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Multivariable calculus : a geometric approach

Author: F Beatrous; Caspar R Curjel
Publisher: Upper Saddle River, N.J. : Prentice Hall, ©2002.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Combining reform ideas, traditional ideas, and original ideas, this book is designed to teach concepts and computations about the geometry of 3D space. It also presents core concepts of multivariable  Read more...

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Document Type: Book
All Authors / Contributors: F Beatrous; Caspar R Curjel
ISBN: 0130304379 9780130304377
OCLC Number: 47073134
Notes: Includes index.
Description: xii, 456 pages : illustrations ; 26 cm
Contents: Preface. 1. Vectors and Curves. Vectors in the Plane. Lines and Curves in the Plane. Acceleration. The Dot Product. Coordinates and Vectors in Space. Lines in Space. The Dot Product of Space Vectors. The Cross Product. Planes. Curves in Space. Normals of Curves.2. Functions and Differentiation. Functions of Two Variables. Functions of Three Variables. Limits and Continuity. Partial Derivatives. Linear Approximation. The Chain Rule. Directional Derivatives: Functions of Two Variables. Directional Derivatives: Functions of Three Variables. Higher Order Approximations. Local (or Relative) Extrema. Constrained Extrema. Global (or Absolute) Extrema.3. Integration. Double Integrals I - Description and Properties. Double Integrals II - Cartesian Coordinates. Double Integrals in Polar Coordinates. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates.4. Vector Fields. Vector Fields in the Plane. Flow Lines of a Vector Field in the Plane. Vector Fields in Space. The Symbol o.5. Line Integrals. Force Fields and Work. Work and Line Integrals. Conservative Vector Fields. The Curl-Test.6. Surface Integrals. Parametrized Planes. Parametrized Surfaces. Velocity Fields and Flux. Flux and Surface Integrals.7. The Theorems of Green, Gauss, and Stokes. The Boundary of Solids, Surfaces, and Curves. Gauss' Divergence Theorem. Stokes' Theorem.Answers to Odd Problems.
Responsibility: Frank Beatrous, Caspar R. Curjel.

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