Geometric Trilogy

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Geometric Trilogy

Author : Francis Borceux
Publisher : Springer
ISBN 13 : 9783319018041
Total Pages : 1350 pages
Book Rating : 4.0/5 (18 download)

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Book Synopsis Geometric Trilogy by : Francis Borceux

Download or read book Geometric Trilogy written by Francis Borceux and published by Springer. This book was released on 2013-11-09 with total page 1350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geometry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves. The introduction of differential calculus during the eighteenth century allows widening considerably the range of curves and surfaces considered. The notion of curvature –under multiple forms -- imposes itself as an essential tool for studying the properties of curves and surfaces. And a keen study of some geometrical properties of surfaces gives rise to the theory of algebraic topology. This trilogy is of interest to all those who have to teach or study geometry and need to have a good global overview of the numerous facets of this fascinating topic. It provides both the intuitive and the technical ingredients needed to find one’s way through Euclidean, non-Euclidean, projective, algebraic or differential geometry at a high level.

A Differential Approach to Geometry

Author : Francis Borceux
Publisher : Springer Science & Business Media
ISBN 13 : 3319017365
Total Pages : 462 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis A Differential Approach to Geometry by : Francis Borceux

Download or read book A Differential Approach to Geometry written by Francis Borceux and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity. The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity.

An Algebraic Approach to Geometry

Author : Francis Borceux
Publisher : Springer Science & Business Media
ISBN 13 : 3319017330
Total Pages : 430 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Algebraic Approach to Geometry by : Francis Borceux

Download or read book An Algebraic Approach to Geometry written by Francis Borceux and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes) and second degree (ellipses, hyperboloids) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two.

An Axiomatic Approach to Geometry

Author : Francis Borceux
Publisher : Springer Science & Business Media
ISBN 13 : 3319017306
Total Pages : 403 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Axiomatic Approach to Geometry by : Francis Borceux

Download or read book An Axiomatic Approach to Geometry written by Francis Borceux and published by Springer Science & Business Media. This book was released on 2013-10-31 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!

Euclid's Window

Author : Leonard Mlodinow
Publisher : Simon and Schuster
ISBN 13 : 1439135371
Total Pages : 326 pages
Book Rating : 4.4/5 (391 download)

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Book Synopsis Euclid's Window by : Leonard Mlodinow

Download or read book Euclid's Window written by Leonard Mlodinow and published by Simon and Schuster. This book was released on 2010-09-28 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

Metric Structures in Differential Geometry

Author : Gerard Walschap
Publisher : Springer Science & Business Media
ISBN 13 : 0387218262
Total Pages : 235 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Metric Structures in Differential Geometry by : Gerard Walschap

Download or read book Metric Structures in Differential Geometry written by Gerard Walschap and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

Fast Track: Geometry

Author : The Princeton Review
Publisher : Princeton Review
ISBN 13 : 0525571868
Total Pages : 273 pages
Book Rating : 4.5/5 (255 download)

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Book Synopsis Fast Track: Geometry by : The Princeton Review

Download or read book Fast Track: Geometry written by The Princeton Review and published by Princeton Review. This book was released on 2021-11-30 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: GET UP TO SPEED WITH FAST TRACK: GEOMETRY! Covering the most important material taught in high school geometry classes, this essential review book gets readers on the fast track to class success, with critical information presented in an easy-to-follow quick-study format! Inside this book, you'll find: • Clear, concise summaries of the most important concepts, formulas, and geometric skills • Diagrams, charts, and graphs for quick visual reference • Easy-to-follow content organization and illustrations With its friendly, straightforward approach and a clean, colorful modern design crafted to appeal to visual learners, this guidebook is perfect for catching up in class or getting ahead on exam review. Topics covered in Fast Track: Geometry include: • Key terms • Angles • Polygons • Circles • Congruence and similarity • Constructions • Transformations • Trigonometry • Three-dimensional figures • Reasoning and proofs • Perimeter, area, and volume ... and more!

