 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 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 19120 students have viewed full stepbystep answer. The full stepbystep solution to problem in Multivariable Calculus, were answered by , our top Calculus solution expert on 01/22/18, 03:30PM. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Imaginary axis
See Complex plane.

Implied domain
The domain of a function’s algebraic expression.

Initial value of a function
ƒ 0.

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Negative numbers
Real numbers shown to the left of the origin on a number line.

Open interval
An interval that does not include its endpoints.

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Partial fraction decomposition
See Partial fractions.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Subtraction
a  b = a + (b)

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is