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Notation for differentiation
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In differential calculus, there is no single uniform notation for differentiation. Instead, several different notations for the derivative of a function or variable have been proposed by different mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation (and its opposite operation, the antidifferentiation or indefinite integration) are listed below.
Contents
[hide]
1 Leibniz's notation
1.1 Leibniz's notation for antidifferentiation
2 Lagrange's notation
2.1 Lagrange's notation for antidifferentiation
3 Euler's notation
3.1 Euler's notation for antidifferentiation
4 Newton's notation
4.1 Newton's notation for integration
5 Partial derivatives
6 Notation in vector calculus
7 See also
8 References
9 External links
Leibniz's notation[edit]
dy/dx
d2y/dx2
Main article: Leibniz's notation
The original notation employed by Gottfried Leibniz is used throughout mathematics. It is particularly common when the equation y = f(x) is regarded as a functional relationship between dependent and independent variables y and x. Leibniz's notation makes this relationship explicit by writing the derivative as
d y d x . {\displaystyle {\frac {dy}{dx}}.}
The function whose value at x is the derivative of f at x is therefore written
d f d x ( x ) or d f ( x ) d x or d d x f ( x ) . {\displaystyle {\frac {df}{dx}}(x){\text{ or }}{\frac {df(x)}{dx}}{\text{ or }}{\frac {d}{dx}}f(x).}
Higher derivatives are written as
d 2 y d x 2 , d 3 y d x 3 , d 4 y d x 4 , … , d n y d x n . {\displaystyle {\frac {d^{2}y}{dx^{2}}},{\frac {d^{3}y}{dx^{3}}},{\frac {d^{4}y}{dx^{4}}},\ldots ,{\frac {d^{n}y}{dx^{n}}}.}
This is a suggestive notational device that comes from formal manipulations of symbols, as in,
d ( d ( d y d x ) d x ) d x = ( d d x ) 3 y = d 3 y d x 3 . {\displaystyle {\frac {d\left({\frac {d\left({\frac {dy}{dx}}\right)}{dx}}\right)}{dx}}=\left({\frac {d}{dx}}\right)^{3}y={\frac {d^{3}y}{dx^{3}}}.}
Logically speaking, these equalities are not theorems. Instead, they are simply definitions of notation.
The value of the derivative of y at a point x = a may be expressed in two ways using Leibniz's notation:
d y d x | x = a = d y d x ( a ) {\displaystyle \left.{\frac {dy}{dx}}\right|_{x=a}={\frac {dy}{dx}}(a)} .
Leibniz's notation allows one to specify the variable for differentiation (in the denominator). This is especially helpful when considering partial derivatives. It also makes the chain rule easy to remember and recognize:
d y d x = d y d u ⋅ d u d x . {\displaystyle {\frac {dy}{dx}}={\frac {dy}{du}}\cdot {\frac {du}{dx}}.}
Leibniz's notation for differentiation does require assigning a meaning to symbols such as dx or dy on their own, and some authors do not attempt to assign these symbols meaning. Leibniz treated these symbols as infinitesimals. Later authors have assigned them other meanings, such as infinitesimals in non-standard analysis or exterior derivatives.
Leibniz's notation for antidifferentiation[edit]
∫ y dx
∫∫ y dx2
For functions of 2 or more variables, see Multiple integral.
Leibniz introduced the integral symbol ∫ in Analyseos tetragonisticae pars secunda and Methodi tangentium inversae exempla (both from 1675). It is now the standard symbol for integration.
∫ y ′ d x = ∫ f ′ ( x ) d x = f ( x ) + C 0 = y + C 0 ∫ y d x = ∫ f ( x ) d x = F ( x ) + C 1 ∫ ∫ y d x 2 = ∫ ( ∫ y d x ) d x = ∫ X × X f ( x ) d x = ∫ F ( x ) d x = g ( x ) + C 2 ∫ … ∫ ⏟ n y d x … d x ⏟ n = ∫ X × ⋯ × X ⏟ n f ( x ) d x = ∫ s ( x ) d x = S ( x ) + C n {\displaystyle {\begin{aligned}\int y'\,dx&=\int f'(x)\,dx=f(x)+C_{0}=y+C_{0}\\\int y\,dx&=\int f(x)\,dx=F(x)+C_{1}\\\int \int y\,dx^{2}&=\int \left(\int y\,dx\right)dx=\int _{X\times X}f(x)\,dx=\int F(x)\,dx=g(x)+C_{2}\\\underbrace {\int \dots \int } _{\!\!n}y\,\underbrace {dx\dots dx} _{n}&=\int _{\underbrace {X\times \cdots \times X} _{n}}f(x)\,dx=\int s(x)\,dx=S(x)+C_{n}\end{aligned}}}
Lagrange's notation[edit]
f′(x)
f ″(x)
One of the most common modern notations for differentiation is due to Joseph Louis Lagrange. In Lagrange's notation, a prime mark denotes a derivative. If f is a function, then its derivative is written
f ′ ( x ) {\displaystyle f'(x)} .
Lagrange first used the notation in unpublished works, and it appeared in print in 1770.[1]
Higher derivatives are indicated using additional prime marks, as in f ″ ( x ) {\displaystyle f''(x)} for the second derivative and f ‴ ( x ) {\displaystyle f'''(x)} for the third derivative. The use of repeated prime marks eventually becomes unwieldy. Some authors continue by employing Roman numerals, as in
f I V ( x ) , f V ( x ) , f V I ( x ) , … , {\displaystyle f^{\mathrm {IV} }(x),f^{\mathrm {V} }(x),f^{\mathrm {VI} }(x),\ldots ,}
to denote fourth, fifth, sixth, and higher order derivatives. Other authors use Arabic numerals in parentheses, as in
f ( 4 ) ( x ) , f ( 5 ) ( x ) , f ( 6 ) ( x ) , … . {\displaystyle f^{(4)}(x),f^{(5)}(x),f^{(6)}(x),\ldots .}
This notation also makes it possible to describe the nth derivative, where n is a variable. This is written
f ( n ) ( x ) . {\displaystyle f^{(n)}(x).}
Unicode characters related to Lagrange's notation include
U+2032 ◌′ PRIME (derivative)
U+2033 ◌″ DOUBLE PRIME (double derivative)
U+2034 ◌‴ TRIPLE PRIME (third derivative)
U+2057 ◌⁗ QUADRUPLE PRIME (fourth derivative)
When there are two independent variables for a function f(x,y), the following convention may be followed:[2]
f ′ = d f d x = f x f ′ = d f d y = f y f ′ ′ = d 2 f d x 2 = f x x f ′ ′ = ∂ 2 f ∂ x ∂ y = f x y f ′ ′ = d 2 f d y 2 = f y y , {\displaystyle {\begin{aligned}f^{\prime }&={\frac {df}{dx}}=f_{x}\\f_{\prime }&={\frac {df}{dy}}=f_{y}\\f^{\prime \prime }&={\frac {d^{2}f}{dx^{2}}}=f_{xx}\\f_{\prime }^{\prime }&={\frac {\partial ^{2}f}{\partial x\partial y}}\ =f_{xy}\\f_{\prime \prime }&={\frac {d^{2}f}{dy^{2}}}=f_{yy}\,,\end{aligned}}}
Lagrange's notation for antidifferentiation[edit]
f(−1)(x)
f(−2)(x)
When taking the antiderivative, Lagrange followed Leibniz's notation:[1]
f ( x ) = ∫ f ′ ( x ) d x = ∫ y d x . {\displaystyle f(x)=\int f'(x)\,dx=\int y\,dx.}
However, because integration is the inverse of differentiation, Lagrange's notation for higher order derivatives extends to integrals as well. Repeated integrals of f may be written as
f ( − 1 ) ( x ) {\displaystyle f^{(-1)}(x)} for the first integral (this is easily confused with the inverse function f − 1 ( x ) {\displaystyle f^{-1}(x)} ),
f ( − 2 ) ( x ) {\displaystyle f^{(-2)}(x)} for the second integral,
f ( − 3 ) ( x ) {\displaystyle f^{(-3)}(x)} for the third integral, and
f ( − n ) ( x ) {\displaystyle f^{(-n)}(x)} for the nth integral.
