- 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 n-dimensional 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; Higher-order Partial Derivatives
- Chapter 2.5: The Chain Rule
- Chapter 2.6: Directional Derivatives and the Gradient
- Chapter 2.7: Newtons Method (optional)
- Chapter 3: Vector-Valued 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 k-forms
- Chapter 8.3: The Generalized Stokess Theorem
Vector Calculus 4th Edition - Solutions by Chapter
Full solutions for Vector Calculus | 4th Edition
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)
Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point
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.
An interval that has finite length (does not extend to ? or -?)
Complements or complementary angles
Two angles of positive measure whose sum is 90°
A fractional expression in which the numerator or denominator may contain fractions
See Polynomial function
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
The behavior of a graph of a function as.
Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.
Horizontal shrink or stretch
See Shrink, stretch.
Power rule of logarithms
logb Rc = c logb R, R 7 0.
Present value of an annuity T
he net amount of your money put into an annuity.
The collection of probabilities of outcomes in a sample space assigned by a probability function.
An expression that can be written as a ratio of two polynomials.
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.
Shrink of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.
The line segment whose endpoints are the vertices of a hyperbola.
A special form for a system of linear equations that facilitates finding the solution.
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