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Solutions for Chapter 8.2: Manifolds and Integrals of k-forms

Vector Calculus | 4th Edition | ISBN: 9780321780652 | Authors: Susan J. Colley

Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652

Vector Calculus | 4th Edition | ISBN: 9780321780652 | Authors: Susan J. Colley

Solutions for Chapter 8.2: Manifolds and Integrals of k-forms

This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8.2: Manifolds and Integrals of k-forms includes 15 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Since 15 problems in chapter 8.2: Manifolds and Integrals of k-forms have been answered, more than 13491 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
  • Algebraic expression

    A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

  • Arccosecant function

    See Inverse cosecant function.

  • Average velocity

    The change in position divided by the change in time.

  • Base

    See Exponential function, Logarithmic function, nth power of a.

  • Binomial coefficients

    The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

  • Circular functions

    Trigonometric functions when applied to real numbers are circular functions

  • Degree of a polynomial (function)

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

  • Differentiable at x = a

    ƒ'(a) exists

  • End behavior

    The behavior of a graph of a function as.

  • Exponential decay function

    Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

  • Gaussian elimination

    A method of solving a system of n linear equations in n unknowns.

  • Higher-degree polynomial function

    A polynomial function whose degree is ? 3

  • Horizontal asymptote

    The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

  • Inverse sine function

    The function y = sin-1 x

  • Parametric equations for a line in space

    The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

  • Product of complex numbers

    (a + bi)(c + di) = (ac - bd) + (ad + bc)i

  • Radian

    The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

  • Reference triangle

    For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle

  • RRAM

    A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.

  • yz-plane

    The points (0, y, z) in Cartesian space.

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