Chases and Escapes
Chases and Escapes

Author: Paul Nahin

Publisher: Princeton University Press

Published: 2012-07-22

Total Pages: 285

ISBN-13: 1400842069

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We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion. Some images inside the book are unavailable due to digital copyright restrictions.

Visual Complex Analysis
Visual Complex Analysis

Author: Tristan Needham

Publisher: Oxford University Press

Published: 1997

Total Pages: 620

ISBN-13: 9780198534464

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This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Visual Differential Geometry and Forms
Visual Differential Geometry and Forms

Author: Tristan Needham

Publisher: Princeton University Press

Published: 2021-07-13

Total Pages: 584

ISBN-13: 0691219893

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An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Mathematical Methods for Accident Reconstruction
Mathematical Methods for Accident Reconstruction

Author: Harold Franck

Publisher: CRC Press

Published: 2009-09-15

Total Pages: 310

ISBN-13: 1420089013

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Over the past 25 years, Harold and Darren Franck have investigated hundreds of accidents involving vehicles of almost every shape, size, and type imaginable. In Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, these seasoned experts demonstrate the application of mathematics to modeling accident reconstructions

Innovating the Future Through Manufacturing
Innovating the Future Through Manufacturing

Author: Vivekanandu Shanmuganathan

Publisher: Alpha Science Int'l Ltd.

Published: 2005

Total Pages: 1038

ISBN-13: 9788173196805

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Attempts to provide a holistic view of the changing scenario and current research trends in manufacturing. This volume can provide the necessary information to all researchers, professionals and beginners alike in introducing innovating manufacturing practices and furthering research on newer and improved manufacturing technologies.

An Introduction to Differential Equations and Their Applications
An Introduction to Differential Equations and Their Applications

Author: Stanley J. Farlow

Publisher: Courier Corporation

Published: 2012-10-23

Total Pages: 642

ISBN-13: 0486135136

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This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Putting Two and Two Together
Putting Two and Two Together

Author: Burkard Polster

Publisher: American Mathematical Society

Published: 2021-12-10

Total Pages: 274

ISBN-13: 1470460114

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Putting Two and Two Together is a humorous and quirky collection of unusual, ingenious, and beautiful morsels of mathematics. Authors Burkard Polster (YouTube's Mathologer) and Marty Ross delve into mathematical puzzles and phenomena in engaging stories featuring current events, sports, and history, many flavored with a distinctive bit of Australiana. Each chapter ends with “puzzles to ponder” that will spur further reflection. These stories were written for a general audience, and originally appeared in the Maths Masters column in The Age newspaper. The book offers mathematical entertainment for curious readers of all ages, and assumes a minimum of mathematical background. Polster and Ross are masters of the genre this book represents: a cornucopia of offerings, from across the mathematical spectrum. Their articles are entertaining, captivating, and informative, and will appeal to everyone from interested amateurs to old pros. On top of all that, the prose is clear, concise and a lot of fun—happily with a charmingly Aussie flavo(u)r. Crack the spine and enjoy! —Michael Berg, Loyola Marymount University, Los Angeles The American Mathematical Society must be congratulated on publishing a singularly amusing synthesis of cultural anthropology coupled with mathematical entertainment. —Tushar Das, University of Wisconsin–La Crosse Polster and Ross are as good as the original master, Martin Gardner! They are also as good as that other great popularizer of mathematics, Ian Stewart, who took up Gardner's mantle, and as good as Douglas Hofstedter, who also followed in Gardner's footsteps as popularizers of mathematics within regular columns in “Scientific American”, and elsewhere. I recommend this new book very highly! Like Poster and Ross's first collection of columns, it is one that you can happily read from cover to cover, or dip into at any random point, and find treasures. You will then often return, savouring, and often laughing, while also learning, and responding to thoughtful challenges! —John Gough, Deakin University, Geelong, Australia