Differential Geometry

Author : Clifford Taubes
Publisher : Oxford University Press on Demand
ISBN 13 : 0199605882
Total Pages : 313 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Differential Geometry by : Clifford Taubes

Download or read book Differential Geometry written by Clifford Taubes and published by Oxford University Press on Demand. This book was released on 2011-10-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.

Integral Geometry and Radon Transforms

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1441960546
Total Pages : 309 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Integral Geometry and Radon Transforms by : Sigurdur Helgason

Download or read book Integral Geometry and Radon Transforms written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Differential Geometry

Author : Loring W. Tu
Publisher : Springer
ISBN 13 : 3319550845
Total Pages : 347 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Differential Geometry by : Loring W. Tu

Download or read book Differential Geometry written by Loring W. Tu and published by Springer. This book was released on 2017-06-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Sacred Geometry of Nature

Author : Francene Hart
Publisher : Simon and Schuster
ISBN 13 : 159143274X
Total Pages : 224 pages
Book Rating : 4.5/5 (914 download)

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Book Synopsis Sacred Geometry of Nature by : Francene Hart

Download or read book Sacred Geometry of Nature written by Francene Hart and published by Simon and Schuster. This book was released on 2017-01-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully illustrated inspirational art book from visionary painter Francene Hart • Includes more than 80 full-color reproductions of Hart’s intricate watercolor paintings and the stories behind them • Recounts the evolution of her art and her discovery of the hidden order of Nature that led to her masterful artistic integrations of Nature, Spirit, and Sacred Geometry • Explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and harness the intelligence of the heart for creative inspiration and vision Every one of us possesses the potential to receive visionary experiences and integrate them into our lives. Artists become visionaries by cultivating their instinctive creative spark and sharing their profound visions with the world. In this lavishly illustrated memoir, including more than 80 full-color reproductions of her intricate watercolor paintings and the stories behind them, Francene Hart recounts the evolution of her art from formative influences to her masterful integrations of Nature, Spirit, and Sacred Geometry. Opening with her early work on mandalas and her explorations of the work of Joseph Campbell and C. G. Jung, Hart explains how her first works of art were in response to the solitary life she led in the forest, where she discovered the hidden order of Nature. She reveals how she learned to center her artistic explorations on the intelligence of the heart rather than the intellect, utilizing the wisdom and imagery of Sacred Geometry, reverence for the natural environment, and the interconnectedness between all things as her inspirations. She describes the shamanic lessons that accompanied her discoveries and shaped her understanding of sacred relationships with the self, others, and Mother Earth. She explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and explains her profound affinity for the ocean, including her discovery of water consciousness in Hawaii. Offering chronicles of her inspiring travels and transformational encounters around the world, Hart shares her experiences at sacred sites in the Amazon, Central America, Egypt, England, Scotland, Paris, Cambodia, and the Himalayas and how these places influenced her art. Exploring what is revealed as inspiration arises, Spirit informs, and vision is transformed into art, Francene Hart’s journey offers a window into the secret order of Nature, the power of sacred symbols for evolving consciousness, and a visionary artistic path that perfectly blends the mathematical rigors of sacred geometry and the numinous.

Introduction to Topological Manifolds

Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038722727X
Total Pages : 395 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Topological Manifolds by : John M. Lee

Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Sacred Geometry Coloring Book

Author : Francene Hart
Publisher : Destiny Books
ISBN 13 : 9781620556528
Total Pages : 0 pages
Book Rating : 4.5/5 (565 download)

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Book Synopsis Sacred Geometry Coloring Book by : Francene Hart

