Calculus in Context

Calculus in Context

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 ...

Author: Alexander J. Hahn

Publisher: JHU Press

ISBN: 9781421422305

Category: Mathematics

Page: 712

View: 745

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.
Categories: Mathematics

Calculus in Context

Calculus in Context

Callahan fully embraces the calculus reform movement in technology and pedagogy, while taking it a step further with a unique organization and applications to real-world problems.

Author: James Callahan

Publisher: W H Freeman & Company

ISBN: 0716726300

Category: Mathematics

Page: 818

View: 461

For courses currently engaged, or leaning toward calculus reform. Callahan fully embraces the calculus reform movement in technology and pedagogy, while taking it a step further with a unique organization and applications to real-world problems.
Categories: Mathematics

Calculus Concepts and Contexts

Calculus  Concepts and Contexts

CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion.

Author: James Stewart

Publisher: Cengage Learning

ISBN: 9780495557425

Category: Mathematics

Page: 1152

View: 349

Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Mathematics

Single Variable Calculus Concepts and Contexts

Single Variable Calculus  Concepts and Contexts

CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion.

Author: James Stewart

Publisher: Cengage Learning

ISBN: 9780495559726

Category: Mathematics

Page: 784

View: 687

Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Mathematics

Multivariable Calculus Concepts and Contexts

Multivariable Calculus  Concepts and Contexts

CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion.

Author: James Stewart

Publisher: Cengage Learning

ISBN: 9780495560548

Category: Mathematics

Page: 512

View: 150

Stewart's Multivariable CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. The Multivariable Calculus edition contains chapters 11-18 of the full text, and is intended to serve as a single-semester text. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Mathematics

Advanced Calculus

Advanced Calculus

The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.

Author: James J. Callahan

Publisher: Springer Science & Business Media

ISBN: 144197332X

Category: Mathematics

Page: 526

View: 462

With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
Categories: Mathematics

College Algebra in Context

College Algebra in Context

"College Algebra in Context is a higher-education textbook that teaches algebra based on data analysis, modeling, and real-life applications from the management, life, and social sciences"--

Author: Ronald J. Harshbarger

Publisher:

ISBN: 0135757762

Category: Algebra

Page: 784

View: 157

"College Algebra in Context is a higher-education textbook that teaches algebra based on data analysis, modeling, and real-life applications from the management, life, and social sciences"--
Categories: Algebra

Learning Basic Calculus

Learning Basic Calculus

This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame.

Author: Alexander Hahn

Publisher: Springer Science & Business Media

ISBN: 0387946063

Category: Mathematics

Page: 545

View: 337

This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame. The book develops calculus, as well as the necessary trigonometry and analytic geometry, from witin the relevant historical context, and yet it is not a textbook in the history of mathematics as such. The notation is modern, and the material is selected to cover the basics of the subject. Special emphasis is placed on pedagogy throughout. Whhile emphasizing the broad applications of the subject, emphasis is placed on the mathematical content of the subject.
Categories: Mathematics

Multivariable Calculus

Multivariable Calculus

The ideas of multivariable calculus are presented in a context that is informed by their non-mathematical applications.

Author: David B Damiano

Publisher: Jones & Bartlett Publishers

ISBN: 9780763782474

Category: Mathematics

Page: 541

View: 811

Written for mathematics, science, and engineering majors who have completed the traditional two-term course in single variable calculus, Multivariable Calculus bridges the gap between mathematical concepts and their real-world applications outside of mathematics. The ideas of multivariable calculus are presented in a context that is informed by their non-mathematical applications. It incorporates collaborative learning strategies and the sophisticated use of technology, which asks students to become active participants in the development of their own understanding of mathematical ideas. This teaching and learning strategy urges students to communicate mathematically, both orally and in writing. With extended examples and exercises and a student-friendly accessible writing style, Multivariable Calculus is an exciting and engaging journey into mathematics relevant to students everyday lives.
Categories: Mathematics

College Algebra Concepts and Contexts

College Algebra  Concepts and Contexts

This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context.

Author: James Stewart

Publisher: Cengage Learning

ISBN: 9780495387893

Category: Mathematics

Page: 816

View: 485

This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the students' majors. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Mathematics

Calculus Early Transcendentals

Calculus  Early Transcendentals

In the Seventh Edition of CALCULUS: EARLY TRANSCENDENTALS, Stewart continues to set the standard for the course while adding carefully revised content.

Author: James Stewart

Publisher: Cengage Learning

ISBN: 9780538497909

Category: Mathematics

Page: 1344

View: 170

James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of CALCULUS: EARLY TRANSCENDENTALS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Mathematics

From Past to Future Gra mann s Work in Context

From Past to Future  Gra  mann s Work in Context

EuEv/ So, from the general system of geometrical calculus we have obtained the
minimum system. The theory of homographies is well presented and analyzed in
the treatise Analyse vectorielle générale. Burali-Forti and Marcolongo define a ...

