The Mathematics Of Soap Films Explorations With Maple PDF Download
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| Author | : John Oprea |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 2000 |
| Genre | : JUVENILE NONFICTION |
| ISBN | : 9781470421274 |
Download The Mathematics of Soap Films Book in PDF, ePub and Kindle
Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the MapleR applications, the reader is given tools for creating the shapes that are being studied. Thus, you can ``see'' a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the ``true'' shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.
| Author | : John Oprea |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 284 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821884461 |
Download The Mathematics of Soap Films Book in PDF, ePub and Kindle
Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.
| Author | : John Oprea |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 2000 |
| Genre | : Computers |
| ISBN | : 0821821180 |
Download The Mathematics of Soap Films: Explorations with Maple Book in PDF, ePub and Kindle
Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.
| Author | : Michael A. Brilleslyper |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 373 |
| Release | : 2012-12-31 |
| Genre | : Mathematics |
| ISBN | : 1614441081 |
Download Explorations in Complex Analysis Book in PDF, ePub and Kindle
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
| Author | : John A. Pelesko |
| Publisher | : CRC Press |
| Total Pages | : 332 |
| Release | : 2007-05-21 |
| Genre | : Science |
| ISBN | : 1584886889 |
Download Self Assembly Book in PDF, ePub and Kindle
Hailed as one of the key areas of nanoscience likely to shape future scientific research, self-assembly offers the most promising route to true molecular nanotechnology. Focusing on this dynamic new field, Self Assembly: The Science of Things That Put Themselves Together explores nature's self-assembly of structures, the use of it to build engineer
| Author | : John Oprea |
| Publisher | : American Mathematical Society |
| Total Pages | : 497 |
| Release | : 2024-07-01 |
| Genre | : Mathematics |
| ISBN | : 1470477912 |
Download Differential Geometry and Its Applications Book in PDF, ePub and Kindle
Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
| Author | : Wiesława J. Kaczor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 369 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821832980 |
Download Problems in Mathematical Analysis III Book in PDF, ePub and Kindle
Abstract:
| Author | : C. Barry Carter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 775 |
| Release | : 2013-01-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1461435234 |
Download Ceramic Materials Book in PDF, ePub and Kindle
Ceramic Materials: Science and Engineering is an up-to-date treatment of ceramic science, engineering, and applications in a single, comprehensive text. Building on a foundation of crystal structures, phase equilibria, defects, and the mechanical properties of ceramic materials, students are shown how these materials are processed for a wide diversity of applications in today's society. Concepts such as how and why ions move, how ceramics interact with light and magnetic fields, and how they respond to temperature changes are discussed in the context of their applications. References to the art and history of ceramics are included throughout the text, and a chapter is devoted to ceramics as gemstones. This course-tested text now includes expanded chapters on the role of ceramics in industry and their impact on the environment as well as a chapter devoted to applications of ceramic materials in clean energy technologies. Also new are expanded sets of text-specific homework problems and other resources for instructors. The revised and updated Second Edition is further enhanced with color illustrations throughout the text.
| Author | : John Adam |
| Publisher | : Princeton University Press |
| Total Pages | : 408 |
| Release | : 2011-10-02 |
| Genre | : Mathematics |
| ISBN | : 1400841011 |
Download Mathematics in Nature Book in PDF, ePub and Kindle
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.
| Author | : Steven R. Finch |
| Publisher | : Cambridge University Press |
| Total Pages | : 783 |
| Release | : 2018-12-06 |
| Genre | : Mathematics |
| ISBN | : 110860403X |
Download Mathematical Constants II Book in PDF, ePub and Kindle
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