Euler's notation[edit]
Dxy
D2f
Leonhard Euler's notation uses a differential operator suggested by Louis François Antoine Arbogast, denoted as D (D operator)[3] or D̃ (Newton–Leibniz operator)[4] When applied to a function f(x), it is defined by
D f = d f d x . {\displaystyle Df={\frac {df}{dx}}.}
Higher derivatives are notated as powers of D, as in[2]
D 2 f {\displaystyle D^{2}f} for the second derivative,
D 3 f {\displaystyle D^{3}f} for the third derivative, and
D n f {\displaystyle D^{n}f} for the nth derivative.
Euler's notation leaves implicit the variable with respect to which differentiation is being done. However, this variable can also be notated explicitly. When f is a function of a variable x, this is done by writing[2]
D x f {\displaystyle D_{x}f} for the first derivative,
D x 2 f {\displaystyle D_{x}^{2}f} for the second derivative,
D x 3 f {\displaystyle D_{x}^{3}f} for the third derivative, and
D x n f {\displaystyle D_{x}^{n}f} for the nth derivative.
When f is a function of several variables, it's common to use a "∂" rather than D. As above, the subscripts denote the derivatives that are being taken. For example, the second partial derivatives of a function f(x, y) are:[2]
∂ x x f = ∂ 2 f ∂ x 2 , {\displaystyle \partial _{xx}f={\frac {\partial ^{2}f}{\partial x^{2}}},}
∂ x y f = ∂ 2 f ∂ x ∂ y , {\displaystyle \partial _{xy}f={\frac {\partial ^{2}f}{\partial x\partial y}},}
∂ y x f = ∂ 2 f ∂ y ∂ x , {\displaystyle \partial _{yx}f={\frac {\partial ^{2}f}{\partial y\partial x}},}
∂ y y f = ∂ 2 f ∂ y 2 . {\displaystyle \partial _{yy}f={\frac {\partial ^{2}f}{\partial y^{2}}}.}
See § Partial derivatives.
Euler's notation is useful for stating and solving linear differential equations, as it simplifies presentation of the differential equation, which can make seeing the essential elements of the problem easier.
Euler's notation for antidifferentiation[edit]
D−1
xy
D−2f
Euler's notation can be used for antidifferentiation in the same way that Lagrange's notation is.[5] as follows[4]
D − 1 f ( x ) {\displaystyle D^{-1}f(x)} for a first antiderivative,
D − 2 f ( x ) {\displaystyle D^{-2}f(x)} for a second antiderivative, and
D − n f ( x ) {\displaystyle D^{-n}f(x)} for an nth antiderivative.
Newton's notation[edit]
ẋ
ẍ
Newton's notation for differentiation (also called the dot notation for differentiation) places a dot over the dependent variable. That is, if y is a function of t, then the derivative of y with respect to t is
y ˙ {\displaystyle {\dot {y}}}
Higher derivatives are represented using multiple dots, as in
y ¨ , y . . . {\displaystyle {\ddot {y}},{\overset {...}{y}}}
Newton extended this idea quite far:[6]
y ¨ ≡ d 2 y d t 2 = d d t ( d y d t ) = d d t ( y ˙ ) = d d t ( f ′ ( t ) ) = D t 2 y = f ″ ( t ) = y t ″ y . . . = y ¨ ˙ ≡ d 3 y d t 3 = D t 3 y = f ‴ ( t ) = y t ‴ y ˙ 4 = y . . . . = y ¨ ¨ ≡ d 4 y d t 4 = D t 4 y = f I V ( t ) = y t ( 4 ) y ˙ 5 = y . . . ¨ = y ¨ ¨ ˙ = y ¨ ˙ ¨ ≡ d 5 y d t 5 = D t 5 y = f V ( t ) = y t ( 5 ) y ˙ 6 = y . . . . . . ≡ d 6 y d t 6 = D t 6 y = f V I ( t ) = y t ( 6 ) y ˙ 7 = y . . . . . . ˙ ≡ d 7 y d t 7 = D t 7 y = f V I I ( t ) = y t ( 7 ) y ˙ 10 = y ¨ ¨ ¨ ¨ ¨ ≡ d 10 y d t 10 = D t 10 y = f X ( t ) = y t ( 10 ) y ˙ n ≡ d n y d t n = D t n y = f ( n ) ( t ) = y t ( n ) {\displaystyle {\begin{aligned}{\ddot {y}}&\equiv {\frac {d^{2}y}{dt^{2}}}={\frac {d}{dt}}\left({\frac {dy}{dt}}\right)={\frac {d}{dt}}{\Bigl (}{\dot {y}}{\Bigr )}={\frac {d}{dt}}{\Bigl (}f'(t){\Bigr )}=D_{t}^{2}y=f''(t)=y''_{t}\\{\overset {...}{y}}&={\dot {\ddot {y}}}\equiv {\frac {d^{3}y}{dt^{3}}}=D_{t}^{3}y=f'''(t)=y'''_{t}\\{\overset {\,4}{\dot {y}}}&={\overset {....}{y}}={\ddot {\ddot {y}}}\equiv {\frac {d^{4}y}{dt^{4}}}=D_{t}^{4}y=f^{IV}(t)=y_{t}^{(4)}\\{\overset {\,5}{\dot {y}}}&={\ddot {\overset {...}{y}}}={\dot {\ddot {\ddot {y}}}}={\ddot {\dot {\ddot {y}}}}\equiv {\frac {d^{5}y}{dt^{5}}}=D_{t}^{5}y=f^{V}(t)=y_{t}^{(5)}\\{\overset {\,6}{\dot {y}}}&={\overset {...}{\overset {...}{y}}}\equiv {\frac {d^{6}y}{dt^{6}}}=D_{t}^{6}y=f^{VI}(t)=y_{t}^{(6)}\\{\overset {\,7}{\dot {y}}}&={\dot {\overset {...}{\overset {...}{y}}}}\equiv {\frac {d^{7}y}{dt^{7}}}=D_{t}^{7}y=f^{VII}(t)=y_{t}^{(7)}\\{\overset {\,10}{\dot {y}}}&={\ddot {\ddot {\ddot {\ddot {\ddot {y}}}}}}\equiv {\frac {d^{10}y}{dt^{10}}}=D_{t}^{10}y=f^{X}(t)=y_{t}^{(10)}\\{\overset {\,n}{\dot {y}}}&\equiv {\frac {d^{n}y}{dt^{n}}}=D_{t}^{n}y=f^{(n)}(t)=y_{t}^{(n)}\end{aligned}}}
Unicode characters related to Newton's notation include:
U+0307 ◌̇ COMBINING DOT ABOVE (derivative)
U+0308 ◌̈ COMBINING DIAERESIS (double derivative)
U+20DB ◌⃛ COMBINING THREE DOTS ABOVE (third derivative) ← replaced by "combining diaeresis" + "combining dot above".
U+20DC ◌⃜ COMBINING FOUR DOTS ABOVE (fourth derivative) ← replaced by "combining diaeresis" twice.
U+030D ◌̍ COMBINING VERTICAL LINE ABOVE (integral)
U+030E ◌̎ COMBINING DOUBLE VERTICAL LINE ABOVE (second integral)
U+25AD ▭ WHITE RECTANGLE (integral)
U+20DE ◌⃞ COMBINING ENCLOSING SQUARE (integral)
U+1DE0 ◌ᷠ COMBINING LATIN SMALL LETTER N (nth derivative)
Newton's notation is generally used when the independent variable denotes time. If location y is a function of t, then y ˙ {\displaystyle {\dot {y}}} denotes velocity[7] and y ¨ {\displaystyle {\ddot {y}}} denotes acceleration.[8] This notation is popular in physics and mathematical physics. It also appears in areas of mathematics connected with physics such as differential equations. It is only popular for first and second derivatives, but in applications these are usually the only derivatives that are necessary.
