 Chapter 1: Vectors
 Chapter 1.1: Vectors in Two and Three Dimensions
 Chapter 1.2: More About Vectors
 Chapter 1.3: The Dot Product
 Chapter 1.4: The Cross Product
 Chapter 1.5: Equations for Planes; Distance Problems
 Chapter 1.6: Some ndimensional Geometry
 Chapter 1.7: New Coordinate Systems
 Chapter 2: Differentiation in Several Variables
 Chapter 2.1: Functions of Several Variables; Graphing Surfaces
 Chapter 2.2: Limits
 Chapter 2.3: The Derivative
 Chapter 2.4: Properties; Higherorder Partial Derivatives
 Chapter 2.5: The Chain Rule
 Chapter 2.6: Directional Derivatives and the Gradient
 Chapter 2.7: Newtons Method (optional)
 Chapter 3: VectorValued Functions
 Chapter 3.1: Parametrized Curves and Keplers Laws
 Chapter 3.2: Arclength and Differential Geometry
 Chapter 3.3: Vector Fields: An Introduction
 Chapter 3.4: Gradient, Divergence, Curl, and the Del Operator
 Chapter 4: Maxima and Minima in Several Variables
 Chapter 4.1: Differentials and Taylors Theorem
 Chapter 4.2: Extrema of Functions
 Chapter 4.3: Lagrange Multipliers
 Chapter 4.4: Some Applications of Extrema
 Chapter 5: Multiple Integration
 Chapter 5.1: Introduction: Areas and Volumes
 Chapter 5.2: Double Integrals
 Chapter 5.3: Changing the Order of Integration
 Chapter 5.4: Triple Integrals
 Chapter 5.5: Change of Variables
 Chapter 5.6: Applications of Integration
 Chapter 5.7: Numerical Approximations of Multiple Integrals (optional)
 Chapter 6: Line Integrals
 Chapter 6.1: Scalar and Vector Line Integrals
 Chapter 6.2: Greens Theorem
 Chapter 6.3: Conservative Vector Fields
 Chapter 7: Surface Integrals and Vector Analysis
 Chapter 7.1: Parametrized Surfaces
 Chapter 7.2: Surface Integrals
 Chapter 7.3: Stokess and Gausss Theorems
 Chapter 7.4: Further Vector Analysis; Maxwells Equations
 Chapter 8: Vector Analysis in Higher Dimensions
 Chapter 8.1: An Introduction to Differential Forms
 Chapter 8.2: Manifolds and Integrals of kforms
 Chapter 8.3: The Generalized Stokess Theorem
Vector Calculus 4th Edition  Solutions by Chapter
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Vector Calculus  4th Edition  Solutions by Chapter
Get Full SolutionsThis expansive textbook survival guide covers the following chapters: 47. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since problems from 47 chapters in Vector Calculus have been answered, more than 6515 students have viewed full stepbystep answer. The full stepbystep solution to problem in Vector Calculus were answered by Patricia, our top Calculus solution expert on 03/05/18, 06:59PM. Vector Calculus was written by Patricia and is associated to the ISBN: 9780321780652.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Chord of a conic
A line segment with endpoints on the conic

Direction vector for a line
A vector in the direction of a line in threedimensional space

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Function
A relation that associates each value in the domain with exactly one value in the range.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Leastsquares line
See Linear regression line.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Linear regression equation
Equation of a linear regression line

Modulus
See Absolute value of a complex number.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.

Right triangle
A triangle with a 90° angle.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.