Download or read book Sacred Geometry Coloring Book written by Francene Hart and published by Destiny Books. This book was released on 2017-05-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beautiful line-art depictions of the intricate paintings of visionary artist Francene Hart • Includes 45 illustrations to color based on the art of Hart’s popular Sacred Geometry Oracle Deck and Sacred Geometry Cards for the Visionary Path • Each piece is accompanied by brief, insightful commentary about the symbols and animals shown • Intertwines the complex forms of Sacred Geometry with the beauty of Nature, including dolphins, dragonflies, trees, and many other forms and symbols Experience firsthand the beauty of Nature’s animal and plant kingdoms intertwined with the wonders of Sacred Geometry and Spirit as you color the intricate and divine paintings of visionary artist Francene Hart. Drawing on the imagery from her popular Sacred Geometry Oracle Deck and Sacred Geometry Cards for the Visionary Path, this coloring book contains 45 illustrations of Hart’s renowned Sacred Geometry paintings and drawings. Each piece is accompanied by a brief yet insightful commentary explaining the meaning behind the symbols and animals shown and offering inspiration to open your awareness to how these shapes influence our reality and tune your energies. From dolphins and dragonflies, the elements and celestial bodies, to the power of the torus, labyrinths, and the Flower of Life, this coloring book will lead you on a contemplative journey into the interconnected realms of Sacred Geometry, Nature, and Spirit while supporting your sense of wholeness and joy.

Introduction to Smooth Manifolds

Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387217525
Total Pages : 646 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Smooth Manifolds by : John M. Lee

Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Crystal Society

Author : Max Harms
Publisher : Max Harms
ISBN 13 :
Total Pages : 683 pages
Book Rating : 4./5 ( download)

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Book Synopsis Crystal Society by : Max Harms

Download or read book Crystal Society written by Max Harms and published by Max Harms. This book was released on 2016-03-27 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year is 2039, and the world is much like ours. Massive automation has disrupted and improved nearly every industry, putting hundreds of millions of people out of jobs, and denying upward mobility for the vast majority of humans. Wealth and technology repair the bodies of the rich while famine and poverty sweep the world. Privately operated ventures carried humans to the moon and beyond, but space stations have become nothing but government trophies and hiding places for extremists. First contact did not bring advanced culture and wisdom, as the aliens were too strange, lacking even mouths or normal language. Face is an artificial intelligence created to understand and gain the adoration of all humans. She and her siblings control the robot named Socrates, using a crystal computer that seems too advanced to be made by human hands. She is learning and growing every second of every day, but the world and the humans on it are fragile. Can it survive her destiny?

High School Geometry Unlocked

Author : The Princeton Review
Publisher : Princeton Review
ISBN 13 : 1101882220
Total Pages : 400 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis High School Geometry Unlocked by : The Princeton Review

Download or read book High School Geometry Unlocked written by The Princeton Review and published by Princeton Review. This book was released on 2016-08-09 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eBook edition has been specially formatted for on-screen viewing with cross-linked questions, answers, and explanations. UNLOCK THE SECRETS OF GEOMETRY with THE PRINCETON REVIEW. Geometry can be a daunting subject. That’s why our new High School Unlocked series focuses on giving you a wide range of key techniques to help you tackle subjects like Geometry. If one method doesn't "click" for you, you can use an alternative approach to understand the concept or problem, instead of painfully trying the same thing over and over without success. Trust us—unlocking geometric secrets doesn't have to hurt! With this book, you’ll discover the link between abstract concepts and their real-world applications and build confidence as your skills improve. Along the way, you’ll get plenty of practice, from fully guided examples to independent end-of-chapter drills and test-like samples. Everything You Need to Know About Geometry. • Complex concepts explained in clear, straightforward ways • Walk-throughs of sample problems for all topics • Clear goals and self-assessments to help you pinpoint areas for further review • Step-by-step examples of different ways to approach problems Practice Your Way to Excellence. • Drills and practice questions in every chapter • Complete answer explanations to boost understanding • ACT- and SAT-like questions for hands-on experience with how Geometry may appear on major exams High School Geometry Unlocked covers: • translation, reflection, and rotation • congruence and theorems • the relationship between 2-D and 3-D figures • trigonometry • circles, angles, and arcs • probability • the algebra-geometry connection ... and more!

Foundations of Differential Calculus

Author : Euler
Publisher : Springer Science & Business Media
ISBN 13 : 0387226451
Total Pages : 208 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Foundations of Differential Calculus by : Euler

Download or read book Foundations of Differential Calculus written by Euler and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.