- 8.3.1: In Exercises 17, determine d, where is as indicated. = exyz
- 8.3.2: In Exercises 17, determine d, where is as indicated. = x 3 y 2x z2 ...
- 8.3.3: In Exercises 17, determine d, where is as indicated. = (x 2 + y2) d...
- 8.3.4: In Exercises 17, determine d, where is as indicated. = x1 dx2 x2 dx...
- 8.3.5: In Exercises 17, determine d, where is as indicated. = xz dx dy y2z...
- 8.3.6: In Exercises 17, determine d, where is as indicated. = x1x2x3 dx2 d...
- 8.3.7: = n i=1 x 2 i dx1 dx'i dxn (Note: dx'i means that the term dxi is o...
- 8.3.8: Let u be a unit vector and f a differentiable function. Show that d...
- 8.3.9: If = F(x,z) dy + G(x, y) dz is a (differentiable) 1- form on R3, wh...
- 8.3.10: Verify the generalized Stokess theorem (Theorem 3.2) for the 3-mani...
- 8.3.11: Verify the generalized Stokess theorem (Theorem 3.2) for the 3-mani...
- 8.3.12: (a) Let M be a parametrized 3-manifold in R3 (i.e., a solid). Show ...
Solutions for Chapter 8.3: The Generalized Stokess Theorem
Full solutions for Vector Calculus | 4th Edition
An equation that relates variable quantities associated with phenomena being studied
See Inverse tangent function.
See Exponential function, Logarithmic function, nth power of a.
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.
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.
Chord of a conic
A line segment with endpoints on the conic
Constant of variation
See Power function.
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
Two angles having the same initial side and the same terminal side
Differentiable at x = a
Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2
A series whose terms form a geometric sequence.
Higher-degree polynomial function
A polynomial function whose degree is ? 3
Imaginary part of a complex number
See Complex number.
Variable representing the domain value of a function (usually x).
The difference between the third quartile and the first quartile.
See Linear regression line.
Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible
See Division algorithm for polynomials.
Symmetric about the y-axis
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