Calculus Explorations with Geometry Expressions
Calculus Explorations with Geometry Expressions

Author: Irina Lyublinskaya

Publisher:

Published: 2010-11

Total Pages: 320

ISBN-13: 9781882564194

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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.

Advanced Calculus (Revised Edition)
Advanced Calculus (Revised Edition)

Author: Lynn Harold Loomis

Publisher: World Scientific Publishing Company

Published: 2014-02-26

Total Pages: 595

ISBN-13: 9814583952

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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Explorations in Mathematical Physics
Explorations in Mathematical Physics

Author: Don Koks

Publisher: Springer Science & Business Media

Published: 2006-11-30

Total Pages: 549

ISBN-13: 0387327932

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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.

The Language of Physics
The Language of Physics

Author: Elizabeth Garber

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 410

ISBN-13: 1461217660

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This work is the first explicit examination of the key role that mathematics has played in the development of theoretical physics and will undoubtedly challenge the more conventional accounts of its historical development. Although mathematics has long been regarded as the "language" of physics, the connections between these independent disciplines have been far more complex and intimate than previous narratives have shown. The author convincingly demonstrates that practices, methods, and language shaped the development of the field, and are a key to understanding the mergence of the modern academic discipline. Mathematicians and physicists, as well as historians of both disciplines, will find this provocative work of great interest.

Teaching and Learning of Calculus
Teaching and Learning of Calculus

Author: David Bressoud

Publisher: Springer

Published: 2016-06-14

Total Pages: 44

ISBN-13: 3319329758

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This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics
Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics

Author: Alejandro Uribe A.

Publisher: American Mathematical Soc.

Published: 2020-05-21

Total Pages: 178

ISBN-13: 1470452707

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This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.

Mathematics as a Service Subject
Mathematics as a Service Subject

Author: A. G. Howson

Publisher: Cambridge University Press

Published: 1988-05-27

Total Pages: 100

ISBN-13: 9780521357036

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Based on the 1987 International Commission on Mathematical Instruction conference, this volume comprises key papers on the role of mathematics in applied subjects.

Visualizing with CAD
Visualizing with CAD

Author: Daniela Bertol

Publisher: Springer

Published: 2013-11-11

Total Pages: 390

ISBN-13: 1475769466

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I spent the first twenty six years of my life in Rome. I used to go for ice cream to a popular place near the Pantheon and I remem ber the excitement I felt, beyond the chocolate and whipped cream, when I entered this ancient Roman temple. After staring at the "shower" of light coming from the circular opening at the center of the dome, as strong as a spotlight, I remember being attracted almost hypnotically to the place below the opening. I remember counting the coffers carving the concave dome, com posed in five rows of circular arrays, and could feel the power and protection created by the concave space. I also recall going every Sunday to Piazza San Pietro. This Baroque square is well known for its colonnades, which have an oval shape defined by two interlocking circles. For each of these circles there is a mark, located approximately at its center, from which the four aligned rows of columns appear as one. Before entering the church, almost as a part of a ritual, I had to find the mark in the pavement of the oval square. I was amazed by how the rows of columns could appear and disappear according to my position in relation to the mark:.