When taking the derivative of a dependent variable y = f(x), an alternative notation exists:[9]
y ˙ x ˙ = y ˙ : x ˙ ≡ d y d t : d x d t = d y d t d x d t = d y d x = d d t ( f ( x ) ) = D y = f ′ ( x ) = y ′ {\displaystyle {\frac {\dot {y}}{\dot {x}}}={\dot {y}}:{\dot {x}}\equiv {\frac {dy}{dt}}:{\frac {dx}{dt}}={\frac {\frac {dy}{dt}}{\frac {dx}{dt}}}={\frac {dy}{dx}}={\frac {d}{dt}}{\Bigl (}f(x){\Bigr )}=Dy=f'(x)=y'}
Newton developed the following partial differential operators using side-dots on a curved X ( ⵋ ). Definitions given by Whiteside are below:[10][11]
X = f ( x , y ) , ⋅ X = x ∂ f ∂ x = x f x , X ⋅ = y ∂ f ∂ y = y f y , : X or ⋅ : X = x 2 ∂ 2 f ∂ x 2 = x 2 f x x , X : or ⋅ X ⋅ = y 2 ∂ 2 f ∂ y 2 = y 2 f y y , ⋅ X ⋅ or X : ⋅ = x y ∂ 2 f ∂ x ∂ y = x y f x y , {\displaystyle {\begin{aligned}{\mathcal {X}}\ &=\ f(x,y)\,,\\\cdot {\mathcal {X}}\ &=\ x{\frac {\partial f}{\partial x}}=xf_{x}\,,\\{\mathcal {X}}\cdot \ &=\ y{\frac {\partial f}{\partial y}}=yf_{y}\,,\\\colon {\mathcal {X}}\,{\text{ or }}\,\cdot \colon {\mathcal {X}}\ &=\ x^{2}{\frac {\partial ^{2}f}{\partial x^{2}}}=x^{2}f_{xx}\,,\\{\mathcal {X}}\colon \,{\text{ or }}\,\cdot {\mathcal {X}}\cdot \ &=\ y^{2}{\frac {\partial ^{2}f}{\partial y^{2}}}=y^{2}f_{yy}\,,\\\cdot {\mathcal {X}}\cdot \,{\text{ or }}\,{\mathcal {X}}\colon \cdot \ &=\ xy{\frac {\partial ^{2}f}{\partial x\partial y}}=xyf_{xy}\,,\end{aligned}}}
Newton's notation for integration[edit]
x̍
x̎
Newton developed many different notations for integration in his Quadratura curvarum (1704) and later works: he wrote a small vertical bar or prime above the dependent variable (y̍), a prefixing rectangle (▭y), or the inclosure of the term in a rectangle (y) to denote the fluent or time integral (absement).
y = ◻ y ˙ ≡ ∫ y ˙ d t = ∫ f ′ ( t ) d t = D t − 1 ( D t y ) = f ( t ) + C 0 = y t + C 0 y ′ = ◻ y ≡ ∫ y d t = ∫ f ( t ) d t = D t − 1 y = F ( t ) + C 1 {\displaystyle {\begin{aligned}y&=\Box {\dot {y}}\equiv \int {\dot {y}}\,dt=\int f'(t)\,dt=D_{t}^{-1}(D_{t}y)=f(t)+C_{0}=y_{t}+C_{0}\\{\overset {\,\prime }{y}}&=\Box y\equiv \int y\,dt=\int f(t)\,dt=D_{t}^{-1}y=F(t)+C_{1}\end{aligned}}}
To denote multiple integrals, Newton used two small vertical bars or primes (y̎), or a combination of previous symbols ▭y̍ y̍, to denote the second time integral (absity).
y ′ ′ = ◻ y ′ ≡ ∫ y ′ d t = ∫ F ( t ) d t = D t − 2 y = g ( t ) + C 2 {\displaystyle {\overset {\,\prime \prime }{y}}=\Box {\overset {\,\prime }{y}}\equiv \int {\overset {\,\prime }{y}}\,dt=\int F(t)\,dt=D_{t}^{-2}y=g(t)+C_{2}}
Higher order time integrals were as follows:[12]
y ′ ′ ′ = ◻ y ′ ′ ≡ ∫ y ′ ′ d t = ∫ g ( t ) d t = D t − 3 y = G ( t ) + C 3 y ′ ′ ′ ′ = ◻ y ′ ′ ′ ≡ ∫ y ′ ′ ′ d t = ∫ G ( t ) d t = D t − 4 y = h ( t ) + C 4 y ′ n = ◻ y ′ n − 1 ≡ ∫ y ′ n − 1 d t = ∫ s ( t ) d t = D t − n y = S ( t ) + C n {\displaystyle {\begin{aligned}{\overset {\,\prime \prime \prime }{y}}&=\Box {\overset {\,\prime \prime }{y}}\equiv \int {\overset {\,\prime \prime }{y}}\,dt=\int g(t)\,dt=D_{t}^{-3}y=G(t)+C_{3}\\{\overset {\,\prime \prime \prime \prime }{y}}&=\Box {\overset {\,\prime \prime \prime }{y}}\equiv \int {\overset {\,\prime \prime \prime }{y}}\,dt=\int G(t)\,dt=D_{t}^{-4}y=h(t)+C_{4}\\{\overset {\;n}{\overset {\,\prime }{y}}}&=\Box {\overset {\;n-1}{\overset {\,\prime }{y}}}\equiv \int {\overset {\;n-1}{\overset {\,\prime }{y}}}\,dt=\int s(t)\,dt=D_{t}^{-n}y=S(t)+C_{n}\end{aligned}}}
This mathematical notation didn't become widespread because of printing difficulties and the Leibniz–Newton calculus controversy.
Partial derivatives[edit]
fx
fxy
When more specific types of differentiation are necessary, such as in multivariate calculus or tensor analysis, other notations are common.
For a function f(x), we can express the derivative using subscripts of the independent variable:
f x = d f d x f x x = d 2 f d x 2 . {\displaystyle {\begin{aligned}f_{x}&={\frac {df}{dx}}\\f_{xx}&={\frac {d^{2}f}{dx^{2}}}.\end{aligned}}}
This type of notation is especially useful for taking partial derivatives of a function of several variables.
∂f/∂x
Partial derivatives are generally distinguished from ordinary derivatives by replacing the differential operator d with a "∂" symbol. For example, we can indicate the partial derivative of f(x, y, z) with respect to x, but not to y or z in several ways:
∂ f ∂ x = f x = ∂ x f . {\displaystyle {\frac {\partial f}{\partial x}}=f_{x}=\partial _{x}f.}
Other notations can be found in various subfields of mathematics, physics, and engineering, see for example the Maxwell relations of thermodynamics. The symbol ( ∂ T ∂ V ) S {\displaystyle \left({\frac {\partial T}{\partial V}}\right)_{S}} is the derivative of the temperature T with respect to the volume V while keeping constant the entropy (subscript) S, while ( ∂ T ∂ V ) P {\displaystyle \left({\frac {\partial T}{\partial V}}\right)_{P}} is the derivative of the temperature with respect to the volume while keeping constant the pressure P.
