 16.1: What is a vector field? Give three examples that have physical mean...
 16.2: (a) What is a conservative vector field? (b) What is a potential fu...
 16.3: (a) Write the definition of the line integral of a scalar function ...
 16.4: (a) Define the line integral of a vector field along a smooth curve...
 16.5: State the Fundamental Theorem for Line Integrals.
 16.6: (a) What does it mean to say that is independent of path? (b) If yo...
 16.7: State Greens Theorem.
 16.8: Write expressions for the area enclosed by a curve in terms of line...
 16.9: Suppose is a vector field on . (a) Define curl . (b) Define div . (...
 16.10: If , how do you test to determine whether is conservative? What if ...
 16.11: (a) What is a parametric surface? What are its grid curves? (b) Wri...
 16.12: (a) Write the definition of the surface integral of a scalar functi...
 16.13: (a) What is an oriented surface? Give an example of a nonorientable...
 16.14: State Stokes Theorem.
 16.15: State the Divergence Theorem.
 16.16: In what ways are the Fundamental Theorem for Line Integrals, Greens...
 16.17: Use Greens Theorem to evaluate , where is the circle with countercl...
 16.18: Find curl and div if
 16.19: Show that there is no vector field such that
 16.20: Show that, under conditions to be stated on the vector fields and ,
 16.21: If is any piecewisesmooth simple closed plane curve and and are di...
 16.22: If and are twice differentiable functions, show that
 16.23: If is a harmonic function, that is, , show that the line integral i...
 16.24: (a) Sketch the curve with parametric equations (b)Find .
 16.25: Find the area of the part of the surface that lies above the triang...
 16.26: (a) Find an equation of the tangent plane at the point to the param...
 16.27: Evaluate the surface integral. , where is the part of the paraboloi...
 16.28: Evaluate the surface integral. , where is the part of the plane tha...
 16.29: Evaluate the surface integral. , where and is the sphere with outwa...
 16.30: Evaluate the surface integral. , where and is the part of the parab...
 16.31: Verify that Stokes Theorem is true for the vector field , where is ...
 16.32: Use Stokes Theorem to evaluate , where , is the part of the sphere ...
 16.33: Use Stokes Theorem to evaluate , where , and is the triangle with v...
 16.34: Use the Divergence Theorem to calculate the surface integral , wher...
 16.35: Verify that the Divergence Theorem is true for the vector field , w...
 16.36: Compute the outward flux of through the ellipsoid .
 16.37: Let Evaluate , where is the curve with initial point and terminal p...
 16.38: Let Evaluate , where is shown in the figure.
 16.39: Find , where and is the outwardly oriented surface shown in the fig...
 16.40: If the components of have continuous second partial derivatives and...
 16.41: If is a constant vector, , and is an oriented, smooth surface with ...
Solutions for Chapter 16: VECTOR CALCULUS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 16: VECTOR CALCULUS
Get Full SolutionsMultivariable Calculus, was written by and is associated to the ISBN: 9780538497879. Since 41 problems in chapter 16: VECTOR CALCULUS have been answered, more than 22527 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 16: VECTOR CALCULUS includes 41 full stepbystep solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Circle graph
A circular graphical display of categorical data

Complex conjugates
Complex numbers a + bi and a  bi

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Domain of a function
The set of all input values for a function

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Logistic regression
A procedure for fitting a logistic curve to a set of data

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Parametrization
A set of parametric equations for a curve.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Quartic regression
A procedure for fitting a quartic function to a set of data.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Range screen
See Viewing window.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Symmetric about the yaxis
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

xyplane
The points x, y, 0 in Cartesian space.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.