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Worldwide Multivariable Calculus

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DIGITAL: Worldwide Multivariable Calculus
$14.95
PRINT: Worldwide Multivariable Calculus
$39.95
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Author: David B. Massey
ISBN-10: 0-9842071-3-9
ISBN-13: 978-0-9842071-3-8
©2012 Worldwide Center of Mathematics, LLC

Available in Digital or Print.
Digital: Full-Color PDF
Print: Black & White, Perfect-bound Paperback

Worldwide Multivariable Calculus

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Worldwide Multivariable Calculus covers the Calculus, both differential and integral, of functions of more than one variable. Most sections are divided into two or three subsections: Basics, More Depth, and +Linear Algebra. The Basics portions contain the typical material that would be covered in a class. The More Depth portions contain harder examples, more-advanced theory, and some proofs. The +Linear Algebra portions present certain aspects of multivariable Calculus in terms of linear algebra; these subsections are intended for students who already know linear algebra, or for those who are willing to learn linear algebra on-the-fly. Links to online linear algebra articles are included. The textbook begins with a general discussion of Euclidean space, vectors, the dot product, orthogonal projection, the cross product, lines and planes in space, multivariable functions and graphs. The second chapter contains the differential aspects of multivariable Calculus, including: partial derivatives, the total derivative, linear approximation, the tangent plane, the multivariable Chain Rule, the directional derivative, changes of coordinates, level sets, gradient vectors, parameterizing surfaces, optimization, Lagrange multipliers, implicit differentiation, and multivariable Taylor polynomials and series. Chapter 3 contains the integral aspects of multivariable Calculus, including: iterated integrals, definite integrals in Euclidean n-space, integration in polar, cylindrical, and spherical coordinates, volume, average value, mass, centers of mass, moments of inertia, and surface area. Chapter 4 contains the material on vector fields and integration; this includes: line integrals, conservative vector fields, the Fundamental Theorem of Line Integrals, Green’s Theorem, flux, the Divergence Theorem, and Stokes’ Theorem.

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