What this page adds. The
basic calculator takes the first
derivative by the central difference and the first integral by the trapezoid rule,
in your browser, on up to three columns. This page takes any number of columns,
derivatives and integrals up to order 4, the forward, backward and Savitzky-Golay
derivatives, Simpson's rule, and your own integration constants. To do that it
sends your table to the server, computes there, and sends the
numbers back. Nothing is stored, but the data does leave your machine. If that
matters for your data, use the basic page. The
derivative and integral article
explains each method.
Each derivative order multiplies the noise: on measured data a second derivative
is a stretch and a fourth is mostly noise. Use Savitzky-Golay, or
smooth the data first. Savitzky-Golay
needs evenly spaced x.
- Paste your data into the Input grid — straight from a
spreadsheet, or as CSV/TSV text — or import a CSV/TSV file.
Column x, then any number of y columns. Rows are sorted by x; every x must be
different.
- Pick the Operation, the Method and the Order (1 to 4).
- Derivative: Forward difference, Backward difference and
Central difference are applied Order times; one-sided at the first and last
rows. Savitzky-Golay fits a polynomial of degree Polyorder over a Window of
samples and reads the derivative of Order from it in one pass; Polyorder must
be at least the Order.
- Integral: Trapezoid or Simpson, as a running sum from the
first x, repeated Order times. Simpson takes uneven x and an odd number of
panels with SciPy's correction.
- Constants (integral only): every order starts at 0 at the first
x. Open Constants, pick the order k, and set its C_k; the curve redraws at once.
- Press calculate. The upper chart shows your data, the lower
chart the result of the chosen Order. The Output grid lists x, then the result
for each y column. Export saves it as a CSV/TSV file. The server
time shows beside the button.
- Area over a range (integral only) — under the charts, set From
and To and pick Signed (area below the axis subtracts) or Absolute (every part
adds). At Order 1 it is the area under your data; at a higher Order, the area under
the integral one order below, so that it equals the change of the result over the
range.
- Real time range — on Window, Polyorder, C_k, From and To.
- ▲▼ buttons or the mouse wheel over the
box: the value moves by one step and the server recomputes at once.
- Digit wheel: over the box, the wheel steps the digit just
left of the mouse pointer.
- Limits: Window 5 to 101, odd; Polyorder 1 to 6; From and To
inside the data's x - outside is refused with a reason, never moved for you.
- Typing or the arrow keys change the box only; press
calculate to recompute.