1. Reconstructing a Function from its Gradient

2. Differentials
We begin by reviewing the one-variable case. If f is differentiable at x, then for small h, the increment
Δf = f (x + h) − f (x)
can be approximated by the differential
d f = f´(x) h.

3. Differentials

4. Differentials is called the increment of f , and the dot product
is called the differential (more formally, the total differential).

5. Differentials
As in the one-variable case, for small h, the differential and the increment are approximately equal:

6. Differentials

7. Example

8. Theorem

9. Examples