- 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
ISBN: 9780321780652
This expansive textbook survival guide covers the following chapters: 47. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since problems from 47 chapters in Vector Calculus have been answered, more than 50909 students have viewed full step-by-step answer. The full step-by-step solution to problem in Vector Calculus were answered by , our top Calculus solution expert on 03/05/18, 06:59PM. Vector Calculus was written by and is associated to the ISBN: 9780321780652.
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Constant term
See Polynomial function
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Cosecant
The function y = csc x
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Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
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Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .
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Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.
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Interval
Connected subset of the real number line with at least two points, p. 4.
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Left-hand limit of f at x a
The limit of ƒ as x approaches a from the left.
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Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative
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Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x
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Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c
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LRAM
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
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Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
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Orthogonal vectors
Two vectors u and v with u x v = 0.
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Quadratic regression
A procedure for fitting a quadratic function to a set of data.
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Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.
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Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.
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Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
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Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.
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x-axis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.
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y-axis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.