- 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
Absolute value of a vector
See Magnitude of a vector.
See Inverse cotangent function.
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once
See Arithmetic sequence.
Interest compounded using the formula A = Pert
Direction angle of a vector
The angle that the vector makes with the positive x-axis
An identity involving a trigonometric function of 2u
Arrows that have the same magnitude and direction.
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
The instantaneous rate of change of a position function with respect to time, p. 737.
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.
Principle of mathematical induction
A principle related to mathematical induction.
See Viewing window.
Semiperimeter of a triangle
One-half of the sum of the lengths of the sides of a triangle.
Standard form: equation of a circle
(x - h)2 + (y - k2) = r 2
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
A special form for a system of linear equations that facilitates finding the solution.
Vector of length 1.
The directed distance from the y-axis yz-plane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.