1. Gradient, Divergence and Curl in Computer Science

2. Outcomes  What is Gradient, Divergence and Curl  It’s applications in Computer Science  What is Gradient, Divergence and Curl  It’s applications in Computer Science

3. Before we proceed, In 3 dimension: Partial derivative

4. Gradient The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to move) that:  Points in the direction of greatest increase of a function  Is zero at a local maximum or local minimum (because there is no single direction of increase) [Source: Better Explained]Better Explained The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to move) that:  Points in the direction of greatest increase of a function  Is zero at a local maximum or local minimum (because there is no single direction of increase) [Source: Better Explained]Better Explained Operating onScalar field

5. Divergence The divergence of a vector field simply measures how much the flow is expanding at a given point. It does not indicate in which direction the expansion is occurring. [Source: Math Insight]Math Insight The divergence of a vector field simply measures how much the flow is expanding at a given point. It does not indicate in which direction the expansion is occurring. [Source: Math Insight]Math Insight +- -+ ++

6. Curl  Curl is simply the circulation per unit area, circulation density, or rate of rotation. [Source: Better Explained]Better Explained  Curl is simply the circulation per unit area, circulation density, or rate of rotation. [Source: Better Explained]Better Explained

7. Commonly Acts OnProduces Scalar fieldVector field Scalar field Vector field

8. Applications  Graphics Processing Unit - GPU  Computer Graphics  Various kind simulations  Numerical analysis  Machine learning – Interpolation and extrapolation  Computational Fluid Dynamics – CFD (e.g. Navier Stokes Equation) and etc.  Graphics Processing Unit - GPU  Computer Graphics  Various kind simulations  Numerical analysis  Machine learning – Interpolation and extrapolation  Computational Fluid Dynamics – CFD (e.g. Navier Stokes Equation) and etc.

9. For your attention Any questions?