Higher-order partial derivatives with respect to one variable are expressed as
∂ 2 f ∂ x 2 = f x x {\displaystyle {\frac {\partial ^{2}f}{\partial x^{2}}}=f_{xx}}
∂ 3 f ∂ x 3 = f x x x . {\displaystyle {\frac {\partial ^{3}f}{\partial x^{3}}}=f_{xxx}.}
Mixed partial derivatives can be expressed as
∂ 2 f ∂ y ∂ x = f x y . {\displaystyle {\frac {\partial ^{2}f}{\partial y\partial x}}=f_{xy}.}
In this last case the variables are written in inverse order between the two notations, explained as follows:
( f x ) y = f x y {\displaystyle (f_{x})_{y}=f_{xy}}
∂ ∂ y ( ∂ f ∂ x ) = ∂ 2 f ∂ y ∂ x {\displaystyle {\frac {\partial }{\partial y}}\left({\frac {\partial f}{\partial x}}\right)={\frac {\partial ^{2}f}{\partial y\partial x}}}
Notation in vector calculus[edit]
Vector calculus concerns differentiation and integration of vector or scalar fields. Several notations specific to the case of three-dimensional Euclidean space are common.
Assume that (x, y, z) is a given Cartesian coordinate system, that A is a vector field with components A = ( A x , A y , A z ) {\displaystyle \mathbf {A} =(\mathbf {A} _{x},\mathbf {A} _{y},\mathbf {A} _{z})} , and that φ = φ ( x , y , z ) {\displaystyle \varphi =\varphi (x,y,z)} is a scalar field.
The differential operator introduced by William Rowan Hamilton, written ∇ and called del or nabla, is symbolically defined in the form of a vector,
∇ = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) , {\displaystyle \nabla =\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right),}
where the terminology symbolically reflects that the operator ∇ will also be treated as an ordinary vector.
∇φ
Gradient: The gradient g r a d φ {\displaystyle \mathrm {grad\,} \varphi } of the scalar field φ {\displaystyle \varphi } is a vector, which is symbolically expressed by the multiplication of ∇ and scalar field φ {\displaystyle \varphi } ,
grad  φ = ( ∂ φ ∂ x , ∂ φ ∂ y , ∂ φ ∂ z ) = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) φ = ∇ φ {\displaystyle {\begin{aligned}\operatorname {grad} \varphi &=\left({\frac {\partial \varphi }{\partial x}},{\frac {\partial \varphi }{\partial y}},{\frac {\partial \varphi }{\partial z}}\right)\\&=\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right)\varphi \\&=\nabla \varphi \end{aligned}}}
∇∙A
Divergence: The divergence d i v A {\displaystyle \mathrm {div} \,\mathbf {A} } of the vector field A is a scalar, which is symbolically expressed by the dot product of ∇ and the vector A,
div  A = ∂ A x ∂ x + ∂ A y ∂ y + ∂ A z ∂ z = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) ⋅ A = ∇ ⋅ A {\displaystyle {\begin{aligned}\operatorname {div} \mathbf {A} &={\partial A_{x} \over \partial x}+{\partial A_{y} \over \partial y}+{\partial A_{z} \over \partial z}\\&=\left({\frac {\partial }{\partial x}},{\frac {\partial }{\partial y}},{\frac {\partial }{\partial z}}\right)\cdot \mathbf {A} \\&=\nabla \cdot \mathbf {A} \end{aligned}}}
∇2φ
Laplacian: The Laplacian div  grad  φ {\displaystyle \operatorname {div} \operatorname {grad} \varphi } of the scalar field φ {\displaystyle \varphi } is a scalar, which is symbolically expressed by the scalar multiplication of ∇2 and the scalar field φ,
div  grad  φ = ∇ ⋅ ( ∇ φ ) = ( ∇ ⋅ ∇ ) φ = ∇ 2 φ = Δ φ {\displaystyle {\begin{aligned}\operatorname {div} \operatorname {grad} \varphi &=\nabla \cdot (\nabla \varphi )\\&=(\nabla \cdot \nabla )\varphi \\&=\nabla ^{2}\varphi \\&=\Delta \varphi \\\end{aligned}}}
∇×A
Rotation: The rotation c u r l A {\displaystyle \mathrm {curl} \,\mathbf {A} } , or r o t A {\displaystyle \mathrm {rot} \,\mathbf {A} } , of the vector field A is a vector, which is symbolically expressed by the cross product of ∇ and the vector A,
curl  A = ( ∂ A z ∂ y − ∂ A y ∂ z , ∂ A x ∂ z − ∂ A z ∂ x , ∂ A y ∂ x − ∂ A x ∂ y ) = ( ∂ A z ∂ y − ∂ A y ∂ z ) i + ( ∂ A x ∂ z − ∂ A z ∂ x ) j + ( ∂ A y ∂ x − ∂ A x ∂ y ) k = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z A x A y A z | = ∇ × A {\displaystyle {\begin{aligned}\operatorname {curl} \mathbf {A} &=\left({\partial A_{z} \over {\partial y}}-{\partial A_{y} \over {\partial z}},{\partial A_{x} \over {\partial z}}-{\partial A_{z} \over {\partial x}},{\partial A_{y} \over {\partial x}}-{\partial A_{x} \over {\partial y}}\right)\\&=\left({\partial A_{z} \over {\partial y}}-{\partial A_{y} \over {\partial z}}\right)\mathbf {i} +\left({\partial A_{x} \over {\partial z}}-{\partial A_{z} \over {\partial x}}\right)\mathbf {j} +\left({\partial A_{y} \over {\partial x}}-{\partial A_{x} \over {\partial y}}\right)\mathbf {k} \\&={\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\cfrac {\partial }{\partial x}}&{\cfrac {\partial }{\partial y}}&{\cfrac {\partial }{\partial z}}\\A_{x}&A_{y}&A_{z}\end{vmatrix}}\\&=\nabla \times \mathbf {A} \end{aligned}}}
Many symbolic operations of derivatives can be generalized in a straightforward manner by the gradient operator in Cartesian coordinates. For example, the single-variable product rule has a direct analogue in the multiplication of scalar fields by applying the gradient operator, as in
( f g ) ′ = f ′ g + f g ′ ⟹ ∇ ( ϕ ψ ) = ( ∇ ϕ ) ψ + ϕ ( ∇ ψ ) . {\displaystyle (fg)'=f'g+fg'~~~\Longrightarrow ~~~\nabla (\phi \psi )=(\nabla \phi )\psi +\phi (\nabla \psi ).}
Further notations have been developed for more exotic types of spaces. For calculations in Minkowski space, the d'Alembert operator, also called the d'Alembertian, wave operator, or box operator is represented as ◻ {\displaystyle \Box } , or as Δ {\displaystyle \Delta } when not in conflict with the symbol for the Laplacian.
See also[edit]
Analytical Society
Derivative
Jacobian matrix
Hessian matrix
References[edit]
^ Jump up to: a b Lagrange, Nouvelle méthode pour résoudre les équations littérales par le moyen des séries (1770), p. 25-26. http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=PPN308900308%7CLOG_0017&physid=PHYS_0031
^ Jump up to: a b c d The Differential and Integral Calculus (Augustus De Morgan, 1842). pp. 267-268
Jump up ^ "The D operator - Differential - Calculus - Maths Reference with Worked Examples". www.codecogs.com. Archived from the original on 2016-01-19.
^ Jump up to: a b Weisstein, Eric W. "Differential Operator." From MathWorld--A Wolfram Web Resource. "Archived copy". Archived from the original on 2016-01-21. Retrieved 2016-02-07.
Jump up ^ Weisstein, Eric W. "Repeated Integral." From MathWorld--A Wolfram Web Resource. "Archived copy". Archived from the original on 2016-02-01. Retrieved 2016-02-07.
Jump up ^ Newton's notation reproduced from:
1st to 5th derivatives: Quadratura curvarum (Newton, 1704), p. 7 (p. 5r in original MS: "Archived copy". Archived from the original on 2016-02-28. Retrieved 2016-02-05. ).
