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: 483

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.

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: 275

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.

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: 258

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.

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: 393

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.

Alexander J. Hahn, Calculus in Context: Background, Basics, and Applications,
Johns Hopkins University Press, Baltimore, MD, 2017. https://jhupbooks.press.jhu
.edu/content/calculus-context 3. The Infrared Processing & Analysis Center ...

Author: Alexander J. Hahn

Publisher: Springer Nature

ISBN: 9783030248680

Category: Mathematics

Page: 375

View: 477

Intended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories. The remarkable spacecraft missions to the inner and outermost reaches of our solar system have been one of the greatest success stories of modern human history. Much of the underlying mathematical story is presented alongside the astonishing images and extensive data that NASA’s Voyager, NEAR-Shoemaker, Cassini, and Juno missions have sent back to us. First and second year college students in mathematics, engineering, or science, and those seeking an enriching independent study, will experience the mathematical language and methods of single variable calculus within their application to relevant conceptual and strategic aspects of the navigation of a spacecraft. The reader is expected to have taken one or two semesters of the basic calculus of derivatives, integrals, and the role that limits play. Additional prerequisites include knowledge of coordinate plane geometry, basic trigonometry, functions and graphs, including trig, inverse, exponential, and log functions. The discussions begin with the rich history of humanity’s efforts to understand the universe from the Greeks, to Newton and the Scientific Revolution, to Hubble and galaxies, to NASA and the space missions. The calculus of polar functions that plays a central mathematical role is presented in a self-contained way in complete detail. Each of the six chapters is followed by an extensive problem set that deals with and also expands on the concerns of the chapter. The instructor has the flexibility to engage them with greater or lesser intensity. “I have been an aerospace engineer for 39 years and honestly, it would be hard for me to overstate how valuable I believe this book will be to numerous scientific and engineering disciplines and in particular to the future of aerospace engineering ... This book is perfectly crafted to motivate, educate, and prepare the scientists and engineers who wish to reach for the sky and beyond.” —Dr. Mario Zoccoli, Aerospace Engineer, NASA and Lockheed Martin

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: 269

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.

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: 153

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.

Author: Hans-Joachim PetschePublish On: 2010-12-16

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: 259

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).

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: 724

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.

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: 420

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.

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: 129

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.

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: 980

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.

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: 532

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}

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: 981

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.

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: 331

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.

This result has been shown in [MOY 10, MOY 09] when looking at the causality
problem in the real-time calculus context, while considering the prefix of traces in
the context of simulation. Some algorithms have been given in [ALT 11] for the ...

Author: Anne Bouillard

Publisher: John Wiley & Sons

ISBN: 9781848218529

Category: Computers

Page: 350

View: 601

Deterministic network calculus is a theory based on the (min,plus) algebra. Its aim is to compute worst-case performance bounds in communication networks. Our goal is to provide a comprehensive view of this theory and its recent advances, from its theoretical foundations to its implementations. The book is divided into three parts. The first part focuses on the (min,plus) framework and its algorithmic aspects. The second part defines the network calculus model and analyzes one server in isolation. Different service and scheduling policies are discussed, particularly when data is packetized. The third part is about network analyses. Pay burst only once and pay multiplexing only once phenomena are exhibited, and different analyses are proposed and compared. This includes the linear programming approaches that compute tight performance bounds. Finally, some partial results on the stability are detailed.

In the first part language reconstruction systems which are based essentially on
an extension of the l - calculus are brought into the foreground . In the second
part logics of context change are in the center of discussion . This is not the place
to ...

Author: Dwight E. NeuenschwanderPublish On: 2014-11-04

Chapter 8 takes us on a brief tour of tensors as seen in the context of abstract
algebra, as mappings from a set of vectors to the real numbers. This elegant
mathematical approach begins with the abstract notion of “multilinear forms” and
wends ...

Author: Dwight E. Neuenschwander

Publisher: JHU Press

ISBN: 9781421415642

Category: Mathematics

Page: 248

View: 683

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class). Dwight E. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.

Chapter 2 BASIC NOTIONS OF A CALCULUS OF SPEECH ACTS So far we have
presented a simple version of the theory of ... We will call the context in which an
illocutionary act is performed by an utterance the context of utterance .

Author: John R. Searle

Publisher: CUP Archive

ISBN: 0521263247

Category: Philosophy

Page: 227

View: 875

This is a formal and systematic study of the logical foundations of speech act theory. The study of speech acts has been a flourishing branch of the philosophy of language and linguistics over the last two decades, and John Searle has of course himself made some of the most notable contributions to that study in the sequence of books Speech Acts (1969), Expression and Meaning (1979) and Intentionality (1983). In collaboration with Daniel Vanderveken he now presents the first formalised logic of a general theory of speech acts, dealing with such things as the nature of an illocutionary force, the logical form of its components, and the conditions of success of elementary illocutionary acts. The central chapters present a systematic exposition of the axioms and general laws of illocutionary logic.

While most mathematics faculty are very positive about the course , of the nine
upper division mathematics majors with whom we met , several strongly disliked
the approach of Calculus in Context , and the majority said that even in retrospect
...