- 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: THREE-DIMENSIONAL 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: SECOND-ORDER DIFFERENTIAL EQUATIONS
- Chapter 17.1: SECOND-ORDER LINEAR EQUATIONS
- Chapter 17.2: NONHOMOGENEOUS LINEAR EQUATIONS
- Chapter 17.3: APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS
- Chapter 17.4: SERIES SOLUTIONS
Multivariable Calculus, 7th Edition - Solutions by Chapter
Full solutions for Multivariable Calculus, | 7th Edition
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)
Axis of symmetry
See Line of symmetry.
Chord of a conic
A line segment with endpoints on the conic
A letter or symbol that stands for a specific number,
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable
Points that satisfy the constraints in a linear programming problem.
Index of summation
See Summation notation.
See Mathematical induction.
Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.
Left-hand limit of f at x a
The limit of ƒ as x approaches a from the left.
Line of travel
The path along which an object travels
Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x
Measure of spread
A measure that tells how widely distributed data are.
See Right circular cone.
One-to-one rule of logarithms
x = y if and only if logb x = logb y.
Product of functions
(ƒg)(x) = ƒ(x)g(x)
Zeros of a function that are rational numbers.
An equation found by regression and which can be used to predict unknown values.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>