1st to 7th, nth and (n+1)th derivatives: Method of Fluxions (Newton, 1736), pp. 313-318 and p. 265 (p. 163 in original MS: "Archived copy". Archived from the original on 2017-04-06. Retrieved 2016-02-05. )
1st to 5th derivatives : A Treatise of Fluxions (Colin MacLaurin, 1742), p. 613
1st to 4th and nth derivatives: Articles "Differential" and "Fluxion", Dictionary of Pure and Mixed Mathematics (Peter Barlow, 1814)
1st to 4th, 10th and nth derivatives: Articles 622, 580 and 579 in A History of Mathematical Notations (F .Cajori, 1929)
1st to 6th and nth derivatives: The Mathematical Papers of Isaac Newton Vol. 7 1691-1695 (D. T. Whiteside, 1976), pp.88 and 17
1st to 3rd and nth derivatives: A History of Analysis (Hans Niels Jahnke, 2000), pp. 84-85
The dot for nth derivative may be omitted ( y n {\displaystyle {\overset {\,n}{y}}} )
Jump up ^ Weisstein, Eric W. "Overdot." From MathWorld--A Wolfram Web Resource. "Archived copy". Archived from the original on 2015-09-05. Retrieved 2016-02-05.
Jump up ^ Weisstein, Eric W. "Double Dot." From MathWorld--A Wolfram Web Resource. "Archived copy". Archived from the original on 2016-03-03. Retrieved 2016-02-05.
Jump up ^ Article 580 in Florian Cajori, A History of Mathematical Notations (1929), Dover Publications, Inc. New York. ISBN 0-486-67766-4
Jump up ^ "Patterns of Mathematical Thought in the Later Seventeenth Century", Archive for History of Exact Sciences Vol. 1, No. 3 (D. T. Whiteside, 1961), pp. 179-388
Jump up ^ S.B. Engelsman has given more strict definitions in Families of Curves and the Origins of Partial Differentiation (2000), pp. 223-226
Jump up ^ Newton's notation for integration reproduced from:
1st to 3rd integrals: Quadratura curvarum (Newton, 1704), p. 7 (p. 5r in original MS: "Archived copy". Archived from the original on 2016-02-28. Retrieved 2016-02-05. )
1st to 3rd integrals: Method of Fluxions (Newton, 1736), pp. 265-266 (p. 163 in original MS: "Archived copy". Archived from the original on 2017-04-06. Retrieved 2016-02-05. )
4th integrals: The Doctrine of Fluxions (James Hodgson, 1736), pp. 54 and 72
1st to 2nd integrals: Articles 622 and 365 in A History of Mathematical Notations (F .Cajori, 1929)
The nth integral notation is deducted from the nth derivative. It could be used in Methodus Incrementorum Directa & Inversa (Brook Taylor, 1715)
External links[edit]
Earliest Uses of Symbols of Calculus, maintained by Jeff Miller.
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Alan Hale Jr.
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
For other people with similar names, see Alan Hale (disambiguation).
Alan Hale Jr.
Alan Hale Jr. in 1959
Born
Alan Hale MacKahan
(1921-03-08)March 8, 1921[1][2]
Los Angeles,[2] California, U.S.
Died
January 2, 1990(1990-01-02) (aged 68)
Los Angeles, California, U.S.
Cause of death
Thymus cancer
Occupation
Actor, restaurateur
Years active
1931–1988
Known for
Gilligan's Island
Spouse(s)
Bettina Doerr Hale (m. 1943; div. 1963)[2]
Naomi Ingram (m. 1964; his death 1990)
Children
4
Parent(s)
Alan Hale Sr.[2]
Gretchen Hartman Hale[2]
Alan Hale Jr. (born Alan Hale MacKahan,[2] March 8, 1921[2] – January 2, 1990) was an American actor and restaurateur. Hale Jr. was the son of major movie character actor Alan Hale Sr.[2] Hale Jr.'s television career, which spanned four decades, was most noted for his co-starring role on the 1960s series Gilligan's Island. He also appeared on several talk and variety shows.
Appearing in over 200 films and television roles, Hale's long acting career began in films in 1941, appearing primarily in Westerns, playing opposite Kirk Douglas in The Big Trees (1952), Audie Murphy in Destry (1954), Ray Milland in A Man Alone (1955), Robert Wagner in The True Story of Jesse James (1957) and Hugh Marlowe in The Long Rope (1961). He also appeared in musical comedies, playing opposite Don DeFore in It Happened on Fifth Avenue (1947), James Cagney in The West Point Story (1950) and Judy Canova in Honeychile (1951). He achieved continuing success on the CBS sitcom Gilligan's Island (1964–1967), playing the secondary lead role of the Skipper. After its cancellation, the series would remain a popular staple in syndication. Hale reprised the role of Skipper in three Gilligan's Island television films and two spin-off cartoon series.
Contents
[hide]
1 Early life
2 Career
2.1 Gilligan's Island
2.2 Later years
2.3 Other ventures
3 Personal life
4 Death
5 Stage career
6 Selected filmography
7 References
8 External links
Early life[edit]
Alan Hale MacKahan was born in Los Angeles, California, on March 8, 1921.[2] His father was character actor Rufus Edward McKahan,[2] who used the stage name of Alan Hale (1892–1950), and his mother was silent film actress Gretchen Hartman[2] (1897-1979). Appearing in over 235 films, his father had a successful screen career both as a leading man in silent films and as a supporting actor in sound movies.[3]
During World War II, Hale Jr., enlisted in the United States Coast Guard.[2] After the death of his father in 1950, Hale dropped the "Junior" from his name.[4]
Career[edit]
Hale and Celeste Holm in Follow the Sun (1961)
In 1931, Hale made his Broadway stage debut in Caught Wet. The play opened on November 4 and closed later that month. He made his screen debut two years later in Wild Boys of the Road. Although his role was deleted from that film's final release, he still received screen credit for his performance.[5] He later appeared in roles in To the Shores of Tripoli (1942), Yanks Ahoy (1943), Sweetheart of Sigma Chi (1946), and When Willie Comes Marching Home (1950). During the late 1940s and early 1950s, he frequently appeared in Gene Autry films and also had a recurring role from 1950 to 1952 on The Gene Autry Show.[6]
By the early 1950s, Hale began to perform increasingly on the rapidly expanding medium of television. In 1952 he landed the starring role in CBS's Biff Baker, U.S.A., but the series was canceled in 1954. He continued his career on the "small screen" by appearing in guest spots on a variety of other series, such as The Range Rider (five times), Annie Oakley, Fireside Theater, Frontier, Matinee Theater, Fury, Northwest Passage, and The Man from Blackhawk.
The year 1957 proved to be an especially busy one for Hale on television series. In addition to performing the role of Shawnee Bill on the Western Wanted Dead or Alive, he played a folksy rancher, Les Bridgeman, in "Hired Gun", an episode of the ABC/Warner Brothers series Cheyenne, with Clint Walker in the title role. Later that year Hale landed another starring role in the syndicated television series Casey Jones, which aired thirty-two episodes before it was canceled in 1958.[7] Then, from 1958 to 1960, he was cast in a recurring role on Rory Calhoun's CBS Western The Texan. Hale also returned to the series Cheyenne in 1960 to portray the character Tuk in the episode "Road to Three Graves".[7]
Throughout the early 1960s, Hale continued in guest-starring roles on episodes of Gunsmoke, Bonanza, Rawhide, The Real McCoys, Mister Ed, Assignment: Underwater, Hawaiian Eye, Adventures in Paradise, Lock Up, The Andy Griffith Show, Lassie, Tales of Wells Fargo, Route 66 and Hazel. He was featured in two episodes of Perry Mason, first as murderer Lon Snyder in the 1961 episode "The Case of the Unwelcome Bride", and then in 1963 as Nelson Barclift in "The Case of the Bouncing Boomerang".[7]
Despite his growing commitment to roles on television, Hale throughout the 1950s and into 1960s continued his work in supporting roles in feature films. Some of those include The Gunfighter (1950), At Sword's Point (1952), Silver Lode (1954), The Sea Chase (1955), The Three Outlaws (1956), The True Story of Jesse James (1957), Up Periscope (1959), Thunder in Carolina (1960), The Long Rope (1961), Bullet for a Badman (1964), Advance to the Rear (1964), and Hang 'Em High (1968).[6]
Gilligan's Island[edit]
In 1964, Hale won the co-starring role as the Skipper on the CBS sitcom Gilligan's Island. The series aired for a total of 98 episodes from 1964 to 1967. His character proved to be the most prominent role of Hale’s career, as the show continued to be popular with later generations of viewers due to syndicated reruns. The popularity of the show typecast its actors, making it difficult for them to successfully pursue diversified acting opportunities. They received no substantial residual payments for their roles, and the difficulty in finding new roles often created financial hardship and resentment. However, Hale did not mind being so closely identified with the Skipper.[8] According to Sherwood Schwartz, he often visited children in hospitals dressed as the Skipper.
