- 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 matrix that represents a system of equations.
The change in position divided by the change in time.
A stemplot with leaves on either side used to compare two distributions.
A polynomial with exactly two terms
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
The left side of u(v + w) = uv + uw.
Inverse tangent function
The function y = tan-1 x
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
A local maximum or a local minimum
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval
Measure of center
A measure of the typical, middle, or average value for a data set
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.
A function that assigns real-number values to the outcomes in a sample space.
Slope-intercept form (of a line)
y = mx + b
A number that measures a quantitative variable for a sample from a population.
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.
The directed distance from the y-axis yz-plane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.
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