#

• _, 4.4
• _C, 4.1, 4.2
• _R, 3.2
• _S, 3.3
• (x,y,z) (u,v,w), 3.5
• (x,y), 3.6
• ^2, 4.6
• 2, 1.1
• 3, 1.1

A

• acceleration, 1.1, 1.8
• angle, 1.3
• annulus, 4.3
• arc length, 1.9
• area element, 3.2
• average value, 3.4

B

• B\'ezier curve, 1.8
• Beta function, 3.5

C

• C^1, C^, 1.9
• capping surface, 4.5
• Cauchy-Schwarz Inequality, 1.3
• center of mass, 3.6
• centroid, 3.6
• Chain Rule, 1.9, 4.2
• change of variable, 3.5
• circulation, 4.5
• closed curve, 4.2
• closed surface, 4.4
• collinear, 1.5
• conical helix, 4.5
• conservative field, 4.2
• constrained critical point, 2.7
• continuity, 1.8, 2.1
• continuously differentiable, 1.9, 2.4
• coordinates, 1.1
  • Cartesian, 1.1
  • curvilinear, 1.7
  • cylindrical, 1.7, 4.6
  • ellipsoidal, 4.4
  • left-handed, 1.1
  • polar, 1.7, 3.5
  • rectangular, 1.1
  • right-handed, 1.1
  • spherical, 1.7, 4.6
• coplanar, 1.4
• correlation, 3.7
• covariance, 3.7
• critical point, 2.5
• cross product, 1.4
• curl, 4.5, 4.6, 4.6
• curvature, 1.9
• cylinder, 1.6

D

• D, 2.5
• density, 3.6
• derivative, 1.1
  • directional, 2.4
  • mixed partial, 2.2
  • partial, 2.2
  • vector-valued function, 1.8
• determinant, 1.4
• differential, 4.1
• differential form, 4.1
• directed curve, 4.2
• direction angles, 1.3
• direction cosines, 1.3
• directional derivative, 2.4
• distance, 1.1
  • between points, 1.1
  • from point to line, 1.5
  • point to plane, 1.5, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6
• distribution function, 3.7
  • joint, 3.7
  • normal, 3.7
• divergence, 4.4, 4.6, 4.6
• Divergence Theorem, 4.4
• dot product, 1.3
• double integral, 3.1, 3.2
  • polar coordinates, 3.5
• doubly ruled surface, 1.6
• dr, 4.1
• Dvf, 2.4

E

• e_r, e_ , e_z, e_ , e_, 4.6
• ellipsoid, 1.6, 3.5, 4.4
• elliptic cone, 1.6
• elliptic paraboloid, 1.6
• Euclidean space, 1.1
• exact differential form, 4.1, 4.3, 4.5
• expected value, 3.7
• extreme point, 2.5

F

• f x, 2.2
• flux, 4.4
• force, 1.8
• function, 1.1
  • continuous, 2.1
  • scalar, 1.8
  • vector-valued, 1.8

G

• Gaussian blur, 2.1
• global maximum, 2.5
• global minimum, 2.5
• gradient, 2.4, 4.6
• Green's identities, 4.6
• Green's Theorem, 4.3

H

• harmonic, 4.6
• helicoid, 1.7
• helix, 1.8, 1.9, 4.5
• hyperbolic paraboloid, 1.6
• hyperboloid, 1.6
  • one sheet, 1.6
  • two sheets, 1.6
• hypersurface, 3.3
• hypervolume, 3.3

I

• i, j, k, 1.2
• improper integral, 3.2
• integral, 1.9
  • double, 3.1, 3.2
  • improper, 3.2
  • iterated, 3.1
  • multiple, 3.1
  • surface, 4.4
  • triple, 3.3
• irrotational, 4.5
• iterated integral, 3.1

J

• Jacobi identity, 1.4
• Jacobian, 3.5
• joint distribution, 3.7

L

• Lagrange multiplier, 2.7
• lamina, 3.6
• Laplacian, 4.6
• level curve, 2.1
• limit, 2.1
  • vector-valued function, 1.8
• line, 1.5
  • intersection of planes, 1.5
  • parallel, 1.5
  • parametric representation, 1.5
  • perpendicular, 1.5
  • skew, 1.5
  • symmetric representation, 1.5
  • through two points, 1.5
  • vector representation, 1.5
• line integral, 4.1
• local maximum, 2.5
• local minimum, 2.5

