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Partial Functional Dependency Indicates that if A and B are attributes of a table , B is partially dependent on A if there is some attribute that can be removed from A and yet the dependency still holds. Say for Ex, consider the following functional dependency that exists in the Tbl_Staff table: StaffID,Name -------> BranchID BranchID is functionally dependent on a subset of A (StaffID,Name), namely StaffID. Source :http://www.mahipalreddy.com/dbdesign/dbqa.htm
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How do we find the gradient?
To find the gradient of a function, you calculate the partial derivatives of the function with respect to each variable. For a function ( f(x, y) ), the gradient is represented as a vector ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) ). This vector points in the direction of the steepest ascent of the function and its magnitude indicates the rate of increase. You can compute the gradient using calculus techniques, such as differentiation.
What are exact and inexact differentials?
Exact differentials refer to changes in a function that can be expressed as the total differential of that function, meaning there exists a scalar function whose differential equals the given expression. Inexact differentials, on the other hand, cannot be derived from a single function and typically arise in contexts like thermodynamics, where they represent changes in quantities that are path-dependent. In mathematical terms, an exact differential ( df ) satisfies the condition ( \frac{\partial^2 f}{\partial y \partial x} = \frac{\partial^2 f}{\partial x \partial y} ), while inexact differentials, such as ( dQ ) or ( dW ), do not meet this criterion.
What does gradient mean in maths?
In mathematics, particularly in calculus and vector analysis, the gradient refers to a multi-variable generalization of the derivative. It represents the rate and direction of change of a scalar field, typically a function of several variables. The gradient is a vector that points in the direction of the steepest ascent of the function, and its magnitude indicates the rate of increase. Mathematically, for a function ( f(x, y, z) ), the gradient is denoted as ( \nabla f ) and is calculated as the vector of partial derivatives: ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) ).
Where can one learn about partial differential equations?
Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
What is the use of a differential?
Differentials can be used to approximate a nonlinear function as a linear function. They can be used as a "factory" to quickly find partial derivatives. They can be used to test if a function is smooth.
How do we find the gradient?
To find the gradient of a function, you calculate the partial derivatives of the function with respect to each variable. For a function ( f(x, y) ), the gradient is represented as a vector ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) ). This vector points in the direction of the steepest ascent of the function and its magnitude indicates the rate of increase. You can compute the gradient using calculus techniques, such as differentiation.
What is the derivative of a function with respect to a vector?
The derivative of a function with respect to a vector is a matrix of partial derivatives.
What is the partial word added to the end of a root word to change its meaning or function?
It is a suffix - hence the category into which you have put the question!
What does gradient mean in maths?
In mathematics, particularly in calculus and vector analysis, the gradient refers to a multi-variable generalization of the derivative. It represents the rate and direction of change of a scalar field, typically a function of several variables. The gradient is a vector that points in the direction of the steepest ascent of the function, and its magnitude indicates the rate of increase. Mathematically, for a function ( f(x, y, z) ), the gradient is denoted as ( \nabla f ) and is calculated as the vector of partial derivatives: ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) ).
What is the derivative with respect to vector of the given function?
The derivative with respect to a vector of a function is a vector of partial derivatives of the function with respect to each component of the vector.
Where can one learn about partial differential equations?
Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
A partial word added to the end of a root word to change its meaning or function?
Suffix
What is the use of a differential?
Differentials can be used to approximate a nonlinear function as a linear function. They can be used as a "factory" to quickly find partial derivatives. They can be used to test if a function is smooth.
What is the shortcut for calculating the Cobb-Douglas demand function?
The shortcut for calculating the Cobb-Douglas demand function is to take the partial derivative of the function with respect to the price of the good in question.
How many n th - order partial derivatives does a function of three variables have?
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What is the formula of the divergence of the function?
The divergence of the function is generally a cross product of partial derivatives and the vector field of F. Mathematically, the formula is: div(F) = ∂P/∂x i + ∂Q/∂y j + ∂R/∂z k where: F = Pi + Qj + Rk has the continuous partial derivatives.
What is a partial derivative?
A partial derivative is the derivative of a function of more than one variable with respect to only one variable. When taking a partial derivative, the other variables are treated as constants. For example, the partial derivative of the function f(x,y)=2x2 + 3xy + y2 with respect to x is:?f/?x = 4x + 3yhere we can see that y terms have been treated as constants when differentiating.The partial derivative of f(x,y) with respect to y is:?f/?y = 3x + 2yand here, x terms have been treated as constants.