Hale reprised the role of the Skipper in three television films, Rescue from Gilligan's Island (1978), The Castaways on Gilligan's Island (1979), and The Harlem Globetrotters on Gilligan's Island (1981). He also voiced the Skipper in two cartoon versions of the series, The New Adventures of Gilligan from 1974 to 1977 and Gilligan's Planet from 1982 to 1983. Hale also appeared as the Skipper in two unrelated sitcoms, The New Gidget in 1987 and ALF in 1989. He also promoted Gilligan's Island reruns on TBS, alongside Bob Denver. Denver and Hale also appeared as their characters at various promotional events.[9]
Dawn Wells said in a 2014 interview on CRN.com with Larry and Nancy Manetti, when asked if Alan Hale Jr. was the consummate professional of the Gilligan's Island series: "Well, that is so interesting, because Alan Jr. and his father looked so much alike, you don't know, who was who. His father did all the Errol Flynn ... I used to say to Alan, 'How was it growing up in a household, with all those movie stars?' Alan was absolutely, the consummate professional, wonderful gentleman, jovial, never complained ... he was the exact same size of my dad. Every time he picked me up and hugged me, I thought he was my father, he was my dad." Wells also responded to the question if she ever went to her acting mentor's restaurant (that Hale once owned in Los Angeles): "It was a lobster house on La Cienega Blvd., and he would greet you with his sea hat on, as you can.... but that was after the show; and he had his friend, Anthony, there, with some good food, too." The last question asked of Dawn was if Gilligan's Island, was nearly his (Hale's) show: "No, no... as a matter of fact, it was interesting when you go back and find the people that they should thought say the other characters, and I understand Alan was doing a movie in Utah and they wanted to bring him to audition and he couldn't get a flight out, so ... he hitchhiked, hitchhiked on the highway and then, he came in to audition."[10] After the show's cancellation, and until Hale's death, Wells not only stayed in touch with him but they were also frequently neighbors. After Hale's mother Gretchen died in 1979 the friendship between Hale and Wells grew closer.
Later years[edit]
After the end of Gilligan's Island, Hale continued his career in television. He guest-starred on several more series, including The Wild Wild West, Here Come the Brides, Land of the Giants, The Virginian, Here's Lucy, Marcus Welby, M.D., The Paul Lynde Show, The Love Boat and Crazy Like a Fox.
Hale performed as well in additional feature films during the 1970s and the 1980s. He starred in The Giant Spider Invasion (1975) and Angels Revenge (1978), both of which were later featured on Mystery Science Theater 3000 (as was his 1963 film The Crawling Hand). In 1983, Hale costarred in comedy-drama film Hambone and Hillie, starring Lillian Gish. The following year, he had a role in the comedy Johnny Dangerously and became a spokesman for a car dealership in Victoria, British Columbia. In 1987, Hale starred in the horror film Terror Night. Later that same year, he made his final film appearance in a cameo role with Bob Denver in Back to the Beach. Also in 1987, he reprised his role as the Skipper on The New Gidget with his childhood friend and classmate William Schallert and Bob Denver, and on an episode of ALF.
Other ventures[edit]
In addition to acting, Hale co-owned Alan Hale's Lobster Barrel, a restaurant he opened in the mid-1970s. The Lobster Barrel was located on La Cienega Boulevard on Los Angeles's Restaurant Row. According to Hale's agent, Hale was "phased out" of the business in 1982. He later opened Alan Hale's Quality and Leisure Travel office.[9]
Personal life[edit]
Hale was married twice; his first marriage was on March 12, 1943 [2] in Hollywood [2] to Bettina Doerr Hale [2] with whom he had four children: Alan Brian, Chris, Lana, and Dorian. The couple later divorced.[4][11] In 1964, Hale married former singer Naomi Ingram, to whom he would remain married until his death.[12][13]
Death[edit]
Hale died on January 2, 1990, of thymus cancer at St. Vincent Medical Center in Los Angeles at age 68. His body was cremated, and his ashes were sprinkled into the Pacific Ocean.[3][14] His Gilligan's Island co-star Dawn Wells was in attendance, representing the surviving members of the cast.
For his contribution to the television industry, Alan Hale Jr. has a star on the Hollywood Walk of Fame located at 6653 Hollywood Blvd.[15]
Stage career[edit]
Date
Production
Role
1931 Caught Wet Brewster
1934–1935 Small Miracle George Nelson
1935 Ceiling Zero Tay Lawson
1937 Red Harvest Private Breen
1940 The Scene of the Crime Bob Hanley
1952 Hook n' Ladder Mr. Gilkens
Selected filmography[edit]
