Designed for sophomore-level courses in multivariable calculus, this text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. It is useful to those with a background in single-variable calculus.
Product Identifiers
Publisher
Prentice Hall PTR
ISBN-10
0131858742
ISBN-13
9780131858749
eBay Product ID (ePID)
1840070
Product Key Features
Number of Pages
576 Pages
Language
English
Publication Name
Vector Calculus
Publication Year
2005
Subject
Calculus
Type
Textbook
Subject Area
Mathematics
Author
Susan Jane Colley
Format
Hardcover
Dimensions
Item Height
1.1 in
Item Weight
43.2 Oz
Item Length
8.3 in
Item Width
10.4 in
Additional Product Features
Edition Number
3
LCCN
2005-004445
Dewey Edition
23
Target Audience
College Audience
Illustrated
Yes
Dewey Decimal
515/.63
Lc Classification Number
Qa433.C635 2006
Table of Content
(NOTE: Each chapter concludes with True/False Exercises and Miscellaneous Exercises.) 1. Vectors. Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some n -Dimensional Geometry. New Coordinate Systems. 2. Differentiation in Several Variables. Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newton's Method. The Chain Rule. Directional Derivatives and the Gradient. 3. Vector-Valued Functions. Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator. 4. Maxima and Minima in Several Variables. Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. 5. Multiple Integration. Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. 6. Line Integrals. Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. 7. Surface Integrals and Vector Analysis. Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations. 8. Vector Analysis in Higher Dimensions. An Introduction to Differential Forms. Manifolds and Integrals of k -forms. The Generalized Stokes's Theorem. Suggestions for Further Reading. Answers to Selected Exercises. Index.