Calculus Explorations With Geometry Expressions
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Calculus Explorations With Geometry Expressions
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Author : Irina Lyublinskaya
language : en
Publisher:
Release Date : 2010-11
Calculus Explorations With Geometry Expressions written by Irina Lyublinskaya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11 with Mathematics categories.
Teachers know the difficulties in motivating many students to develop the habits of mind and critical thinking skills necessary to thoroughly understand the concepts of calculus. The purpose of this book is to use Geometry Expressions software in order to facilitate and enhance the calculus syllabus by allowing students to ground calculus concepts in a geometric way. The 29 student explorations in this book cover the major topics of a standard course of calculus, and are completed with the help of the constraint-based dynamic software package, Geometry Expressions. Using Geometry Expressions in learning calculus, students have the opportunity to develop general investigation skills, make connections between geometric and algebraic representations of major calculus ideas, interpret analytic problems visually and geometric problems algebraically, and develop facility with using a computer to prove general mathematics statements. Geometry Expressions enables more extensive calculus investigation than is possible in a traditional course of calculus. Open-ended explorations and investigations reinforce students' intellectual development. Students appreciate challenges and enjoy taking ownership in the problem solving process. This book, together with Geometry Expressions enables the student to do just that.
Explorations In Mathematical Physics
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Author : Don Koks
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-15
Explorations In Mathematical Physics written by Don Koks and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-15 with Science categories.
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Calculus With Analytic Geometry
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Author : Murray H. Protter
language : en
Publisher: Jones & Bartlett Learning
Release Date : 1988
Calculus With Analytic Geometry written by Murray H. Protter and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Calculus Explorations
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Author : Paul A. Foerster
language : en
Publisher:
Release Date : 1998
Calculus Explorations written by Paul A. Foerster and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Calculus categories.
Cameos For Calculus
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Author : Roger B. Nelsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31
Cameos For Calculus written by Roger B. Nelsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.
A thespian or cinematographer might define a cameo as a brief appearance of a known figure, while a gemologist or lapidary might define it as a precious or semiprecious stone. This book presents fifty short enhancements or supplements (the cameos) for the first-year calculus course in which a geometric figure briefly appears. Some of the cameos illustrate mainstream topics such as the derivative, combinatorial formulas used to compute Riemann sums, or the geometry behind many geometric series. Other cameos present topics accessible to students at the calculus level but not usually encountered in the course, such as the Cauchy-Schwarz inequality, the arithmetic mean-geometric mean inequality, and the Euler-Mascheroni constant. There are fifty cameos in the book, grouped into five sections: Part I. Limits and Differentiation, Part II. Integration, Part III. Infinite Series, Part IV. Additional Topics, and Part V. Appendix: Some Precalculus Topics. Many of the cameos include exercises, so Solutions to all the Exercises follows Part V. The book concludes with references and an index. Many of the cameos are adapted from articles published in journals of the MAA, such as The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal. Some come from other mathematical journals, and some were created for this book. By gathering the cameos into a book the [Author]; hopes that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.
Calculus In Context
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Author : Alexander J. Hahn
language : en
Publisher: JHU Press
Release Date : 2017-04-15
Calculus In Context written by Alexander J. Hahn and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-15 with Mathematics categories.
A new approach to teaching calculus that uses historical examples and draws on applications from science and engineering. Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: • the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development • a brief, introductory calculus from the works of Newton and Leibniz • a modern development of the essentials of differential and integral calculus • the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration—for students and instructors alike—of a discipline that is both rich in conceptual beauty and broad in its applied relevance.
Calculus And Analytic Geometry
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Author : George Brinton Thomas (Jr.)
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1979
Calculus And Analytic Geometry written by George Brinton Thomas (Jr.) and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
This book contains a variety of interesting professional applications of calculus to business, economics, and the life sciences.
Calculus With Analytic Geometry
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Author : Ralph Crouch
language : en
Publisher: Prindle Weber & Schmidt
Release Date : 1971
Calculus With Analytic Geometry written by Ralph Crouch and has been published by Prindle Weber & Schmidt this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Strange Curves Counting Rabbits Other Mathematical Explorations
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Author : Keith Ball
language : en
Publisher: Princeton University Press
Release Date : 2011-10-16
Strange Curves Counting Rabbits Other Mathematical Explorations written by Keith Ball and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-16 with Mathematics categories.
How does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.
Calculus With Analytic Geometry
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Author : Ron Larson
language : en
Publisher:
Release Date : 1990
Calculus With Analytic Geometry written by Ron Larson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.