A parabole y=x2+x and its first (fx=2*x+1) and second order (fxx=2) derivatives.
Figure 4.26 Example: Runge-Kutta integration C program
... up the finite-difference weights, and have used three-point windows on the edges to avoid introducing supplementary bands in the derivation matrix.
Since acceleration is the time derivative of velocity, the material acceleration can be derived from the definition of material derivative as follows:
Using only direction of vector
UNIT 2: DERIVATIVES
For an alternative derivation, we can make use of the usual vector operations to express the total second derivative of the absolute position vector r.
Vector addition for vectors at any angle | Adding vectors | How to add vectors
Vector addition for perpendicular vectors | Adding vectors | How to add vectors