Author: Hans-Joachim Petsche

Publisher: Springer Science & Business Media

ISBN: 9783034604055

Category: Mathematics

Page: 580

View: 654

On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Graßmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Graßmann (the father).
Categories: Mathematics

CONCUR 94 Concurrency Theory

CONCUR  94  Concurrency Theory

In this paper, we consider a strict generalization of context- free processes, the
pushdown processes, which are ... iterative model-checking algorithm is
developed that decides the alternation-free part of the modal mu-calculus for
context-free ...

Author: Bengt Jonsson

Publisher: Springer Science & Business Media

ISBN: 3540583297

Category: Computers

Page: 528

View: 529

This volume constitutes the proceedings of the Fifth International Conference on Concurrency Theory, CONCUR '94, held at Uppsala, Sweden in August 1994. In total, 29 refereed research papers selected from 108 submissions for the conference are presented together with full papers or abstracts of the 5 invited talks by prominent speakers. The book contains recent results on all relevant aspects of concurrency research and thus competently documents the progress of the field since the predecessor conference CONCUR '93, the proceedings of which are published as LNCS 715.
Categories: Computers

Secondary Calculus and Cohomological Physics

Secondary Calculus and Cohomological Physics

A systematic use of the algebraic language of the differential calculus over
commutative algebras in these texts becomes almost indispensable in the
Secondary Calculus context. See [40, 38 and [44] for alternative approaches. The
concept of ...

Author: Marc Henneaux

Publisher: American Mathematical Soc.

ISBN: 9780821808283

Category: Mathematics

Page: 287

View: 534

This collection of invited lectures (at the Conference on Secondary Calculus and Cohomological Physics, Moscow) reflects the state-of-the-art in a new branch of mathematics and mathematical physics arising at the intersection of geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. This is the first comprehensive and self-contained book on modern quantum field theory in the context of cohomological methods and the geometry of nonlinear PDEs. It features: an up-to-date and self-contained exposition of the newest results in cohomological aspects of quantum field theory and the geometry of PDEs; a new look at interrelations among cohomology theory, the geometry of PDEs, and field theory; and, application to Batalin-Vilkovisky formalism, BRST formalism, anomalies, and quantum dynamics.
Categories: Mathematics

Gottlob Frege Frege s philosophy in context

Gottlob Frege  Frege s philosophy in context

CALCULUS RATIOCINATOR VERSUS CHARACTERISTICA UNIVERSALIS ?
The two traditions in logic , revisited Volker Peckhaus Source : History and
Philosophy of Logic 25 ( February 2004 ) : 3 - 14 . 1 . Introduction It is a
commonplace ...

Author: Michael Beaney

Publisher: Taylor & Francis

ISBN: 0415306027

Category:

Page: 424

View: 163

This collection brings together recent scholarship on Frege, including new translations of German material which is made available to Anglophone scholars for the first time.
Categories:

Lexical Meaning in Context

Lexical Meaning in Context

To build a formal model of predication and to express lexical meaning, I will use
the lambda calculus. The lambda calculus is the oldest, most expressive, and
best understood framework for meaning representation; and its links to various ...

Author: Nicholas Asher

Publisher: Cambridge University Press

ISBN: 9781139501316

Category: Language Arts & Disciplines

Page:

View: 479

This is a book about the meanings of words and how they can combine to form larger meaningful units, as well as how they can fail to combine when the amalgamation of a predicate and argument would produce what the philosopher Gilbert Ryle called a 'category mistake'. It argues for a theory in which words get assigned both an intension and a type. The book develops a rich system of types and investigates its philosophical and formal implications, for example the abandonment of the classic Church analysis of types that has been used by linguists since Montague. The author integrates fascinating and puzzling observations about lexical meaning into a compositional semantic framework. Adjustments in types are a feature of the compositional process and account for various phenomena including coercion and copredication. This book will be of interest to semanticists, philosophers, logicians and computer scientists alike.
Categories: Language Arts & Disciplines

Hermeneutics in Agile Systems Development

Hermeneutics in Agile Systems Development

Chapter 3 - Dimensions of Context Calculus Those doing structured methodology
felt there was one dimension to system development - function. The methodology
failed because there are many dimensions to a system. Here we discuss the ...

Author: Dr. Jerome Heath

Publisher: UberMann

ISBN:

