Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Videos > Question Bank for GATE Computer Science Engineering > Vector Calculus: Gradient & Directional Directive
Vector Calculus: Gradient & Directional Directive Video Lecture | Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
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FAQs on Vector Calculus: Gradient & Directional Directive Video Lecture - Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
| 1. What is the gradient in vector calculus? |  |
Ans. The gradient in vector calculus is a vector operator that operates on a scalar function to produce a vector whose components are the partial derivatives of the function with respect to each coordinate direction.
| 2. How is the gradient related to the directional derivative in vector calculus? | |
Ans. The directional derivative in vector calculus measures the rate at which a function changes in a particular direction. The gradient of the function gives the direction in which the function changes the most rapidly, and the magnitude of the gradient represents the maximum rate of change in that direction.
| 3. How is the gradient used in computer science engineering? | |
Ans. In computer science engineering, the gradient is commonly used in optimization algorithms to find the minimum or maximum of a function. It is also used in machine learning algorithms, such as gradient descent, to iteratively update model parameters for better performance.
| 4. What is the relationship between the gradient and the Jacobian matrix? | |
Ans. The Jacobian matrix is a matrix of partial derivatives that represents the rate of change of a vector-valued function. The gradient of a scalar-valued function can be seen as a special case of the Jacobian matrix, where the function outputs a single scalar value.
| 5. How can I calculate the gradient of a function in vector calculus? | |
Ans. To calculate the gradient of a function, you need to find the partial derivatives of the function with respect to each coordinate direction. These partial derivatives can then be combined to form a vector, which represents the gradient of the function.
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