Calculus In Context
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Calculus In Context
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Author : James J. Callahan
language : en
Publisher:
Release Date : 1993
Calculus In Context written by James J. Callahan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Calculus categories.
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 In Context
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Author : James Callahan
language : en
Publisher: W H Freeman & Company
Release Date : 1995
Calculus In Context written by James Callahan and has been published by W H Freeman & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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 In Context
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Author : James Callahan
language : en
Publisher:
Release Date : 1994
Calculus In Context written by James Callahan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Calculus categories.
Designing the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. Our starting points are thus our summary of what calculus is really about. Our curricular goals are what we aim to convey about the subject in the course. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Starting Points Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the questions that give rise to these relationships. Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers and graphing calculators are much more than tools for teaching the traditional calculus. The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level. The process of successive approximation is a key tool of calculus, even when the outcome of the process--the limit--cannot be explicitly given in closed form. Curricular Goals Develop calculus in the context of scientific and mathematical questions. Treat systems of differential equations as fundamental objects of study. Construct and analyze mathematical models. Use the method of successive approximations to define and solve problems. Develop geometric visualization with hand-drawn and computer graphics. Give numerical methods a more central role. Functional Goals Encourage collaborative work. Enable students to use calculus as a language and a tool. Make students comfortable tackling large, messy, ill-defined problems. Foster an experimental attitude towards mathematics. Help students appreciate the value of approximate solutions. Teach students that understanding grows out of working on problems. Impact of Technology Differential equations can now be solved numerically, so they can take their rightful place in the introductory calculus course. The ability to handle data and perform many computations makes exploring messy, real-world problems possible. Since we can now deal with credible models, the role of modelling becomes much more central to the subject. The text illustrates how we have pursued the curricular goals. Each goal is addressed within the first chapter which begins with questions about describing and analyzing the spread of a contagious disease. A model is built: a model which is actually a system of coupled non-linear differential equations. We then begin a numerical exploration on those equations, and the door is opened to a solution by successive approximations. Our implementation of the functional goals is also evident. The text has many more words than the traditional calculus book--it is a book to be read. The exercises make unusual demands on students. Most are not just variants of examples that have been worked in the text. In fact, the text has rather few "template'' examples. Shifts in Emphasis It will also become apparent to you that the text reflects substantial shifts in emphasis in comparison to the traditional course. Here are some of the most striking: How the emphasis shifts: increase: concepts, geometry, graphs, brute force, numerical solutions decrease: techniques, algebra, formulas, elegance, closed-form solutions Since we all value elegance, let us explain what we mean by "brute force." Euler's method is a good example. It is a general method of wide applicability. Of course when we use it to solve a differential equation like y'(t) = t, we are using a sledgehammer to crack a peanut. But at least the sledgehammer works. Moreover, it works with coconuts (like y' = y(1 - y/10)), and it will even knock down a house (like y' = cos2(t)). Students also see the elegant special methods that can be invoked to solve y' = t and y' = y(1 - y/10) (separation of variables and partial fractions are discussed in chapter 11), but they understand that they are fortunate indeed when a real problem will succumb to such methods.
Calculus In Context
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Author : Callahan
language : en
Publisher: W.H. Freeman
Release Date : 1995
Calculus In Context written by Callahan and has been published by W.H. Freeman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Calculus categories.
Calculus In Context
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Author : H.A. Calahan
language : en
Publisher: W.H. Freeman
Release Date : 1995-05
Calculus In Context written by H.A. Calahan and has been published by W.H. Freeman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05 with categories.
This instructor's manual accompanies the text, Calculus in Context, which covers the standard agenda for a two-term course on calculus, but moves the course from purely theoretical realms to real-world problems where calculus is applied.
Calculus In Context
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Author : James Callahan
language : en
Publisher: W.H. Freeman
Release Date : 1993
Calculus In Context written by James Callahan and has been published by W.H. Freeman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Calculus categories.
Covering the standard agenda for a two-term course, the book is designed for classes where computers are used to teach and demonstrate calculus concepts. Students go to work on real-life problems where calculus is applied, and learn through problems-to-principles methodology.
Calculus Deconstructed
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Author : Zbigniew H. Nitecki
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-11
Calculus Deconstructed written by Zbigniew H. Nitecki and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-11 with Mathematics categories.
Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.
Calculus A Modeling And Computational Thinking Approach
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Author : Eric Stade
language : en
Publisher: Springer Nature
Release Date : 2023-04-13
Calculus A Modeling And Computational Thinking Approach written by Eric Stade and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-13 with Mathematics categories.
This book is intended for a first-semester course in calculus, which begins by posing a question: how do we model an epidemic mathematically? The authors use this question as a natural motivation for the study of calculus and as a context through which central calculus notions can be understood intuitively. The book’s approach to calculus is contextual and based on the principle that calculus is motivated and elucidated by its relevance to the modeling of various natural phenomena. The authors also approach calculus from a computational perspective, explaining that many natural phenomena require analysis through computer methods. As such, the book also explores some basic programming notions and skills.
Advanced Calculus
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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-09
Advanced Calculus written by James J. Callahan 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 2010-09-09 with Mathematics categories.
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.