Category: Computers

Page: 92

View: 189

Agile is the new world view of systems development. Structured design is being relegated to systems that have a short development time, the way to develop the software is already known (there is no need for design), and the system will not change in any way during the design. Agile methodologies have been developed over time from developers experiencing success by rejecting the ideas of the structured methodology and the waterfall style of project management. The main strengths of Agile methods are: Visibility (through the looking glass) Adaptability (context calculus) Business Value (incrementally increasing the value) Less Risk (changes are made on a Just In Time bases) The biggest problems with the waterfall techniques are: Risky and expensive. Inability to deal with changing requirements. Problems with late integration. Always required extensive rework to make software usable Business advantages of Agile development: Benefits can be realized early. First to market and early and regular releases. Testing is integrated so there is early recognition of any quality issues. Excellent visibility for key stakeholders ensures expectations are managed. Customer satisfaction through project visibility; customers own the project. Incremental releases reduce risks. Change is accepted, even expected. Cost control - the scope and features are variable, not the cost. Developers feel that they are part of the project and enjoy doing the work. In any form of agile development you are using post-modernist methodologies. Agile is post-modern or post structural. Agile and quality-productivity are the most effective post-modernist movements. Older development methodologies used some rather regulated processes of analyzing the information of a system. In fact they were using hermeneutic since hermeneutics is analysis of information. But their methodology put thought fences around this analysis. This book is proposing using all the powers of hermeneutics in developing software. In particular I include the methods developed in post-structuralist hermeneutics. So we study the system to determine what artifacts are present and how they might fit together in a new system. This process is called archeological layering; and renders artifacts that are associated in layers that belong together in the new system. This provides us with the meanings we need for the system. As we have completed this archeological layering in our present cycle we need to redefine the artifacts and their association to each other into what they will become as useful parts of the new system. I call this Formation Data Context. It is a study if the formation of data through the system we are building. It combines the new data to data already analyzed for formation data context. This process requires recognizing how definitions of terms and even the understanding of meanings is important to making a system useful. Thus we base our development of these understandings on pragmatism. This ultimately leads us in developing a system that is useful. This gives the developer a more complete understanding of the meaning of the information about the system from a proper use of hermeneutics. The process of using the more modern methodologies of hermeneutics also provides a more useful way of putting the information back together in the new system developed out of the project. Dr. Jerome Heath, Ph. D p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times; color: #000000; -webkit-text-stroke: #000000} p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times; color: #000000; -webkit-text-stroke: #000000; min-height: 14.0px} span.s1 {font-kerning: none}
Categories: Computers

Principles of Physics A Calculus Based Text

Principles of Physics  A Calculus Based Text

Context. Problems. and. Perspectives. We have now investigated the principles
of quantum physics and have seen ... for the Cosmic Connection Context: How
can we connect the physics of microscopic particles to the physics ofthe Universe
?

Author: Raymond A. Serway

Publisher: Cengage Learning

ISBN: 9781133712749

Category: Education

Page: 656

View: 738

PRINCIPLES OF PHYSICS is the only text specifically written for institutions that offer a calculus-based physics course for their life science majors. Authors Raymond A. Serway and John W. Jewett have revised the Fifth Edition of PRINCIPLES OF PHYSICS to include a new worked example format, new biomedical applications, two new Contexts features, a revised problem set based on an analysis of problem usage data from WebAssign, and a thorough revision of every piece of line art in the text. The Enhanced WebAssign course for PRINCIPLES OF PHYSICS is very robust, with all end-of-chapter problems, an interactive YouBook, and book-specific tutorials. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Categories: Education

Kindergarten of Fractional Calculus

Kindergarten of Fractional Calculus

CALCULUS. 9.1. Introduction. We will start the chapter by generalising the
concept of term-by-term differentiation as obtained for classical calculus, for the
fractional differ-integration context, and then we will formalise the composition
rules for ...

Author: Shantanu Das

Publisher: Cambridge Scholars Publishing

ISBN: 9781527547117

Category: Mathematics

Page: 533

View: 999

This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
Categories: Mathematics

The Logic of Mind

The Logic of Mind

The propositional calculus is context-free as is a certain normal form of
FORTRAN, lots of English, parts of the first order predicate calculus, and so forth.
Is all of English context-free?” Where in this hierarchy is English (Chomsky,
1975a, p.

Author: R.J. Nelson

Publisher: Springer Science & Business Media

ISBN: 9789400925953

Category: Philosophy

Page: 394

View: 267

This book presents a mechanist philosophy of mind. I hold that the human mind is a system of computational or recursive rules that are embodied in the nervous system; that the material presence of these rules accounts for perception, conception, speech, belief, desire, intentional acts, and other forms of intelligence. In this edition I have retained the whole of the fIrst edition except for discussion of issues which no longer are relevant in philosophy of mind and cognitive psychology. Earlier reference to disputes of the 1960's and 70's between hard-line empiricists and neorationalists over the psychological status of grammars and language acquisition, for instance, has simply been dropped. In place of such material I have entered some timely or new topics and a few changes. There are brief references to the question of computer versus distributed processing (connectionist) theories. Many of these questions dissolve if one distinguishes as I now do in Chapter II between free and embodied algorithms. I have also added to my comments on artifIcal in telligence some reflections. on Searle's Chinese Translator. The irreducibility of machine functionalist psychology in my version or any other has been exaggerated. Input, output, and state entities are token identical to physical or biological things of some sort, while a machine system as a collection of recursive rules is type identical to representatives of equivalence classes. This nuld technicality emerges in Chapter XI. It entails that so-called "anomalous monism" is right in one sense and wrong in another.
Categories: Philosophy