 Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES
 Chapter 10.1: CURVES DEFINED BY PARAMETRIC EQUATIONS
 Chapter 10.2: CALCULUS WITH PARAMETRIC CURVES
 Chapter 10.3: POLAR COORDINATES
 Chapter 10.4: AREAS AND LENGTHS IN POLAR COORDINATES
 Chapter 10.5: CONIC SECTIONS
 Chapter 10.6: CONIC SECTIONS IN POLAR COORDINATES
 Chapter 11: INFINITE SEQUENCES AND SERIES
 Chapter 11.1: INFINITE SEQUENCES AND SERIES
 Chapter 11.10: TAYLOR AND MACLAURIN SERIES
 Chapter 11.11: APPLICATIONS OF TAYLOR POLYNOMIALS
 Chapter 11.2: SERIES
 Chapter 11.3: THE INTEGRAL TEST AND ESTIMATES OF SUMS
 Chapter 11.4: THE COMPARISON TESTS
 Chapter 11.5: ALTERNATING SERIES
 Chapter 11.6: ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS
 Chapter 11.7: Strategy for Testing Series
 Chapter 11.8: POWER SERIES
 Chapter 11.9: REPRESENTATIONS OF FUNCTIONS AS POWER SERIES
 Chapter 12: VECTORS AND THE GEOMETRY OF SPACE
 Chapter 12.1: THREEDIMENSIONAL COORDINATE SYSTEMS
 Chapter 12.2: VECTORS
 Chapter 12.3: THE DOT PRODUCT
 Chapter 12.4: THE CROSS PRODUCT
 Chapter 12.5: EQUATIONS OF LINES AND PLANES
 Chapter 12.6: CYLINDERS AND QUADRIC SURFACES
 Chapter 13: VECTOR FUNCTIONS
 Chapter 13.1: VECTOR FUNCTIONS AND SPACE CURVES
 Chapter 13.2: DERIVATIVES AND INTEGRALS OF VECTOR FUNCTIONS
 Chapter 13.3: ARC LENGTH AND CURVATURE
 Chapter 13.4: MOTION IN SPACE: VELOCITY AND ACCELERATION
 Chapter 14: PARTIAL DERIVATIVES
 Chapter 14.1: FUNCTIONS OF SEVERAL VARIABLES
 Chapter 14.2: LIMITS AND CONTINUITY
 Chapter 14.3: PARTIAL DERIVATIVES
 Chapter 14.4: TANGENT PLANES AND LINEAR APPROXIMATIONS
 Chapter 14.5: THE CHAIN RULE
 Chapter 14.6: DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR
 Chapter 14.7: MAXIMUM AND MINIMUM VALUES
 Chapter 14.8: LAGRANGE MULTIPLIERS
 Chapter 15: MULTIPLE INTEGRALS
 Chapter 15.1: DOUBLE INTEGRALS OVER RECTANGLES
 Chapter 15.10: CHANGE OF VARIABLES IN MULTIPLE INTEGRALS
 Chapter 15.2: ITERATED INTEGRALS
 Chapter 15.3: DOUBLE INTEGRALS OVER GENERAL REGIONS
 Chapter 15.4: DOUBLE INTEGRALS IN POLAR COORDINATES
 Chapter 15.5: APPLICATIONS OF DOUBLE INTEGRALS
 Chapter 15.6: SURFACE AREA
 Chapter 15.7: TRIPLE INTEGRALS
 Chapter 15.8: TRIPLE INTEGRALS IN CYLINDRICAL COORDINATES
 Chapter 15.9: TRIPLE INTEGRALS IN SPHERICAL COORDINATES
 Chapter 16: VECTOR CALCULUS
 Chapter 16.1: VECTOR FIELDS
 Chapter 16.2: LINE INTEGRALS
 Chapter 16.3: THE FUNDAMENTAL THEOREM FOR LINE INTEGRALS
 Chapter 16.4: GREENS THEOREM
 Chapter 16.5: CURL AND DIVERGENCE
 Chapter 16.6: PARAMETRIC SURFACES AND THEIR AREAS
 Chapter 16.7: SURFACE INTEGRALS
 Chapter 16.8: STOKES THEOREM
 Chapter 16.9: THE DIVERGENCE THEOREM
 Chapter 17: SECONDORDER DIFFERENTIAL EQUATIONS
 Chapter 17.1: SECONDORDER LINEAR EQUATIONS
 Chapter 17.2: NONHOMOGENEOUS LINEAR EQUATIONS
 Chapter 17.3: APPLICATIONS OF SECONDORDER DIFFERENTIAL EQUATIONS
 Chapter 17.4: SERIES SOLUTIONS
Multivariable Calculus, 7th Edition  Solutions by Chapter
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Multivariable Calculus,  7th Edition  Solutions by Chapter
Get Full SolutionsMultivariable Calculus, was written by Patricia and is associated to the ISBN: 9780538497879. This expansive textbook survival guide covers the following chapters: 66. Since problems from 66 chapters in Multivariable Calculus, have been answered, more than 8113 students have viewed full stepbystep answer. The full stepbystep solution to problem in Multivariable Calculus, were answered by Patricia, our top Calculus solution expert on 01/22/18, 03:30PM. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Acute triangle
A triangle in which all angles measure less than 90°

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Cosine
The function y = cos x

Data
Facts collected for statistical purposes (singular form is datum)

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Doubleangle identity
An identity involving a trigonometric function of 2u

Horizontal shrink or stretch
See Shrink, stretch.

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

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Measure of an angle
The number of degrees or radians in an angle

Multiplicative inverse of a matrix
See Inverse of a matrix

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Terminal side of an angle
See Angle.

Translation
See Horizontal translation, Vertical translation.

Xmax
The xvalue of the right side of the viewing window,.
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