text stringlengths 0 73.6k | source stringclasses 4
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gradient | the gradient of the function f(x,y) is defined to be \vecs ∇f(x,y)=(∂f/∂x)\,\hat{\mathbf i}+(∂f/∂y)\,\hat{\mathbf j}, which can be generalized to a function of any
number of independent variables
gradient field | a vector field \vecs{F} for which there exists a scalar function f such that \vecs ∇f=\vecs{F}; ... | LibreTexts |
instantaneous velocity | The instantaneous velocity of an object with a position function that is given by s(t) is the value that the average velocities on intervals of the
form [t,a] and [a,t] approach as the values of t move closer to a, provided such a value exists
integrable function | a function is integrable if t... | LibreTexts |
linearly dependent | a set of functions f_1(x),f_2(x),…,f_n(x) for whichthere are constants c_1,c_2,…c_n, not all zero, such that c_1f_1(x)+c_2f_2(x)+⋯
+c_nf_n(x)=0 for all \(x\) in the interval of interest
linearly independent | a set of functions f_1(x),f_2(x),…,f_n(x) for which there are no constants c_1,c_2,…c_n, s... | LibreTexts |
normal component of acceleration | the coefficient of the unit normal vector \vecs N when the acceleration vector is written as a linear combination of \vecs T and
\vecs N
normal plane | a plane that is perpendicular to a curve at any point on the curve
normal vector | a vector perpendicular to a plane
normalization | ... | LibreTexts |
polar axis | the horizontal axis in the polar coordinate system corresponding to r≥0
polar coordinate system | a system for locating points in the plane. The coordinates are r, the radial coordinate, and θ, the angular coordinate
polar equation | an equation or function relating the radial coordinate to the angular coo... | LibreTexts |
right-endpoint approximation | the right-endpoint approximation is an approximation of the area of the rectangles under a curve using the right endpoint of each
subinterval to construct the vertical sides of each rectangle
right-hand rule | a common way to define the orientation of the three-dimensional coordinate syst... | LibreTexts |
standard equation of a sphere | (x−a)^2+(y−b)^2+(z−c)^2=r^2 describes a sphere with center (a,b,c) and radius r
standard form | the form of a first-order linear differential equation obtained by writing the differential equation in the form y'+p(x)y=q(x)
standard form | an equation of a conic section showing its proper... | LibreTexts |
trace | the intersection of a three-dimensional surface with a coordinate plane
transcendental function | a function that cannot be expressed by a combination of basic arithmetic operations
transformation | a function that transforms a region GG in one plane into a region RR in another plane by a change of variables
tr... | LibreTexts |
work done by a force | work is generally thought of as the amount of energy it takes to move an object; if we represent an applied force by a vector \vecs{ F} and the
displacement of an object by a vector \vecs{ s}, then the work done by the force is the dot product of \vecs{ F} and \vecs{ s}.
zero vector | the vector ... | LibreTexts |
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Title: Calculus (OpenStax)
Webpages: 285
Applicable Restrictions: Noncommercial
All licenses found:
CC BY-NC-SA 4.0: 99.6% (284 pages)
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Calculus (OpenStax) - CC BY-NC-SA 4.0 2.3E: Exercises for Section 2.3 - CC BY-NC-SA
Front Matter - CC BY-NC-SA 4.0 4.0
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