In vector calculus, the gradient of a scalar-valued differentiable function $${\displaystyle f}$$ of several variables is the vector field (or vector-valued function) See more

Relationship with total derivative
The gradient is closely related to the total derivative (total differential) $${\displaystyle df}$$: they are transpose (dual) to each other. Using the convention that vectors in $${\displaystyle \mathbb {R} ^{n}}$$ are … See more

Jacobian
The Jacobian matrix is the generalization of the gradient for vector-valued functions of several variables and See more

• Korn, Theresa M.; Korn, Granino Arthur (2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. Dover Publications. pp. 157–160. ISBN 0-486-41147-8. OCLC 43864234 See more

Consider a room where the temperature is given by a scalar field, T, so at each point (x, y, z) the temperature is T(x, y, z), independent of time. … See more

Level sets
A level surface, or isosurface, is the set of all points where some function has a given value.
If f is differentiable, then the dot product (∇f )x ⋅ v of the gradient at a point x with a vector v gives the … See more

• Curl – Circulation density in a vector field
• Divergence – Vector operator in vector calculus
• See more