Year
Title
Role
Notes
1933 Wild Boys of the Road One of the Boys Uncredited
1941 I Wanted Wings Cadet Uncredited
1941 Dive Bomber Pilot Trainee Uncredited
1941 All-American Co-Ed Tiny
1942 To the Shores of Tripoli Tom Hall
1942 Eagle Squadron Olsen
1942 Rubber Racketeers Red
1943 No Time for Love Union Checker Uncredited
1943 Watch on the Rhine Boy Uncredited
1946 Monsieur Beaucaire Courtier Uncredited
1946 Sweetheart of Sigma Chi Mike Mitchell
1947 It Happened on Fifth Avenue Whitey Temple
1947 The Spirit of West Point Oklahoma Cutter
1948 Homecoming Military Policeman Uncredited
1948 One Sunday Afternoon Marty
1949 It Happens Every Spring Schmidt
1949 Rim of the Canyon Matt Kimbrough
1950 The Blazing Sun Ben Luber
1950 The Gunfighter Brother
1950 Kill the Umpire Harry Shea Uncredited
1950 The Underworld Story Shaeffer, Durham Warehouse Thug
1950 The West Point Story Bull Gilbert
1951 Home Town Story Slim Haskins
1951 Honeychile Joe Boyd
1952 The Big Trees Tiny
1952 Springfield Rifle Mizzell
1952 At Sword's Point Porthos Jr.
1952 Wait till the Sun Shines, Nellie George Oliphant
1953 The Man Behind the Gun Cpl. Olaf Swenson
1953 Captain John Smith and Pocahontas Fleming
1954 Captain Kidd and the Slave Girl Jay Simpson
1954 Rogue Cop Johnny Stark
1954 Destry Jack Larson
1954 Young at Heart Robert Neary
1955 The Sea Chase Wentz
1955 A Man Alone Acting Sheriff Jim Anderson
1956 The Indian Fighter Will Crabtree
1956 The Killer Is Loose Denny
1957 Battle Hymn Mess Sergeant
1957 The True Story of Jesse James Cole Younger
1957 All Mine to Give Tom Cullen
1958 The Lady Takes a Flyer Frank Henshaw
1959 Up Periscope Lt. Pat Malone
1960 Thunder in Carolina Buddy Schaeffer
1962 The Iron Maiden Paul Fisher
1963 The Crawling Hand Sheriff Townsend
1964 Advance to the Rear Sgt. Beauregard Davis
1964 Bullet for a Badman Leach Alternative title: Renegade Posse
1968 Hang 'Em High Matt Stone, Cooper Hanging Party
1970 Tiger by the Tail Billy Jack Whitehorn
1970 There Was a Crooked Man... Tobaccy
1975 The Giant Spider Invasion Sheriff
1979 The North Avenue Irregulars Harry, the Hat
1979 Angels Brigade Manny Alternative titles: Angels Revenge
Seven from Heaven
1979 The Fifth Musketeer Porthos
1983 Hambone and Hillie McVickers
1984 The Red Fury [16] Doc Kaminsky
1984 Johnny Dangerously Desk Sergeant
1987 Terror Night Jake Nelson Alternative title: Bloody Movie
1987 Back to the Beach Bartender's Buddy
Television
Year
Title
Role
Notes
1950–1952 The Gene Autry Show Tiny – Sidekick 9 episodes
1953 Man Against Crime Lt. Olmstead Episode: "Hide and Seek"
1952–1954 Biff Baker, U.S.A. Biff Baker 26 episodes
1955 The Public Defender Sparky Albright Segment: "The Hitchhiker"
1955 Stage 7 Herb 'Bad News' Loftus Episode: "The Traveling Salesman"
1955 Navy Log Beartracks Episode: "The Pollywog of Yosu"
1956 The Red Skelton Show Muldoon Episode: "Cookie Returns"
1956 Screen Directors Playhouse Bowen Episode: "A Ticket for Thaddeus"
1957 The Millionaire Bill "Buffalo" Walker Episode: "The Professor Amberson Adams Story"
1957 The Alcoa Hour Red Regan Episode: "The Animal Kingdom"
1957 Cheyenne Les Bridgeman Episode: "Hired Gun"
1957–1958 Casey Jones Casey Jones 32 episodes
1958 Northwest Passage Sam Beal Episode: "The Red Coat"
1958 Wanted: Dead or Alive Dan Poe Episode: "Passing of Shawnee Bill"
1958–1960 The Texan Sculley 6 episodes
1959 Bat Masterson Bailey Harper Episode: "A Personal Matter"
1959 Bonanza Swede Lundberg Episode: "The Saga of Annie O'Toole"
1959 The Untouchables Big Bill Phillips Episode: "Tri-State Gang"
1960 The Alaskans Hap Johnson Episode: "Partners"
1960 Shotgun Slade Sheriff Sloan Episode: "Lost Gold"
1960 Maverick Captain Jim (US Marshal) Episode: "Arizona Black Maria"
1960 Cheyenne Tuk Episode: "Road to Three Graves"
1961 The Jack Benny Program McGuire Episode: "Jack Goes to Gym"
1961 Hawaiian Eye Big Mac McConnel Episode: "Dragon Road"
1961 Adventures in Paradise Captain Arthur Butcher 2 episodes, "Captain Butcher" and "The Serpent in the Garden"
1961 Gunsmoke Jake Higgins Episode: "Minnie"
1961 Rawhide Lucas Episode: "The Woman Trap"
1961 Perry Mason Lon Snyder Episode: "The Case of the Unwelcome Bride"
1962 The Andy Griffith Show Jeff Pruitt Episode: "The Farmer Takes a Wife"
1962 Wagon Train Kirby Episode: "The Lonnie Fallon Story"
1962 Follow the Sun Charlie Episode: "The Irresistible Miss Bullfinch"
1962 Maverick Big Jim Watson (as Alan Hale) Episode: "The Troubled Heir"
1963 77 Sunset Strip Baxter Episode: "Tarnished Idol"
1963 Empire Fletcher Episode: "The Convention"
1963 The Lucy Show Fire Academy instructor Episode: "Lucy Puts Out a Fire at the Bank"
1963 Perry Mason Nelson Barclift Episode: "The Case of the Bouncing Boomerang"
1964 The New Phil Silvers Show Charlie Episode: "Pay the Two Dollars"
1964 My Favorite Martian Omar M. Keck Episode: "The Disastro-Nauts"
1964–1967 Gilligan's Island Jonas Grumby (The Skipper) 98 episodes
1966 Gunsmoke Bull Bannock Episode: "Champion of the World"
1967 Batman Gilligan Episode: "The Ogg and I"
Uncredited
1967 Hondo Ben Cobb Episode: "Hondo and the Death Drive"
1968 The Wild Wild West Ned Brown Episode: "The Night of The Sabatini Death"
1968 Daktari Big Joe Wonder Episode: "African Showdown"
1969 Green Acres Sheriff Episode: "A Prize in Every Package"
1969 The Flying Nun Uncle Reggie Overton Perkins 2 episodes
1969 The Good Guys Big Tom 3 episodes
1970 The Andersonville Trial The Board of Military Judges Television movie
1970 Here's Lucy Moose Manley Episode: "Lucy and Wally Cox"
1970 Ironside Laurence Drescher Episode: "The People Against Judge McIntire"
1971 Alias Smith and Jones Andrew J. Greer Episode: "The Girl in Boxcar #3"
1971 The Doris Day Show Charlie Dinser Episode: "Have I Got a Fellow for You!"
1971 O'Hara, U.S. Treasury Episode: "Operation: Moonshine"
1972 Gunsmoke Dave Chaney Episode: "Jubilee"
1973 McMillan & Wife Port Captain Episode: "The Fine Art of Staying Alive"
1974–1975 The New Adventures of Gilligan The Skipper (Voice) 24 episodes
1975 The Wonderful World of Disney Cholly 2 episodes
1978 Rescue from Gilligan's Island The Skipper Television movie
1979 The Castaways on Gilligan's Island The Skipper Television movie
1979 ABC Weekend Special Mayor Episode: "The Revenge of Red Chief"
1979 The Littlest Hobo Harry Episode: "Stand-in"
1979 The Love Boat Jack Tigue Episode: "The Harder They Fall"
1980 Fantasy Island Judge Winston Episode: "Rogues to Riches/Stark Terror"
1981 The Harlem Globetrotters on Gilligan's Island The Skipper Television movie
1982 The Love Boat Gus Dolan Episode: "Meet the Author"
1982–1983 Gilligan's Planet The Skipper (Voice) 13 episodes
1983 Matt Houston Rawson Harmon IV Episode: "The Yacht Club Murders"
1986 Murder, She Wrote Fenton Harris Episode: "Trial by Error"
1986 Magnum, P.I. Russell Tate Episode: "All Thieves on Deck"
1987 Simon & Simon Silk McNabb Episode: "For Old Crime's Sake"
1987 ALF Skipper Jonas Grumby Episode: "Somewhere Over the Rerun"
1987 Growing Pains The Cabbie Episode: "This Is Your Life"
1988 The Law & Harry McGraw Herb Loftus Episode: "Gilhooey's Is History"
References[edit]
Jump up ^ "U.S. Census 1940". Familysearch.org.
^ Jump up to: a b c d e f g h i j k l m n o "Alan Hale (Jr.) MacKahan & Bettina Reed Doerr Marriage Certificate". Familysearch.org.
^ Jump up to: a b Flint, Peter B. (4 January 1990). "Alan Hale Jr., Who Was Skipper on 'Gilligan's Island,' Dies at 71". The New York Times. Retrieved 9 September 2013.
^ Jump up to: a b "Alan Hale's Resemblance To His Father Confusing". The Washington Reporter. June 8, 1965. p. 8. Retrieved 14 December 2012.
Jump up ^ Aaker, Everett (2006). Encyclopedia Of Early Television Crime Fighters: All Regular Cast Members In American Crime and Mystery Series, 1948–1959. McFarland. p. 246. ISBN 0-7864-2476-1.
^ Jump up to: a b "Alan Hale Jr.", Turner Classic Movies (TCM), Turner Broadcasting, a subsidiary of Time Warner, New York, N.Y. Retrieved May 19, 2018.
^ Jump up to: a b c "Alan Hale Jr.", Internet Movie Database (IMDb]), a subsidiary of Amazon, Seattle, Washington. Retrieved May 19, 2018.
Jump up ^ Largo, Michael (2007). The Portable Obituary: How the Famous, Rich, and Powerful Really Died. HarperCollins. p. 94. ISBN 0-06-123166-5.
