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Calculus in Context - Background, Basics, and Applications (Hardcover)
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Calculus in Context - Background, Basics, and Applications (Hardcover)
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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.
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