Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Gradient of a Scalar Field & Directional Derivative
Gradient of a Scalar Field & Directional Derivative Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Gradient of a Scalar Field & Directional Derivative Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a scalar field? |  |
Ans. A scalar field is a mathematical function that assigns a scalar value to every point in space. It represents a physical quantity, such as temperature or pressure, that varies across different points in a region.
| 2. What is the gradient of a scalar field? | |
Ans. The gradient of a scalar field is a vector field that represents the rate of change of the scalar field at each point. It indicates both the magnitude and direction of the steepest ascent or descent of the scalar field.
| 3. How is the gradient of a scalar field calculated? | |
Ans. The gradient of a scalar field is calculated by taking the partial derivatives of the scalar field with respect to each coordinate axis. These partial derivatives are then combined to form a vector, which represents the gradient.
| 4. What is a directional derivative? | |
Ans. A directional derivative is a measure of how a scalar field changes in a particular direction. It represents the rate of change of the scalar field along a specified direction, which can be any vector in the space.
| 5. How is the directional derivative related to the gradient of a scalar field? | |
Ans. The directional derivative of a scalar field in a specific direction can be obtained by taking the dot product of the gradient of the scalar field with the unit vector in that direction. This dot product gives the rate of change of the scalar field in that direction.
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