^ Jump up to: a b Lee, John H. (January 4, 1990). "Alan Hale Jr., 68; Skipper on TV's 'Gilligan's Island'". latimes.com. Retrieved December 15, 2012.
Jump up ^ "PM Show with Larry Manetti - CRN".
Jump up ^ Thomas, Nick (2011). Raised by the Stars: Interviews with 29 Children of Hollywood Actors. Mcfarland. p. 61. ISBN 0-7864-6403-8.
Jump up ^ Shain, Percy (November 21, 1965). "Stars Palsy-Walsy On Gilligan's Isle". Boston Globe. p. B35.
Jump up ^ "Alan Hale Jr., Gillian's big buddy, dies". Ocala Star-Banner. January 4, 1990. p. 2A.
Jump up ^ "Actor Alan Hale Jr., Gilligan's Skipper". The Vindicator. 1990-01-03. p. 34. Retrieved 14 December 2012.
Jump up ^ Lee, John H. (January 4, 1990). "Hollywood Star Walk: 6653 Hollywood Blvd". latimes.com. Retrieved 14 December 2012.
Jump up ^ "The Red Fury (1984)". New York Times. Retrieved December 13, 2013.
External links[edit]
Biography portal
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Hale and his father
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WorldCat Identities
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The Man in 3B
From Wikipedia, the free encyclopedia
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The Man in 3B
Theatrical release poster
Directed by
Trey Haley
Produced by
ND Brown
Carl Weber
Veronica Nichols
Tracey Moore
Screenplay by
Carl Weber
Based on
The Man in 3B
by Carl Weber
Starring
Lamman Rucker
Christian Keyes
Brely Evans
Anthony Montgomery
Robert Ri'chard
Nefessa Williams
DB Woodside
Kellita Smith
James Black
Olivia Longett
Trisha Mann
Jackée Harry
Marla Gibbs
Billy Dee Williams
Music by
Matthew Head
Cinematography
Eric Wycoff
Edited by
Chris Peppé
Production
company
Urban Books Media
Tri Destined Studios
Distributed by
Freestyle Releasing
Release date
February 15, 2015 (2015-02-15) (Pan African Film Festival)
November 6, 2015 (2015-11-06)
Running time
93 minutes
Country
United States
Language
English
Box office
$291,513[1]
The Man in 3B is a 2015 American mystery crime-thriller film directed by Trey Haley. The film is based on the novel of the same name written by The New York Times best-selling author Carl Weber. The Man in 3B stars an ensemble cast that includes Lamman Rucker, Christian Keyes, Anthony Montgomery, Robert Ri'chard, DB Woodside, Kellita Smith, James Black, Jackée Harry, Marla Gibbs, and Billy Dee Williams.[2] The film was released on November 6, 2015.
Contents
[hide]
1 Plot
2 Cast
3 Production
4 Release
5 References
6 External links
Plot[edit]
Darryl Graham moves into an apartment complex, meeting his new neighbors: Connie and Avery, who have a troubled marriage; couple Slim and Krystal, who is Avery's daughter; Ben and his son Benny; and several gossiping women. As Benny helps Darryl move into his apartment, the two become friends. Connie, who initially disbelieves the gossips when they say Darryl is the most attractive man they've ever seen, makes a fool of herself when introducing herself to him. She later encounters Darryl while exercising in the park, explaining that she is trying to get back into shape to save her marriage. Darryl offers to be her personal trainer.
Avery angrily quits his job when a promised promotion goes instead to the owner's incompetent son. Drunk and upset with his disappointing life, he contemplates suicide. He is stopped by a wealthy man named Cain, who explains he, too, considered suicide at the same bridge several years ago. Cain offers him a job and shares his life philosophy: one's old life and problems must be left behind at the bridge. Meanwhile, at the apartment complex, Darryl and Krystal have sex, revealing they had previously been in a relationship. Krystal, however, blows off Darryl once Slim proposes to her.
Benny counsels Darryl to forget about Krystal, impressing Darryl with his maturity for a 20-year-old. As they talk, Benny finds On the Down Low, a non-fiction book about closeted gay African-American men. Benny becomes uncomfortable and quickly leaves. Under Cain's guidance, Avery becomes an armed robber. After spending time with Cain and becoming intoxicated with his decadent lifestyle, Avery tells Connie he wants a divorce. Upset and hurt, Connie turns to Darryl, and the two begin a relationship. She is surprised when the police come asking about Avery and Cain, searching her apartment with a warrant.
Krystal comes on to Darryl, offering to maintain an affair, which Darryl rejects. When Slim catches her coming on Darryl, she accuses Darryl of attempted rape. Darryl's life is further complicated when Benny makes a pass at him, assuming Darryl to be gay. Benny is crushed when Darryl explains he is straight and was only trying to understand his gay brother's struggles by reading On the Down Low. In denial that his son is gay, Ben angrily accuses Darryl of trying to corrupt Benny. At the same time, Avery learns of Darryl's and Connie's relationship. Amid these issues, Darryl is found dead in his apartment after an arson.
Detectives Thomas and Anderson question each of the occupants. Eventually, evidence is found in Ben's apartment, and he confesses to the murder, assuming Benny is the killer. The police become suspicious when they learn Avery was seen in the apartment complex prior to Darryl's death, and they press Connie for details, also learning from Krystal that her mother died mysteriously in a fire. Krystal, who blames Connie for her mother's death, is shocked when the police reveal evidence tying her father to the murder of both her mother and Darryl. After making a plea bargain to avoid jail time for aiding her father's escape, she works with the police to set a trap.
Three months later, Connie leaves the apartment complex. She hands Darryl's brother's number to Benny, who has reconciled with his now-freed father. In Jamaica, she meets up with Darryl, who is revealed to be alive. Connie flashes back to the day of Darryl's faked death: after being abandoned by Cain, Avery returns to the apartment to rob Connie. When Avery threatens to kill Darryl, Connie kills him, then helps Darryl make it look like Avery had killed him. After Connie leads the police to Avery as a suspect, she helps him impersonate Avery by sending incriminating text messages to Krystal, whose trap he ignores.
Cast[edit]
Lamman Rucker as Darryl Graham
Christian Keyes as Slim
Brely Evans as Connie
D. B. Woodside as Det. Thomas
Nafessa Williams as Krystal
Kellita Smith as Det. Anderson
Anthony Montgomery as Avery
Billy Dee Williams as Cain
James Black as Ben
Robert Ri'chard as Benny
Jackée Harry as Miss Bertha
Trisha Mann as Nancy
Olivia Longett as Jerri
Marla Gibbs as Ms. Mamie
Production[edit]
Shooting took place in Los Angeles.[3]
Release[edit]
The Man in 3B premiered at the Pan African Film Festival in February 15, 2015.[4] Freestyle Releasing released it to theaters on November 6, 2016, and it grossed $291,513 in the US.[1]
References[edit]
^ Jump up to: a b "The Man in 3B". Box Office Mojo. Retrieved 2017-03-05.
Jump up ^ Tambay A. Obenson (21 September 2015). "Urbanworld 2015: Lamman Rucker, DB Woodside Headline Ense - Shadow and Act". Shadow and Act.
Jump up ^ "Lamman Rucker, DB Woodside, Billy Dee Williams, Christian Keyes Lead ‘Man in 3B’ (Based on Carl Weber Bestseller)". IndieWire. 2014-09-16. Retrieved 2017-03-05.
Jump up ^ Neale, April (2015-02-06). "“The Man in 3B” Premiere, 23rd Annual Pan African Film & Arts Festival VIDEO". Monsters and Critics. Retrieved 2017-03-05.
External links[edit]
Official website
The Man in 3B on IMDb
The Man in 3B at Box Office Mojo
Retrieved from "https://en.wikipedia.org/w/index.php?title=The_Man_in_3B&oldid=777044917"
Categories:
2015 films
English-language films
2010s thriller films
American films
American crime thriller films
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