The Mathematical Mechanic

Author: Mark Levi
Publisher: Princeton University Press
ISBN: 1400830478
Category : Mathematics
Languages : en
Pages : 197

Book Description
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.

The Mathematical Mechanic

Author: Mark Levi
Publisher: Princeton University Press
ISBN: 0691140200
Category : Mathematics
Languages : en
Pages : 197

Book Description
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.

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Category : Mathematics
Languages : en
Pages : 530

Book Description
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.

Classical Mechanics with Calculus of Variations and Optimal Control

Author: Mark Levi
Publisher: American Mathematical Soc.
ISBN: 0821891383
Category : Mathematics
Languages : en
Pages : 322

Book Description
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.

Why Cats Land on Their Feet

Author: Mark Levi
Publisher: Princeton University Press
ISBN: 1400841720
Category : Mathematics
Languages : en
Pages : 205

Book Description
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.

Mathematical Mechanics: From Particle To Muscle

Author: Ellis D Cooper
Publisher: World Scientific
ISBN: 981446631X
Category : Mathematics
Languages : en
Pages : 390

Book Description
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.

Classical Mechanics

Author: Dieter Strauch
Publisher: Springer Science & Business Media
ISBN: 3540736166
Category : Science
Languages : en
Pages : 414

Book Description
This upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity. The author's writing style attempts to ease students through the primary and secondary results, thus building a solid foundation for understanding applications. Numerous examples illustrate the material and often present alternative approaches to the final results.

Auto Math Handbook

Author: John Lawlor
Publisher: Penguin
ISBN: 9781557880208
Category : Transportation
Languages : en
Pages : 164

Book Description
Offers formulas and equations for calculating brake horsepower and torque, displacement, stroke, bore, compression ratio, and more

Power-Up

Author: Matthew Lane
Publisher: Princeton University Press
ISBN: 0691196389
Category : Computers
Languages : en
Pages : 290

Book Description
"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.

What's Next?

Author: Dylan Thurston
Publisher: Princeton University Press
ISBN: 069116777X
Category : Mathematics
Languages : en
Pages : 436

Book Description
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.