M

• M_x, M_y, 3.6
• M_xy, M_xz, M_yz, 3.6
• mass, 3.6
• matrix, 1.4
• mixed partial derivative, 2.2
• moebius@M\"obius strip, 4.5
• moment, 3.6
• momentum, 1.8
• Monte Carlo method, 3.4
• moving frame fields, 1.9
• multiple integral, 3.1
• multiply connected, 4.3

N

• n-positive@n-positive direction, 4.5
• Newton's algorithm, 2.6
• normal derivative, 4.6
• normal to a curve, 2.4
• normal vector field, 4.5

O

• orientable, 4.5
• orthonormal vectors, 1.9
• outward normal, 4.4

P

• paraboloid, 1.6
  • elliptic, 1.6
  • hyperbolic, 1.6, 2.5
  • of revolution, 1.6
• parallelepiped, 1.4
  • volume, 1.4
• parameter, 1.5, 1.9
• parametrization, 1.9
• partial derivative, 2.2
• partial differential equation, 2.2
• path independence, 4.2, 4.3, 4.5
• piecewise smooth curve, 4.1
• plane, 1.5
  • coordinate, 1.1
  • Euclidean, 1.1
  • in space, 1.5
  • line of intersection, 1.5
  • normal form, 1.5
  • normal vector, 1.5
  • point-normal form, 1.5
  • tangent, 2.3
  • through three points, 1.5
• position vector, 1.8, 4.1
• potential, 4.2
• probability, 3.7
• probability density function, 3.7
• projection, 1.3

Q

• quadric surface, 1.6

R

• random variable, 3.7
• Riemann integral, 4.1
• right-hand rule, 1.4, Appendix B: of the Right-Hand Rule for the Cross Product
• ruled surface, 1.6

S

• saddle point, 2.5
• sample space, 3.7
• scalar, 1.2
  • combination, 1.2
• scalar function, 1.8
• scalar triple product, 1.4
• Second Derivative Test, 2.5
• second moment, 3.7
• second-degree equation, 1.6
• simple closed curve, 4.2
• simply connected, 4.3, 4.5
• smooth function, 1.9, 2.5
• solenoidal, 4.4
• span, 1.3
• sphere, 1.6
• spherical spiral, 1.8
• standard normal distribution, 3.7
• steepest descent, 2.6
• stereographic projection, 1.6
• Stokes' Theorem, 4.5
• surface, 1.6
  • doubly ruled, 1.6
  • orientable, 4.5
  • ruled, 1.6
  • two-sided, 4.5
• surface integral, 4.4

T

• tangent plane, 2.3
• torus, 4.4
• trace, 1.6
• triangle inequality, 1.3
• triple integral, 3.3
  • cylindrical coordinates, 3.5
  • spherical coordinates, 3.5

U

• uniform density, 3.6
• uniform distribution, 3.7
• uniformly distributed, 3.7
• unit disk, 2.1

V

• variance, 3.7
• vector, 1.1
  • addition, 1.2
  • angle between, 1.3
  • basis, 1.2
  • components, 1.2
  • direction, 1.1
  • magnitude, 1.1
  • normal, 1.5, 4.4
  • normalized, 1.2
  • parallel, 1.2
  • perpendicular, 1.3
  • positive unit normal, 4.5
  • principal normal N, 1.9
  • scalar multiplication, 1.2
  • subtraction, 1.2
  • tangent, 1.8
  • translation, 1.1, 1.2
  • unit, 1.2
  • unit binormal B, 1.9
  • unit tangent T, 1.9
  • zero, 1.1
• vector field, 4.1
  • normal, 4.5
  • smooth, 4.3
• vector triple product, 1.4
• velocity, 1.1, 1.8
• volume element, 3.3

W

• wave equation, 2.2
• work, 4.1, 4.5

X

• x, 3.6

Y

• y, 3.6

Z

• z, 3.6
• zenith angle, 1.7