Lane and published by Princeton University Press. This book was released on 2019-11-19 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Did you know that every time you pick up the controller to your PlayStation or Xbox, you are entering a game world steeped in mathematics? Power-Up reveals the hidden mathematics in many of today's most popular video games and explains why mathematical learning doesn't just happen in the classroom or from books--you're doing it without even realizing it when you play games on your cell phone. In this lively and entertaining book, Matthew Lane discusses how gamers are engaging with the traveling salesman problem when they play Assassin's Creed, why it is mathematically impossible for Mario to jump through the Mushroom Kingdom in Super Mario Bros., and how The Sims teaches us the mathematical costs of maintaining relationships. He looks at mathematical pursuit problems in classic games like Missile Command and Ms. Pac-Man, and how each time you play Tetris, you're grappling with one of the most famous unsolved problems in all of mathematics and computer science. Along the way, Lane discusses why Family Feud and Pictionary make for ho-hum video games, how realism in video games (or the lack of it) influences learning, what video games can teach us about the mathematics of voting, the mathematics of designing video games, and much more. Power-Up shows how the world of video games is an unexpectedly rich medium for learning about the beautiful mathematical ideas that touch all aspects of our lives--including our virtual ones."--Dust jacket.
Book Synopsis Why Cats Land on Their Feet by : Mark Levi
Download or read book Why Cats Land on Their Feet written by Mark Levi and published by Princeton University Press. This book was released on 2012-05-27 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to use physical reasoning to solve surprising paradoxes Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics. Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats. Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.
Download or read book MECHANICS written by SUNIL DATTA and published by PHI Learning Pvt. Ltd.. This book was released on 2010-06-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a text for the undergraduate students of Mathematics, this book provides an in-depth analysis on the theoretical and practical applications of Mechanics. The concepts and the theories expressed are treated mathematically with a simple yet logical approach. The book is written to augment the understanding of the students of this discipline. The book comprises the topics like Newton's Laws of motion; concepts of work, energy and impulse; and relative motion. It effectively elucidates the principles of forces in three dimensions, equilibrium of strings, and rectilinear motion like simple harmonic motion. The book explains the motion of the earth, the moon, the stars and other heavenly bodies with the help of principles of mechanics. The topics like motion of a rocket and motion of an artificial satellite are also covered in detail so that the students are introduced to the contemporary subjects like space dynamics. All the chapters are well-supported with figures and illustrative examples. The chapter-end exercises help to judge students’ comprehension on the subject."
Book Synopsis The Math Mechanic Series by : The Math Mechanic
Download or read book The Math Mechanic Series written by The Math Mechanic and published by Virtualbookworm Publishing. This book was released on 2003-04 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Math Mechanic does the dirty work that textbooks and other supplementary books don't. It shows the step-by-step mechanics of solving mathematical problems. To survive in today's world it is imperative that you have the ability to solve mathematical problems. Whether it is working out problems for schoolwork or performing calculations related to money, strong mathematical skills are a necessity. Our books are easy to understand guides that are designed to eliminate the frustration that many Children and Adults have with mathematics. Each book is a combined Tutorial, Workbook, and Reference Manual. From Students to Parents to Professionals, The Math Mechanic Series provides the most potent and comprehensive set of tools for helping anyone to become proficient with mathematics.
Book Synopsis The Math Mechanic by : Kendric L. Bryant
Download or read book The Math Mechanic written by Kendric L. Bryant and published by . This book was released on 2002-04-01 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Math Mechanic does the dirty work that textbooks and other supplementary books don't. It shows the step-by-step mechanics of solving mathematical problems. To survive in today's world it is imperative that you have the ability to solve mathematical problems. Whether it is working out problems for schoolwork or performing calculations related to money, strong mathematical skills are a necessity. Our books are easy to understand guides that are designed to eliminate the frustration that many Children and Adults have with mathematics. Each book is a combined Tutorial, Workbook, and Reference Manual. From Students to Parents to Professionals, The Math Mechanic Series provides the most potent and comprehensive set of tools for helping anyone to become proficient with mathematics.
Download or read book Auto Math Handbook written by John Lawlor and published by Penguin. This book was released on 1991 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers formulas and equations for calculating brake horsepower and torque, displacement, stroke, bore, compression ratio, and more
Download or read book What's Next? written by Dylan Thurston and published by Princeton University Press. This book was released on 2020-07-07 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston (1946-2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and Teichm ller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas. Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also explores how he introduced new ways of thinking about and doing mathematics, innovations that have had a profound and lasting impact on the mathematical community as a whole.
Book Synopsis The Princeton Companion to Mathematics by : Timothy Gowers
Download or read book The Princeton Companion to Mathematics written by Timothy Gowers and published by Princeton University Press. This book was released on 2010-07-18 with total page 1057 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger
Book Synopsis Introduction to Mechanics of Particles and Systems by : Costas J. Papachristou
Download or read book Introduction to Mechanics of Particles and Systems written by Costas J. Papachristou and published by Springer Nature. This book was released on 2020-09-09 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the author’s lecture notes for his Introductory Newtonian Mechanics course at the Hellenic Naval Academy. In order to familiarize students with the use of several basic mathematical tools, such as vectors, differential operators and differential equations, it first presents the elements of vector analysis that are needed in the subsequent chapters. Further, the Mathematical Supplement at the end of the book offers a brief introduction to the concepts of differential calculus mentioned. The main text is divided into three parts, the first of which presents the mechanics of a single particle from both the kinetic and the dynamical perspectives. The second part then focuses on the mechanics of more complex structures, such as systems of particles, rigid bodies and ideal fluids, while the third part consists of 60 fully solved problems. Though chiefly intended as a primary text for freshman-level physics courses, the book can also be used as a supplemental (tutorial) resource for introductory courses on classical mechanics for physicists and engineers
